Abstract:
In particular, the present invention relates to a computerized system and method for clinically assessing motor function comprising correlating geometric indices, computed from digital information obtained from a geometric shape drawn by a subject to be evaluated, with a rating score derived using a “standard of reference” generated by one or more clinical expert. Interpretation is thereby rendered more objective and consistent. Furthermore, the test may be administered and interpreted by physicians who are not skilled or experienced in evaluating motor disorders, for example general practitioners or pediatricians who are not certified in the practice of neurology. The present invention therefore provides a means for evaluating persons early in the course of disease, and for screening patients for motor dysfunction or, in the case of children, disorders of motor development.

Description:
A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of any portion of the patent document, as it appears in any patent granted from the present application or in the Patent and Trademark Office file or records available to the public, but otherwise reserves all copyright rights whatsoever. 
     A microfiche appendix containing source code utilized in practicing an exemplary embodiment of the invention is included as part of the Specification and is hereinafter referred to as Appendix A. Appendix A includes a total of 2 microfiche and a total of 151 frames. 
     FIELD OF THE INVENTION 
     This invention relates in general to the field of neurology and neurological testing. More particularly, the present invention relates to the objective clinical assessment of motor function by computer analysis of a digitized writing sample, as may be used in the diagnosis and monitoring of motor disorders as well as the evaluation of motor development and handedness in children. 
     BACKGROUND OF THE INVENTION 
     A patient may seek medical treatment for a variety of complaints which suggest a disturbance of motor function, such as weakness, stiffness, tremor, clumsiness, or difficulty in executing movements. It then is the physician&#39;s responsibility to correctly diagnose the patient, and to implement the appropriate course of treatment. A number of syndromes which involve motor dysfunction exist, and are defined by their clinical manifestations. 
     For example, Parkinson&#39;s Disease, which results from a degeneration of cells in the basal ganglia of the brain, is associated with slowness of movement (“bradykinesia”), muscle rigidity, and a tremor often said to have a “pill rolling” quality which occurs at rest but tends to diminish with voluntary movements. In addition, patients suffering from Parkinson&#39;s Disease may exhibit a loss of facial expression, a difficulty in initiating movements, and a diminution of their handwriting (“micrographia”). 
     Another fairly common motor disorder is essential tremor, an inherited condition which can present in childhood but more typically appears later in adult life. It usually involves the upper limbs, but may also affect the head, jaw, lips, tongue and pharynx. This tremor may abate upon ingestion of alcohol or beta-adrenergic antagonists. It may interfere with voluntary movements to the point where a sufferer is unable to drink from a glass or raise a spoon without spilling its contents. 
     There are numerous other motor disorders from hyperkinetic conditions such as essential tremor mentioned above to complex akinetic-rigid and other degenerative syndromes. Motor disorders may be considered primary when there are no known causes (other than genetics) and secondary, or symptomatic, when a known etiologic agent exists. Examples of primary motor disorders include Parkinson&#39;s disease, essential tremor and adult onset focal dystonia such as writer&#39;s cramp. Secondary motor disorders are more numerous and include Parkinsonian syndromes, side effects of medications such as tardive dyskinesia from neuroleptic use, immune, ischemic or even traumatic causes. 
     The multitude of motor disorders share many overlapping symptoms and signs. Even though sophisticated rating systems have been developed for some disorders (e.g., Parkinson&#39;s Disease) to aid in the accuracy of diagnosis, in the hands of inexperienced practitioners, or where the disease is in its early stages and clinical signs are subtle, the potential for an erroneous diagnosis is substantial. Diagnosis by a traditional neurologic exam may also be difficult where the patient is unable to comply with fairly detailed instructions for tests used to evaluate motor function. As an example, a young child or a demented adult suspected of having a defect in motor development may be difficult to evaluate. 
     If an error in diagnosis is made, there may be significant adverse consequences. For example, the appropriate therapies for Parkinson&#39;s Disease and essential tremor are very different, in that patients with Parkinson&#39;s Disease are treated with agents that increase or facilitate dopamine activity whereas patients with essential tremor are treated with agents that block beta-adrenergic neurotransmitters. Not only would misdiagnosis result in a lack of a clinical benefit, but administering the inappropriate drug could have undesirable or even toxic side effects. 
     For example, beta adrenergenic blocking agents can adversely affect cardiac or pulmonary functions; unnecessary use in a Parkinson&#39;s Disease patient, particularly an older patient, could be dangerous. Similarly, use of agents that treat Parkinson&#39;s disease in a patient without that condition could have harmful consequences. Specific examples of Parkinson&#39;s Disease treating agents include artane, sinemet and baclofen. Artane, an anticholinergic agent used to treat Parkinsonian tremors and dystonia can severely affect cognition, cardiac, visual and urinary function. Sinemet, a mainstay drug for Parkinson&#39;s disease, causes nausea, vomiting, hallucinations and low blood pressure. Baclofen, an anti-spasmodic agent, and clonazepam, an anxiolytic and muscle relaxant, are used in many motor disorders but can alter mental status, blood pressure and can even be fatal when used inappropriately. 
     Further, even where the correct diagnosis has been made, it is important to be able to evaluate the clinical progress of a patient. Often the methods for measuring progress are extremely subjective. 
     One means by which clinicians have attempted to decrease subjectivity in diagnosis and monitoring motor function has been through the use of standardized clinical tests. Examples of such tests include asking the patient to touch his finger to, alternately, his nose and the outstretched finger of the examiner, or to run her heel up and down her shin, or to touch his or her thumb to, in succession, each of the other fingertips of the same hand. 
     Drawing has been used to evaluate motor function for many years. The famous neuropsychiatrist Kraepelin, at the beginning of this century, adapted an instrument to quantitatively analyze signatures for the evaluation of motor function in schizophrenic patients (Blyler et al., 1997, Schizophrenia Res. 26: 15-23, citing Hoch, 1904, Psychol. Bull. 1:241-257). One common test involves asking the patient to draw an Archimedes spiral. A thorough discussion of the spiral drawing test may be found in Bain &amp; Findley, in “Standards in Neurology, Series A: Assessment, diagnosis and evaluation, Book I: Assessing Tremor Severity,” published by Smith Gordon and Co., Ltd., London, England/Nishimura Co., Ltd., Niigata-Shi, Japan, copies of which can be obtained in the United States through Books International Inc., Herndon, Virginia. According to that reference, the severity of tremor apparent in the spiral is rated from 0-10, where critical factors in determining the grade of a particular spiral are the degree of perpendicular displacement of the track from the intended trajectory and the extent to which tremor persists during each turn (Bain &amp; Findley, p.9). Tremor is said to become more apparent in the outward turns of the spiral. An example of a study which used spiral analysis to quantify the effects of the drug terguride in Parkinson&#39;s Disease patients is reported in Filipova et al., 1988, Eur. Arch. Psychiatr. Neurol. Sci.237:298-303. Another study which used spiral copying ability to evaluate the effect of the drug ondasetron on cerebellar tremor is described in Rice et al., 1997, J. Neurol. Neurosur. &amp; Psychiat. 62:282-284. 
     A number of investigators have attempted to lessen the subjectivity of evaluation by using computer assistance. For example, Elble et al. (1996, Movement Disorders 11:70-78) asked patients with essential tremor to write a series of cursive e&#39;s and l&#39;s and, in some cases, to draw an Archimedes spiral on a digitizing tablet. They reported detecting changes in mean acceleration amplitude and tremor frequency with an accuracy which indicated that use of such a tablet was an accurate and less-costly alternative to accelerometry for tremor evaluation. 
     Wissel et al. (1996, J. Neurol. Neurosurg. &amp; Psychiat. 61:172-175) used a digitizing tablet to measure writing speed in an evaluation of the effectiveness of botulinum toxin for treating writer&#39;s cramp. 
     Eichorn et al., 1996, (Movement Disorders 11:289-297) used a computational analysis of open loop handwriting movements, as captured by a digitizing tablet, to monitor the effect of apomorphine on patients with early untreated Parkinson&#39;s Disease. They reported that computer-assisted analysis of automated handwriting movements can be a quick method for quantifying dopamimetic effects on handwriting movements in parkinsonian patients. However, they also found that there was no statistically significant correlation when changes in the individual handwriting parameters were correlated with a subscore obtained using the Unified Parkinson&#39;s Disease Rating Scale (“UPDRS”; Lang and Fahn, 1989, in “Quantification of neurologic deficit,” Munsat, ed., Butterworth-Heinemann, Storeham, Mass., pp. 285-309) for the writing hand, an observation which they indicated was expected, as the LPDRS assesses different kinds of parkinsonian symptoms, such as rigidity, akinesia, and tremor. 
     Blyler et al. (1997, Schizophrenia Res. 26: 15-23) used line drawing to measure lateralized motor performance in schizophrenic patients. The patients drew lines on a piece of paper, which were then scanned into a computer and a regression was run on the points of the line and used to calculate the deviation from straightness. The results were found to correlate with clinical rating scales of motor function, including the Simpson—Argus Rating Scale (Simpson and Argus, 1970, Acta Psychiatr. Scand. 212 (Suppl.), 9-11) for parkinsonian symptoms. 
     Slavin et al., 1999, J. Internatl. Neuropsychol. Soc. 5:20-25, used a digitizing tablet to analyze writing samples from patients with dementia of Alzheimer&#39;s type (“DAT”). Kinematic measures of stroke length, duration, and peak velocity were expressed in terms of consistency via a signal-to-noise ratio. Patterns typical of DAT but not Parkinson&#39;s disease were observed. 
     Lange-Küttner (1998, Perceptual and Motor Skills 86:1299-1310) report that speeded drawing of basic graphic patterns by young children, as captured on a digitizing tablet, could be used to identify psychophysical problems. 
     Computational analysis of handwriting, for identification or analytical purposes, is described in Singer and Tishby, 1994, Biol. Cybern. 71: 227-237; van den Heuvel et al., 1998, Acta Psychologica 100: 145-159; and Morasso and Sanguineti, 1993, Acta Psychologica 82: 213-235. 
     In recent years the inventor has reported the use of a digitizing tablet and computer analysis of written spirals to evaluate motor disorders such as Parkinson&#39;s Disease and essential tremor (Pullman et al., 1995, Neurology 45 (Suppl 4):A218 (abstract 208S); Yu et al., 1997, Society for Neuroscience Abstracts 23:abstract 737.8; Yu et al., 1998, Society for Neuroscience Abstracts 24:abstract 672.2). During this period of time, the inventor has been developing a method of producing a clinical rating which, unlike Eichorn&#39;s measurements, correlates with the UPDRS score based on the computer analysis of handwritten spirals. This method is not described in any of the foregoing disclosures, but is disclosed herein. 
     SUMMARY OF THE INVENTION 
     The aforedescribed limitations and inadequacies of conventional systems and methods for analyzing movement disorders are substantially overcome by the present invention, in which a primary object is to provide a relatively inexpensive and non-invasive computerized system and method for clinically assessing motor function. Such a system and method can be adapted for analyzing movement disorders such as Parkinson&#39;s disease, essential tremor and dystonia, and for characterizing neurological development and handedness in children. 
     In particular, the present invention relates to a computerized system and method for clinically assessing motor function comprising correlating geometric indices, computed from digital information obtained from a geometric shape drawn by a subject to be evaluated, with a clinical rating score derived using a “standard of reference” generated by one or more clinical expert. By analogy to a biochemical assay, which measures the amount of reactant by comparison to a standard curve, the present invention provides a method and system by which a medical practitioner can evaluate the motor function of a subject by generating a digitized writing sample and computationally comparing geometric indices obtained therefrom with values associated with clinical ratings assigned by skilled neurologists. Interpretation is thereby rendered more objective and consistent. Furthermore, the test may be administered and interpreted by physicians who are not skilled or experienced in evaluating motor disorders, for example general practitioners or pediatricians who are not specialized in the practice of neurology. The present invention therefore provides a means for evaluating persons early in the course of disease, and for screening patients for motor dysfunction or, in the case of children, disorders of motor development. 
     Hence, in accordance with a first aspect of the present invention, a system for clinically assessing motor function in a subject is provided that includes: an electronic digitizing tablet having a writing device for obtaining a geometric pattern handwritten by the subject and providing one or more digital signals representing the pattern; and a microprocessor for processing the signals to derive one or more geometric indices representative of motor function and for computing from the indices, using the aforementioned expert-generated “standard of reference”, a clinical rating score indicative of motor function of the subject. 
     In another aspect of the present invention, a preferred method for analyzing movement disorders includes: a method for clinically assessing motor function in a subject comprising: obtaining a geometric pattern handwritten by the subject on a digitizing tablet; generating one or more digital signals representing the geometric pattern; processing the signals to derive one or more geometric indices representative of motor function; and computing from the geometric indices, using the aforementioned expert-generated “standard of reference”, a clinical rating score indicative of motor function of the subject. 
     Further objects, features and advantages of the invention will become apparent from the following detailed description taken in conjunction with the accompanying figures showing illustrative embodiments of the invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a complete understanding of the present invention and the advantages thereof, reference is now made to the following description taken in conjunction with the accompanying drawings in which like reference numbers indicate like features and wherein: 
     FIG. 1 is a hardware block diagram of a system for analyzing movement disorders in accordance with a preferred embodiment of the present invention; 
     FIG. 2 is a software block diagram corresponding to the system of FIG. 1; 
     FIG. 3 is an illustration of an electronic tablet in accordance with a preferred embodiment of the present invention; 
     FIGS.  4 ( a ) through  4 ( f ) are examples of spirals and corresponding r versus θ plots; 
     FIG. 5 is a regression plot comparing computer generated clinical ratings (degree of severity computations) and expert physician clinical ratings; 
     FIG. 6 is a flow chart showing a preferred method for analyzing movement disorders; 
     FIG. 7 is a flow chart showing a preferred method performed by the acquisition module of FIG. 2; 
     FIG. 8 is a flow chart showing a preferred method for controlling data acquisition in accordance with the method of FIG. 7; 
     FIG. 9 is a flow chart showing a preferred method for acquiring data in accordance with the method of FIG. 7; 
     FIG. 10 is a flow chart showing a preferred method performed by the analysis module of FIG. 2; 
     FIG. 11 is a flow chart showing a preferred method for loading data in accordance with the method of FIG. 10; 
     FIG. 12 is a flow chart showing a preferred method for automatically eliminating error sections in accordance with the method of FIG. 10; 
     FIG. 13 is a flow chart showing a preferred method for manually eliminating error sections in accordance with the method of FIG. 10; 
     FIG. 14 is a flow chart showing a preferred method of analyzing a spiral in accordance with the method of FIG. 10; 
     FIG. 15 is a flow chart showing a preferred method for determining a degree of severity in accordance with the method of FIG. 10; 
     FIG. 16 is a flow chart showing a preferred method for computing a first order smoothness and second order smoothness of a handwritten spiral in accordance with the method of FIG. 10; 
     FIG. 17 is a flow chart showing a preferred method for computing a first order zero-crossing rate and a second order zero-crossing rate of a handwritten spiral in accordance with the method of FIG. 10; 
     FIG. 18 is a flow chart showing a preferred method for characterizing the tightness of a handwritten spiral in accordance with the method of FIG. 10; 
     FIG. 19 is a flow chart showing a preferred method for performing a spectral analysis of X-position, Y-position and pressure data in accordance with the method of FIG. 10; 
     FIG. 20 is a flow chart showing a preferred method for computing speed-time, pressure-time and radius-angle residuals in accordance with the method of FIG. 10; 
     FIG. 21A is a flow chart corresponding to the acquisition module of FIG. 2; 
     FIG. 21B defines the vertical elevation angle  2122  set according to step  2114  in FIG.  21 A and the horizontal rotation angle  2124  set in step  2112  of FIG.  21 A. 
     FIG. 22 is a flow chart corresponding to the acquisition module of FIG. 2; and 
     FIG. 23A-L through  28 A-L present clinical data and its analysis, using the method of the invention, of spiral analysis performed on a patient suffering from Parkinson&#39;s Disease. 
     Appendix A hereto (in Microfiche form) includes a printout of computer source code corresponding to the software elements shown in FIG.  2 . 
     While the subject invention will now be described in detail with reference to the figures, it is done so in connection with the illustrative embodiments. It is intended that changes and modifications can be made to the described embodiments without departing from the true scope and spirit of the subject invention as defined by the appended claims. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 shows a hardware block diagram of a system  10  for clinically assessing motor function in accordance with a preferred embodiment of the present invention. The system  10  includes an electronic digitizing tablet  12  having a writing device  14  for obtaining a geometric pattern handwritten by the subject and providing one or more signals representing the pattern, and a microprocessor  16  for processing the signals to derive one or more geometric indices representative of motor function and for computing from the indices, using an expert-generated “standard of reference,” a clinical rating score indicative of motor function. 
     The term “expert”, as used herein, refers to a person skilled in the assessment of motor function and/or in the diagnosis and assessment of one or more motor disorder. Non-limiting specific examples of suitable experts include physicians, preferably neurologists, and more preferably neurologists specialized in the field of motor disorders. 
     In a preferred embodiment of the present invention, the handwritten samples are freehand Archimedes spiral patterns, drawn on an electronic tablet  12 , that are digitized and analyzed by the microprocessor  16  in accordance with a set of spiral indices shown to be indicative of motor function. Further as shown in FIG. 1, a display device  18  and/or printer  17  are provided for displaying and/or printing an output  19  of the clinical rating, geometric indices and other relevant information. 
     The system of FIG. 1 can be adapted, for example, for diagnosing and/or monitoring movement disorders such as Parkinson&#39;s disease, essential tremor and dystonia, for evaluating neurological development and handedness in children, and for rehabilitative purposes. The spiral analysis program is also capable of analyzing any motor disorder involving the upper limbs, e.g., hand, forearm, arm, shoulder. The system can also be adapted for handwriting identification and psychiatric evaluation purposes. With proper use of controls and normative data, spiral analysis should be of use in any condition from tremors to developmental abnormalities. 
     FIG. 2 shows a software block diagram corresponding to the system of FIG.  1 . In a preferred embodiment of the present invention, the software  20  includes: an input graphical user interface (GUI)  22 , an acquisition module  24 , an analysis module  26 , an analysis database  27  and an output GUI  23  which can deliver the results of analysis via a display device  28  and/or printer output  29 . The acquisition module  24 , via the GUI  22 , instructs the user to provide any user-related information including user-defined parameters for generating a digitized geometric pattern. Handwritten “manual” data  25  is provided by the patient as instructed by the acquisition module. The X-position, Y-position and pressure data is then forwarded to the analysis module  26  for the determination of disorder severity. Software code listings, which are non-limiting working examples for the acquisition and analysis modules of free-hand spirals  24  and  26 , can be found in Appendix A (also referred to herein as “the Appendix”), and incorporate a correlation between the observed indices and a standard of reference established by an expert panel of neurologists, as set forth below. In the Appendix, the acquisition module  24  is embodied in C-language routines, whereas the analysis module is embodied in MatLab routines. 
     Referring again to FIG. 1, the data output from the electronic tablet is provided to the microprocessor  16 , which is preferably an Apple MacIntosh or IBM-compatible personal computer. The microprocessor  16  is coupled to computer memory  20 , which contains the analysis software module  26  shown in FIG.  2 . The microprocessor  16  thus runs the analysis module  26 , which in turn accesses an analysis database  27  (FIG.  2 ). The database  27  is used for storing and retrieving, for example, patient demographics and indices output. The analysis module  26  receives the X-position, Y-position and pressure data from the acquisition module  24  and computes a plurality of geometric indices used to assess the upper limb motor abilities of the patient. Although the analysis module  26  can be applied to analyze a variety of geometric patterns, the analysis module  26  of a preferred specific embodiment of the invention includes an algorithm that analyzes hand-drawn (Archimedean) spirals. 
     FIG. 3 shows an illustration of an electronic tablet  30  for use with the system of FIG.  1 . The electronic tablet  30  is a portable digitizing tablet such as the tablet produced by Kurta. Inc. as the Kurta XGT™ 6″×8″, which is sold together with a pressure pen, and is shown by way of example and not limitation. Other suitable “tablet” devices may include, for example, any stationary or portable digitizing device having a stylus, pen or other active writing device. The electronic tablet  30  of FIG. 3, however, is preferred because it is designed for use with a cordless writing pen (not shown) that writes (i.e., creates a written image) on a sheet of paper placed on top the tablet. As such, the electronic tablet  30  provides a “pen-on-paper” feel that is much like drawing on an ordinary sheet of paper. In addition, a hardcopy original of the patient&#39;s drawing is made available for future reference. Non-limiting examples of other digitizing tablets which may be used according to the invention are the Wacom Digitizer Graphic Tablet No. UD-1212II and the Calcomp 9000 digitizing tablet. In order for the subject to visually monitor his or her drawing, a lightweight paper which shows pen tracings, such as thin thermal fax paper, or a connection to a computer having a screen which displays the image being drawn, may be used, as described, respectively, in Lange-Küttner (1998, Perceptual and Motor Skills 86: 1299-1310) and Van Den Heuvel et al. (1998, Acta Psychologica 100:145-159). 
     The electronic tablet  30  includes a back panel  32  and a digitizing screen  34 . The electronic tablet  30  also includes a microprocessor (not shown), computer memory (not shown) and a computer program for controlling the operation of the electronic tablet. In a preferred embodiment of the present invention, the computer program is the acquisition module  24  described above with respect to FIG.  2 . The digitizing screen  34 , which supports a sheet of paper  36  on which a patient draws a pattern  38 , is a pressure sensitive X-Y plane recording device that generates “tri-axial” signals indicative of the drawing position and the force exerted by the patient. The device normally provides a resolution of 2,540 points/inch (100 points/mm), with an accuracy of ±0.005 inch (0.127 mm) in the X-Y directions. Pressure readings are output using 256 distinct levels, nominally 2.5 gms/level, and optionally can be to assess motor function. 
     Preferably, the electronic tablet outputs an X-position, Y-position, pressure reading and a corresponding time stamp at each sample interval. Preferably, the sample rate is normally 220 samples per second, but must be at least 73 samples per second. 
     In further embodiments of the electronic tablet, a clip, fastener or other equivalent device (not shown) is provided for holding the sheet of paper  36  in a fixed position on top of the digitizing screen  34 . Also, an ergonomically adaptable workstation (not shown) is provided along with the electronic tablet for optimal positioning and comfort. 
     A sample data output from an electronic tablet is provided in FIG. 4, where spiral (a) corresponds to r versus (also indicated herein by a tilda, “˜”) θ plot (d), spiral (b) corresponds to r versus θ plot (e), and spiral (c) corresponds to r versus θ plot (f). FIG.  4 ( a ) shows an ideal, computer generated spiral, as compared to one drawn by a normal subject shown in FIG.  4 ( b ). FIG.  4 ( c ) further shows a spiral drawn by a patient suffering from a movement disorder. 
     Where the analysis module  26  is applied to the analysis of Archimedean spirals, it uses “spiral” indices to objectively characterize a hand-drawn spiral. The spiral is “unraveled” from a two-dimensional graphic representation into indices that capture clinical information, e.g., shape, speed. tremors. pressure applied, etc., related to a patient&#39;s motor function. A list of such indices is provided in the Table 1 below: 
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 List of Geometric Indices 
               
             
          
           
               
                   
                 Index No. 
                 Description 
               
               
                   
                   
               
               
                   
                 I 1   
                 First order smoothness. 
               
               
                   
                 I 2   
                 Second order smoothness. 
               
               
                   
                 I 3   
                 Tightness of Loops. 
               
               
                   
                 I 4   
                 First order “zero” crossing rate. 
               
               
                   
                 I 5   
                 Second order “zero” crossing rate. 
               
               
                   
                 I 6   
                 Residue of radius-angle regression 
               
               
                   
                   
                 (second order polynomial, least square) 
               
               
                   
                 I 7   
                 Residue of pressure-time regression 
               
               
                   
                   
                 (second order polynomial, least square) 
               
               
                   
                 I 8   
                 Residue of speed-time regression 
               
               
                   
                   
                 (second order polynomial, least square) 
               
               
                   
                 I 9   
                 X-axis frequency (dominant). 
               
               
                   
                 I 10   
                 Dominant X-axis frequency power. 
               
               
                   
                 I 11   
                 Y-axis frequency (dominant). 
               
               
                   
                 I 12   
                 Dominant Y-axis frequency power. 
               
               
                   
                 I 13   
                 Angular velocity frequency (dominant). 
               
               
                   
                 I 14   
                 Dominant angular speed frequency power. 
               
               
                   
                 I 15   
                 X-Y combined speed frequency (dominant). 
               
               
                   
                 I 16   
                 Dominant X-Y combined speed frequency power. 
               
               
                   
                 I 17   
                 Residue of angular velocity-time regression. 
               
               
                   
                   
               
             
          
         
       
     
     As described below, some or all of the above-identified indices are used to clinically rate the motor function of the patient. However, in a preferred embodiment of the present invention, the clinical rating score is expressed as a function of I 1 , I 2  and I 5 , as shown below by Equation (1), where an asterisk (*) indicates the operation of multiplication and a tilda (˜) means “versus”: 
     
       
         Clinical Rating Score=0.4615*I 1 +0.0544*I 5 −0.2331*I 1   2 −0.0726*I 2   2 −0.001*I 5   2 +0.2539*I 1 *I 2 +1.3668  Equation (1). 
       
     
     The rating score according to Equation (1) is clinically equivalent to those of the United Parkinson&#39;s Disease Rating Scale (UPDRS) established to rate the degree of severity of Parkinson&#39;s disease and related disorders. The rating score is based on UPDRS scale for upper limb motion with regard to several factors, including tremor, hand movements, handwriting and rigidity, and incorporates a “standard of reference” established by a plurality of expert neurologists. 
     The Clinical Rating Score calculated by Equation (1) may be used to determine whether a subject has normal or abnormal motor function. The abnormal motor function may correlate with a diagnosis of a motor disorder such as, but not limited to, Parkinson&#39;s disease, essential tremor, or dystonia (see infra). Accordingly, if analysis of a spiral drawn by a subject, according to the invention, comprising obtaining spiral indices I 1 , I 2  and I 5  and utilizing these indices in Equation (1), yields a value of between 0 and 1, this indicates that the subject is exhibiting essentially normal motor function as measured by indices I 1 , I 2  and I 5 . If Equation (1) yields a value of between 1 and 2, this would indicate that the subject is exhibiting mildly abnormal motor function. If Equation (1) yields a value of between 2 and 3, this would indicate that the subject is exhibiting moderately abnormal motor function. If Equation (1) yields a value of between 3 and 4 or higher, this would indicate that the subject is exhibiting severely abnormal motor function. If Equation (1) yields a value between these ranges, such as a value of 1, 2, or 3, this would indicate that the subject is exhibiting motor function that is characterized either as borderline normal (value=1), mildly to moderately impaired (value=2), or moderately to severely impaired (value=3). Further, as the value of the Clinical Rating Score increases, the likelihood that the patient is suffering from a motor disorder increases as well. 
     Equation (1) was derived, at least in part, as follows. 
     Spirals and their corresponding indices were obtained from 25 normal control subjects and three groups of 15 patients suffering from Parkinson&#39;s Disease (“PD”), essential tremor (“ET”) and dystonia (“DY”), respectively. Each of the spirals were independently rated by 22 movement disorder specialist neurologists based on a modified UPDRS scale: a 0-1 corresponding to a “normal” spiral; 1-2 corresponding to a “mildly abnormal” spiral; 2-3 corresponding to a “moderately abnormal” spiral; and 3-4 corresponding to a “severely abnormal” spiral. The criteria set forth in Table 2 were provided to aid the neurologists in rating patient spirals. 
     Grade 0: The spiral approaches an ideal spiral with a regular shape, evenly spaced loops, well centered, with a smooth fluid line and 3 to 10 loops. 
     Grade 1: The spiral is well executed but has one or two of the following: 
     mild irregularity of spacing, shape, smoothness of the line, or wandering from the center. 
     Grade 2: The spiral is relatively well executed but has two or three of the following: 
     mild to moderate irregularity of spacing, shape, smoothness of the line, or wandering from the center. 
     Grade 3: The spiral is relatively well executed but has two or three of the following: 
     moderate to severe irregularity of spacing, shape, smoothness of the line, or wandering from the center. 
     Grade 4: The spiral is poorly executed or unrecognizable as a spiral and has more than three of the following: 
     severe irregularity of spacing, shape, smoothness of the line, wandering from the center, many areas of in continuity, or there are more than 10 or less than 3 loops to the spiral. 
     Table 2: Spiral Analysis Rating System 
     To determine the top ten so-called “expert” physicians, a regression was performed between each physician&#39;s clinical ratings and the average clinical rating for each clinical rating (excluding that physician&#39;s own rating). The physicians with the top ten regression coefficients where chosen as the “expert” physicians, and as such the indices computed from the spirals rated by the ten experts were averaged. 
     In order to characterize interdependencies between indices, linear and second order polynomial regressions were then performed for each index against the expert physician averages. Those indices with the most statistical significance and highest regression coefficients (r2), as shown in Table 3, were selected to define the clinical rating expression shown above in Equation (1). The clinical rating equation, which is a function of I 1 , I 2  and I 5  has been shown to provide critical information on motor function and has been useful in quantifying spiral severity that directly correlates with normal subjects (as opposed to an ideal spiral) and clinical status as reflected by the UPDRS. Thus, beyond merely providing a quantitative measurement of motor function, Equation (1) provides a score which, because it correlates with the UPDRS, has a clinical significance readily appreciated by practitioners. Also, as shown in FIG. 5, regression of the original ten physician spiral DOS scores, as well as the new DOS scores, has consistently yielded significant correlations, i.e., r 2  from approximately 0.085 to 0.915 and a statistical significance less than 0.001. 
     
       
         
               
             
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Simple Regression and Significance for Each Index 
               
               
                 (versus Expert Physician Average) 
               
             
          
           
               
                 Index 
                   
                 Regression 
                 Signi- 
               
               
                 No. 
                 Description 
                 Coefficient 
                 ficance 
               
               
                   
               
               
                 I 1   
                 First order smoothness. 
                 0.871 
                 &lt;0.001   
               
               
                 I 2   
                 Second order smoothness. 
                 0.740 
                 &lt;0.001   
               
               
                 I 3   
                 Tightness of Loops. 
                 0.010 
                 0.530 
               
               
                 I 4   
                 First order “zero” crossing rate. 
                 0.000 
                 0.980 
               
               
                 I 5   
                 Second order “zero” crossing rate. 
                 0.540 
                 &lt;0.100   
               
               
                 I 6   
                 Residue of radius-angle regression 
                 0.010 
                 0.040 
               
               
                   
                 (second order polynomial, least square) 
               
               
                 I 7   
                 Residue of pressure-time regression 
                 0.140 
                 0.010 
               
               
                   
                 (second order polynomial, least square) 
               
               
                 I 8   
                 Residue of speed-time regression 
                 0.080 
                 0.060 
               
               
                   
                 (second order polynomial, least square) 
               
               
                 I 9   
                 X-axis frequency (dominant). 
                 0.190 
                 &lt;0.001   
               
               
                 I 10   
                 Dominant X-axis frequency power. 
                 0.120 
                 0.020 
               
               
                 I 11   
                 Y-axis frequency (dominant). 
                 0.160 
                 0.010 
               
               
                 I 12   
                 Dominant Y-axis frequency power. 
                 0.030 
                 0.300 
               
               
                 I 13   
                 Angular velocity frequency (dominant). 
                 0.290 
                 &lt;0.001   
               
               
                 I 14   
                 Dominant angular speed frequency 
                 0.060 
                 0.120 
               
               
                   
                 power. 
               
               
                 I 15   
                 X-Y combined speed frequency 
                 0.300 
                 &lt;0.001   
               
               
                   
                 (dominant). 
               
               
                 I 16   
                 Dominant X-Y combined speed 
                 0.420 
                 &lt;0.001   
               
               
                   
                 frequency power. 
               
               
                 I 17   
                 Residue of angular velocity-time 
                 0.230 
                 0.030 
               
               
                   
                 regression. 
               
               
                   
               
             
          
         
       
     
     In deriving the indices I 1 , I 2  and I 5  of Equation (1), reference is first made to Equation (2) and (3) below which are well known mathematical equations describing the Cartesian coordinates of an ideal spiral: 
     
       
         x=αθ sin(θ+c)  Equation (2); 
       
     
     
       
         y=αθ cos(θ+c)  Equation (3); 
       
     
     where x and y are the Cartesian coordinates, α is a constant parameter, θ is an angle parameter, and c is a constant representing an initial angle. The polar equivalent, as shown by Equation (4) translates the spiral into a linear relation between r and θ while maintaining all clinical information with total fidelity as it is a point-to-point transformation of the original spiral: 
     
       
         r=αθ  Equation (4); 
       
     
     where r=(x 2 +y 2 ). 
     Referring again to Equation (1), first and second order smoothness, indices I 1  and I 2 , are mathematical expressions of spiral “waviness.” These indices do not indicate spiral irregularities and are not direct measures of tremor, i.e., tremor measurement is performed via spectral analysis using Fast Fourier transforms. Rather, smoothness indices I 1  and I 2  are designed to detect variations from a normal spiral shape. The mathematical relations for first and second order smoothness are shown below by Equations (5) and (6):                  I   1     =     ln        (       1   Θ            ∑                              (         Δ                 r     Δθ     -       r   _     θ       )     2             Δθ              )         ;           Equation  (5)                   I   2     =     ln        (       1   Θ            ∑                              (         Δ          Δ                 r     Δθ       Δθ     -     d          r   _     θ         )     2             Δθ              )         ;           Equation  (6)                                
     wherein: Θ is the total angular change, {overscore (r)} θ  is the average slope of r˜θ, Δ is a difference operator reflecting discrete changes due to sampling by the digitizing tablet, and d{overscore (r)} θ  is the average slope of Δr/Δθ ˜θ. 
     The zero-crossing rate indices, I 4  and I 5 , are used to characterize the graphic irregularity, i.e., the “lopsidedness” and “unsmoothess,” of the handwritten spiral. The zero-crossing rate indices are both expressed in percentage terms, i.e., the higher the percentage, the more irregular the spiral. The first order zero crossing index Irregular movements such as dystonic tremors reveal the highest second order zero crossing rates because they are “irregularly” irregular, i.e., the change in the irregularity of the spiral with respect to the change in angle θ. The zero order crossing rate index I 4  is defined below by Equation (7):                  I   4     =         1     2        (     J   -   1     )              ∑     j   =   1       J   -   1                             sign        (         Δ                 r     Δθ               j   +   1            -       r   _     θ         )       -                sign   (         Δ                 r     Δθ             j            -       r   _     θ               )                     *   100      %           ;           Equation  (7)                                
     wherein J is the total number of points collected and sign is a sign function where y=sign (x) and sign(x)=1 for x&gt;0, sign(x)=0 for x=0 and sign(x)=−1 for x&lt;0. 
     The second order zero crossing rate index I 5  is defined below by Equation (8):                        I   5     =         1     2        (     J   -   1     )                ∑     j   =   1       J   -   1                     sign   (       Δ          Δ                 r     Δθ       Δθ            j   +   1       -     d          r   _     θ         )         -       sign   (       Δ          Δ                 r     Δθ       Δθ          j     -       r   _     θ         )          *   100      %     ;           Equation  (8)                                
     Index I 3 , reflecting spiral tightness, is defined below by Equation (9): 
     
       
         I 3 =(Θ/ R −14π)/2π  Equation (9) 
       
     
     Tightness is the mathematical correlate of micrographia and is defined by how many turns of the spirals are drawn over its total angular change within the total radius R, normalized to 7 (or 14π because each full loop equals 2π). Tightness is positive when a spiral is drawn with more that 0.7 “loops” per centimeter of radius and negative when the “loops” are fewer in number or more spread out. 
     The remaining indices listed in Table 1 can be obtained using standard calculations. 
     Thus, the present invention provides for a method for diagnosing, monitoring, and/or assessing Parkinson&#39;s Disease in a subject comprising: obtaining a spiral drawn by the subject on a digitizing tablet; generating one or more digital signals representing the spiral; processing the signals to derive one or more geometric indices representative of motor function, where the indices are preferably one or more of indices I 1 -I 17  as set forth in Table 1 and are more preferably indices I 1 , I 5 , and  2  as set forth in Table 1; and computing from the geometric indices, using an expert-generated “standard of reference”, a clinical rating score indicative of the diagnosis and/or severity of Parkinson&#39;s Disease. Preferably, the clinical rating score (also referred to herein as the “degree of severity”) is calculated using Equation (1): 
     
       
         Clinical Rating Score=0.4615*I 1 +0.0544* I 5 −0.2331*I 1   2 −0.0726*I 2   2 −0.001*I 5   2 +0.2539*I 1 *I 2 +1.3668 
       
     
     The clinical rating score obtained for the subject may then be used, in conjunction with other clinical tests or physical examination, to diagnose Parkinson&#39;s Disease in a subject. In a non-limiting, example, if Equation (1) is used to establish the clinical rating, a score of at least 1, and preterably of at least 2, bears a positive correlation with the diagnosis of Parkison&#39;s Discease in the subject. 
     The clinical rating score may also be used to monitor the progress and/or response to treatment of a subject previously diagnosed as suffering from Parkinson&#39;s Disease. In a particular, nonlimiting embodiment, the present invention provides for a method for monitoring Parkinson&#39;s Disease in a subject comprising, on a first occasion,(a) obtaining a spiral drawn by the subject on a digitizing tablet; (b) generating one or more digital signals representing the spiral;(c) processing the signals to derive one or more geometric indices representative of motor function; and(d) computing from the geometric indices, using an expert-generated standard of reference, a clinical rating score indicative of the diagnosis of Parkinson&#39;s Disease; on a second occasion, separated from the first occasion by an interval of time, repeating steps (a)-(d); and comparing the clinical rating scores obtained at the first occasion and the second occasion, where an increase in the score has a positive correlation with a worsening of motor function and a decrease in the score has a positive correlation with an improvement in motor function. 
     The foregoing embodiments may be varied, for example by asking the subject to draw a geometric pattern other than a spiral, for example, a figure eight, a series of loops, concentric rectangles, etc. In these variations, the equations used to produce the indices would need to be altered so as to be representative of the new pattern, and the correlation with a clinical rating score would need to be calculated with respect to a standard of reference established by ratings, by one or more expert, of a plurality of drawings of the new pattern, as drawn by parkinsonian patients of varying severity and healthy subjects. 
     In other related embodiments, the method of the invention may be used to diagnose, monitor, and/or assess motor disorders other than Parkinson&#39;s disease, including, but not limited to, essential tremor, cerebellar tremor, dystonia, cerebral palsy, tardive dyskinesia, and the motor symptoms of multiple sclerosis and schizophrenia, and any movement abnormality of the upper limb. According to such embodiments, the present invention provides for a method for diagnosing, monitoring, and/or assessing the motor disorder in a subject comprising: obtaining a handwritten spiral (or other geometric pattern) drawn by the subject on a digitizing tablet; generating one or more digital signals representing the spiral (or other geometric pattern); processing the signals to derive one or more geometric indices representative of motor function; and computing a clinical rating from the geometric indices, using an expert—generated “standard of reference” established by one or more expert, preferably by a plurality of neurologists, who assigned scores commensurate with disease severity, using a fixed scale to drawings of a spiral (or other geometric pattern) by patients suffering from varying degrees of severity of the motor disorder as well as normal healthy subjects, where the clinical rating score derived by the method is indicative of the diagnosis and severity of the motor disorder. Using methods analogous to those set forth above with relation to Parkinson&#39;s Disease, the methods of the invention may be used to monitor the progress and/or response to treatment of a subject previously diagnosed as suffering from other motor disorders. 
     FIG. 6 shows a preferred method for clinically assessing motor function according to the present invention. The method 600 includes the steps of: obtaining a geometric pattern handwritten by a subject on a digitizing tablet, step  602 ; generating one or more signals representing the geometric pattern, step  604 ; processing the signals to derive one or more geometric indices representative of motor function, step  606 ; and computing from the geometric indices a clinical rating score indicative of motor function, step  608 . The method of FIG. 6 can be implemented as a computer program in accordance with the system of FIG. 2. A detailed description of such an exemplar program now follows with reference to FIGS. 7 through 22. 
     FIG. 7 shows a flow diagram  700  for the acquisition module  24  of FIG.  2 . An exemplary computer program, trace.c, for performing spiral acquisition tasks is provided in Appendix A. 
     As shown in FIG. 7, after an operator starts the program, step  702 , initial checks are performed to ensure that the electronic tablet is properly configured for data acquisition, steps  706 ,  708  and  714 . These initial checks include checking the area location of the tablet, step  706 , checking the tablet data address, step  708 , and checking for an appropriate tablet driver, step  714 . If any of these initial steps are unsuccessful, a corresponding error condition is generated and program execution is terminated, steps  704 ,  710  and  712 . If the initial tablet checks are successful, the acquisition module continues by initializing a patient information database, step  716 , and prompting the operator for patient information, step  718 . Patient information may include, for example, the patient&#39;s name, age, sex and clinical condition. The program then performs data acquisition control functions, step  800 , which are described below with respect to FIG.  8 . After completion of step  800 , new patient data files or “folders” are created, step  722 , each including raw data and corrected data, steps  724  and  726 , and data acquisition begins, step  900  (see FIG.  9 ). 
     Prior to the start of data acquisition, several additional control steps are executed, step  802 , as shown in FIG. 8 to properly configure the system for data acquisition. These steps include preserving the tablet&#39;s data buffer, step  804 , displaying the tablet resolution, step  806 , detecting and displaying the maximum X-axis and Y-axis position values of the tablet, steps  808 ,  810 ,  814  and  816 , and determining whether the tablet supports pressure data input, step  812 . If the tablet does not support pressure data input, a flag is set indicating that pressure measurement is unavailable, step  818 . If however the tablet supports pressure data input, then the pressure resolution (maximum pressure value) is displayed, step  820 , and the pressure threshold (minimum pressure value) is displayed, step  822  and set, step  824 . 
     FIG. 9 shows a flow diagram of a preferred method  900  for acquiring data in accordance with the method of FIG.  7 . After completion of steps  724  and  726  as shown in FIG. 7, data acquisition begins, step  902 , and a new data file is created to capture spiral data, step  904 . Patient information, such as the patient&#39;s name, age, sex and clinical condition, etc., described above with respect to step  718 , is then copied into the data file, step  906 . The digitizing tablet is then polled, and X-position, Y-position and pressure data is collected, step  908 , and saved to a corresponding buffer, step  910 . If the data is deemed to be unacceptable, another attempt is made to collect the X, Y and pressure data, step  908 . If the collected data is acceptable, the test subject is instructed to draw another spiral, step  914 , if so desired. If the patient draws another spiral, the previously collected data are saved to the data file, step  918 , and steps  904 ,  906 ,  908 ,  910 ,  912  and  914  are repeated. Once no more data is to be entered, data is saved according to step  916  and the data acquisition phase is completed, step  920 . 
     FIG. 10 shows a preferred method  1000  performed by the analysis module of FIG. 2, and refers to methods depicted in greater detail in the flow charts of FIGS. 11,  12 ,  13 ,  14 ,  21  and  22 , and described infra. After spiral data has been saved to the appropriate data file or files, the computerized analysis of the spiral data is initialized as shown by step  1002 . Spiral data is then loaded from a user interface, step  1100 , as described below with reference to FIG.  11 . 
     Subsequent steps will depend upon whether the data relates to a single spiral or multiple spirals and whether or not, step  1004 , the data is corrected. 
     According to FIG. 10, if the data relates to a single spiral and has been corrected, it may be analyzed in step  1400  (FIG.  14 ); otherwise, the data is subjected to step  1300  to eliminate error sections, is depicted in FIG.  13 . Once analysis has been performed, the results may be displayed, step  1020 . Spiral pressure may also be displayed, step  2100 , using steps depicted in FIG. 21, before the program for single spiral analysis finishes, step  1022 . 
     Further according to FIG. 10, if the loaded data includes data for multiple spirals, then an automatic error section elimination procedure is performed, step  1200 , as shown in FIG. 12, before the data is analyzed in step  1400  (FIG.  14 ). Once the multiple spiral data has been analyzed, it may be displayed, step  1006 , saved, step  1008 , and used to produce a spiral analysis document, step  1018 . If a subset of trials in the data are to be analyzed, a set of trials may be selected, step  1010 , and then subjected to the Z-test, step  2200  (FIG. 22) for hypothesis testing for the mean of current loaded data with known variance (normal data). A summary of spiral analysis of the selected trials may be shown, step  1012 , and then it may be determined, step  1014 , whether or not good trials had been selected for analysis. If it is determined that good trials had been selected, the program for multiple spiral analysis may finish, step  1016 ; otherwise, a new set of trials may be selected and subjected to Z-test analysis, step  2200  (FIG.  22 ), as set forth above, and the cycle repeated until a selection of good trials has been made. 
     FIG. 11 is a flow chart showing a preferred method  1100  for loading data in accordance with the method of FIG.  10 . In accordance with FIG. 11, the appropriate spiral data is loaded by displaying a user interface and entering the subject&#39;s last name, steps  1102 ,  1103  and  1104 . The user then has the option of selecting all available trials, individual trials or a set of trials to be analyzed, steps  1106 ,  1108  and  1110 , respectively. If an individual trial is selected, step  1108 , then the user is asked to input the corresponding trial number, step  1112 . If the user desires to select a specified set of trials to be analyzed, step  1110 , then the user is asked to input the desired trial number, step  1114 . After the selections are made, the user can choose to analyze raw data or corrected data according to steps  1116 ,  1120 ,  1118  and  1122 . 
     FIG. 12 shows a preferred method  1200  for automatically eliminating error sections in accordance with the method of FIG.  10 . This routine is initialized, step  1202 , only when errors are to be eliminated in multiple spirals. As shown in FIG. 12, each of the original spirals are displayed to the user, step  1204 , and checks are performed to find the first zero crossing points of the Y-axis (y=0) for each spiral with respect to the beginning points of each spiral, step  1206 , and the first zero crossing of the Y-axis for each spiral with respect to the end points of each spiral, step  1208 . Data occurring between the beginning of the spiral and the first Y-axis zero crossing from the beginning is deleted, step  1210 , along with data occurring between the end of the spiral and the first Y-axis zero crossing from the end, step  1212 . If the spiral data is determined to be satisfactory (“good”), step  1214 , then the corrected spirals are displayed and saved to a file, steps  1216  and  1218 , respectively. If the spiral data is unsatisfactory (“no good”), then error sections are eliminated on a spiral-by-spiral basis, step  1300 , in accordance with the steps shown in FIG.  13 . 
     A “good” spiral is one starting and ending at a Y-axis zero crossing. “Good” spiral data is defined as spiral data remaining after data occurring between the beginning (and/or end) and the first Y-axis zero crossing is deleted. Deletion of this data is often required because hand control is often diminished at the beginning and the end of the spiral. This diminished hand control, it has been found, in turn distorts the Y-axis zero-crossing of the spiral at the beginning and end of the spiral. Thus, in a preferred embodiment of the present invention, data corresponding to the beginning and/or end of the spiral is “edited-out.” 
     FIG. 13 shows a preferred method  1300  for manually eliminating error sections in accordance with the method of FIG.  10 . The error section elimination routine for single spirals is initiated for a single original spiral, step  1302 . The original spiral is then displayed, step  1304 . If the original spiral is good, step  1308 , then it is displayed once again and saved to file, steps  1314  and  1316 , respectively. If the original spiral is not good, then the spiral data is “edited” by removing beginning and/or end points of the spiral according to predefined parameters, step  1310 . Upon completion of the “editing” step, step  1312 , the operator is given an option to “undo” the edits made to the original spiral data, step  1306 . If the corrected spiral data is determined to be good, step  1308 , then the corrected data is displayed and saved according to steps  1314  and  1316 . 
     In accordance with a preferred embodiment of the present invention, the user is allowed to select and delete “bad” portions of a spiral by selecting the corresponding Y-axis zero crossing. However, the spiral may be drawn so tightly that the user makes a mistake and thus selects the wrong point. The “undo” feature is thus provided for recovering any spiral portions that are deleted. 
     FIG. 14 shows a preferred method  1400  for analyzing spiral data in accordance with the method of FIG.  10 . The purpose of the spiral analysis again is to compute the degree of severity of motion disorder, step  1500  (see FIG.  15 ), and the various indices used to derive the degree of severity, e.g., steps  1600  and  1700  (see FIGS.  16  and  17 ). Although the spiral analysis method computes each of the indices shown above in Table 1, the present specific non-limiting embodiment of the spiral analysis method takes into account only the first order smoothness, index I 1 , the second order smoothness, index I 2 , and second order zero crossing rate, index I 5 . The clinical rating score, also referred to as the degree of severity, is computed (step  1502 ) as shown in FIG.  15 . 
     Referring again to FIG. 14, a spiral analysis routine is initialized, step  1402 , and then the original or corrected data saved during data acquisition and error correction is accessed, step  1404 . The spiral analysis then operates on the data, i.e., the time-stamped ( 1410 ) X-position ( 1406 ), Y-position ( 1408 ) and pressure ( 1412 ) data, as described below. The X and Y coordinates are used to calculate the following X-Y related parameters: the frequency spectrum of X and Y position, as determined in steps  1900 . (see FIG.  19 ); the angular change of the spiral over time, step  1414 ; the radius of the spiral (r=(X 2 +Y 2 )), step  1416 ; the speed at which the spiral is drawn, step  1418 ; and the speed spectrum  1420 . Pressure readings are used to calculate the following pressure-related parameters: the frequency spectrum of pressure, step  1900 ; right hemi-pressure applied while drawing the spiral, step  1422 ; left hemi-pressure applied while drawing the spiral, step  1424 ; right/left hemi-pressure, step  1438 , and right-left hemi-pressure, step  1440 ; and the residue of pressure-time, step  2000  (see FIG.  20 ). “Right/left hemi-pressure” is defined as the value of the right hemi-pressure divided by the value of the left hemi-pressure, and the “right-left hemi-pressure” is defined as the value of the right hemi-pressure subtracted by the value of the left hemi-pressure. 
     The X-position, Y-position and pressure parameters are then used to derive the indices shown above in Table 1. For example, the following indices are derived from the angular change, step  1414 , and radius calculations, step  1416 : first order smoothness (I 1 ), step  1600  (see FIG.  16 ); second order smoothness (I 2 ), step  1600  (see FIG.  16 ); tightness of the spiral ( 13 ), step  1800  (FIG.  18 ); first order zero crossing rate (I 4 ), step  1700  (see FIG.  17 ); second order zero crossing rate (I 5 ), step  1700  (see FIG.  17 ); and residue of angle-radius (I 6 ), step  2000  (see FIG.  20 ). 
     FIG. 14 further shows that the residuals of speed-time, index I 8 , is computed from the calculated speed, step  2000  (FIG.  20 ). The following statistics are also computed from the calculated speed: the maximum speed, step  1426 ; the mean speed, step  1428 ; the speed mean slope, i.e., first order curve fitting slope of speed, step  1430 ; acceleration, step  1442 ; the maximum acceleration, step  1432 ; the mean acceleration (step  1434 ); and the acceleration mean slope, i.e., first order curve fitting slope of acceleration, step  1436 . 
     FIG. 15 shows a preferred method for calculating (step  1502 ) a degree of severity (clinical rating score) in accordance with the method of FIG.  10 . The degree of severity again is based on the computed values of the first order smoothness, second order smoothness and the second order zero crossing rate, indices I 1 , I 2  and I 5 . After indices I 1 , I 2  and I 5  are computed to produce values  1612 ,  1626  and  1734 , respectively (see FIGS.  16  and  17 ), the indices are processed in accordance with the derived clinical rating score (degree of severity) of Equation 1, steps  1504 ,  1506 ,  1508 ,  1510 ,  1512 ,  1514  and  1516  to yield the Clinical Rating Score,  1518  (also referred to herein as the “degree of severity”). 
     FIG. 16 shows a preferred method for computing a first order smoothness I 1  ( 1612 ) and second order smoothness I 2  ( 1626 ) of a handwritten spiral in accordance with the method of FIG.  10 . The steps shown in FIG. 16 correspond to Equations 5 and 6 shown above. 
     Where first order smoothness is being calculated, the ratio of radius change (Δr) to angle change (Δθ) is calculated, step  1614 . Further, the first order curve fitting of radius versus angle is calculated, step  1604 . In step  1606 , the average slope determined in step  1604  (i.e., the first order curve fitting of radius versus angle) is subtracted from the ratio Δr/Δθ of step  1614 . Step  1608  sums the square of the result of step  1606 , and then the result of step  1608  is divided by the total angle change, step  1610 . The first order smoothness I 1  ( 1612 ) is then calculated as the natural log (step  1611 ) of the result of step  1610 . 
     To determine second order smoothness, the results of step  1614  are then used to calculate the ratio of Δr/Δθ change to angle change (Δθ), step  1616 , and to calculate the first order curve fitting of Δr/Δθ versus angle, step  1620 . In step  1618 , the average slope of Δr/θ versus angle (from step  1620 ) is subtracted from Δr/Δθ/θ. Step  1622  then sums the square of the result of step  1618 . In step  1624 , the result of step  1622  is divided by the total angle change. To determine the second order smoothness I 2  ( 1626 ), the natural log of the result of step  1624  is calculated, step  1625 . 
     FIG. 17 shows a preferred method  1700  for computing a first order zero-crossing rate and a second order zero-crossing rate of a handwritten spiral in accordance with the method of FIG.  10 . 
     To calculate the first order zero crossing rate I 4  (see Equation (7)), the ratio of the radius change (Δr) to angle change (Δθ) is calculated, step  1716 . A first order curve fitting of the radius versus angle is then performed, step  1704 . In step  1706 , the average slope of the curve determined in step  1704  is subtracted from the result from step  1716 . If (step  1708 ) the sign of the result from step  1706  changes every two points, then the count is incremented by one, step  1710 , and divided by the total number of data points collected and multiplied by 100%, step  1712 . This yields the first order zero-crossing rate I 4  ( 1714 ). If, in step  1708 , the sign does not change every two points, then the count is not incremented (step  1722 ) and one proceeds to step  1712 . 
     The computation of the second order zero-crossing rate I 5  (see Equation (8)) is similar, but involves an extra step, step  1718 , to calculate the second order rate of change of the radius versus angle, namely the ratio of Δr/θ to Δθ. The first order curve fitting of Δr/Δθ versus angle is calculated, step  1720 , and then the average slope from step  1720  is subtracted from the result of step  1718 , step  1724 . If (step  1728 ) the sign of the result from step  1724  changes every two points, then the count is incremented by one, step  1730 , and then divided by the total number of data points collected and multiplied by 100%, step  1732 . This yields the second order zero-crossing rate I 5  ( 1734 ). If, in step  1728 , the sign does not change every two points, then the count is not incremented (step  1726 ) and one proceeds to step  1732 . 
     FIG. 18 shows a preferred method for characterizing the tightness of a handwritten spiral in accordance with the method of FIG.  10 . To calculate spiral tightness (step  1802 ), a “tightness” value of 1 is defined (step  1804 ) when 5 loops are contained within a 10 cm region extending from the center of the spiral. A tightness value of 1 is assigned when a patient draws a spiral having five loops within a 10 cm region. If a patient draws, for example, only three loops within a 10 cm region, the spiral is less tight and the tightness value equals 0.6. The number of loops is calculated as the total angle change divided by 2π, step  1806 , and the maximum radius of the spiral is measured, step  1808 . Then, tightness is calculated as the number of loops divided by the maximum radius, step  1810  (see also Equation (9)). 
     FIG. 19 is a flow chart showing a preferred method ( 1900 ) for performing a spectral analysis of X-position, Y-position and pressure data in accordance with the method of FIG.  10 . Since a primary objective is to characterize the spectrum data caused by tremor, several spectrum analysis techniques are utilized. Most pressure data increases with the spiral radius and creates a high power low frequency peak. To ignore this spectrum, the curve fitting points for X-position, Y-position and pressure are subtracted (step  1906 ) from the measured X-position, Y-position and pressure data, step  1902 . To avoid high frequency noise caused by the discontinuity of selected points, e.g., “leaking” effect of the FFT, the last 10% of end points are so-called “tapered” or eliminated in accordance with step  1908 . In addition, it has been found that X-position, Y-position and pressure data has a basic low frequency component related to spiral loop execution, e.g., if a spiral has five loops drawn over five seconds, a 1 Hz frequency component appears in spectral analysis. Accordingly, a Butterworth filter is used to filter out this low component, step  1910 . Next, as shown by step  1912 , a fast Fourier transform (FFT) is performed on the data resulting from step  1910  with the number of points equal to a power of 2 These operations result in values for the spectrum frequency ( 1914 ) and spectrum power ( 1916 ). 
     FIG. 20 is a flow chart showing a preferred method  2000  for calculating residuals, step  2002 , of speed-time, pressure-time and angle-radius, using measured values for speed ( 2004 ), time ( 2006 ), pressure ( 2008 ), angle ( 2010 ) and radius ( 2012 ) in accordance with the method of FIG.  10 . To compute the speed-time residual, the time-stamped speed information is used to compute the first order curve fit of speed versus time, step  2014 . Each of the actual speed values are then subtracted from each of the corresponding curve-fitted values, step  2016 . The results are squared and then summed, step  2018 , and the square root computed, step  2020 , to derive the speed-time residual ( 2022 ). 
     To compute the pressure-time residual, the time-stamped speed information is used to compute the first order curve fit of pressure versus time, step  2024 . Each of the actual pressure values are then subtracted from each of the corresponding curve-fitted values, step  2026 . The results are squared and then summed, step  2028 , and the square root computed, step  2030 , to derive the pressure-time residual ( 2032 ) 
     To compute the radius versus angle residual, angle and radius measurements are used to compute the first order curve fit of radius versus angle, step  2034 . Each of the actual angle values are then subtracted from each of the corresponding curve-fitted values, step  2036 . The results are squared and then summed, step  2038 , and the square root computed, step  2040 , to derive the radius-angle residual ( 2042 ). 
     FIG. 21A is a flow chart ( 2100 ) showing a preferred method ( 2102 ) for displaying spiral pressure in accordance with the method of FIG.  10 . “Still” ( 2104  and  2108 ) and animated ( 2106  and  2110 ) 2-D and 3-D spirals, wherein different pressure levels are represented by different colors, are examples of spiral pressure displays generated by the preferred method of FIG.  21 A.  2 -D animation reproduces the spiral drawn by the patient in real-time. To show an animated 3-D spiral, the patient can set the horizontal rotation or vertical elevation angle, and then rotate the spiral horizontally or vertically. According to steps  2112  and  2114 , the horizontal rotation and vertical elevation angles are set, representing variables  2124  and  2122 , respectively, as depicted in FIG.  21 B. It is then determined whether the settings provide a good angle of the view, step  2116 , and if so, horizontal rotation and vertical rotation are shown, steps  2118  and  2120 , respectively. 
     FIG. 22 is a flow chart ( 2200 ) showing a preferred nonlimiting method ( 2202 ) for performing a Z-test in accordance with the method of FIG.  10 . First, the number of trials collected from one patient is obtained, step  2204 . If (step  2208 ) this number is greater than 3 (for each hand), the maximum and minimum data are discarded for each index, step  2210 . However, if there are only 3 (or less) trials for each hand, all the data is used (step  2212 ) in the Z-test. The means and standard deviations are calculated from the chosen data, step  2214 . Comparing the results of the Z test using trial data, step  2216 , with normal age-matched data loaded in step  2206 , it is determined whether the data of every index rejects the null hypothesis or not, step  2218 . Rejecting the null hypothesis (step  2222 ) implies that data does not belong to the group of normals, and data mean and standard deviation may be displayed with a special notation, such as, for example, a red asterisk (meaning it is significantly different from the normal). Accepting the null hypothesis (step  2220 ) indicates that the data falls within normal limits. 
     The present invention is further illustrated by the following working examples, presented to more clearly describe the invention but not by way of limitation. 
     EXAMPLE 
     EVALUATION OF A PARKINSON&#39;S DISEASE PATIENT 
     FIGS. 23 through 28 illustrate test results, both graphically and numerically, for a 55 year-old right handed male (whose name has been redacted) who has been treated for Parkinson&#39;s Disease for three years, and who was evaluated by spiral analysis using the above-described methods. The subject was asked to draw 10 spirals with his right hand, and 10 spirals with his left hand, on a Kurta digitizing tablet, e.g., “Draw 10 spirals with each hand starting from the center ‘x’ and stop before you reach the outer boundaries.” The outer boundaries defined a 10 cm×10 cm square. While drawing, the patient was comfortably seated with respect to the digitizing tablet without being subjected to any physical restraints, such as a harness, electrode wires, or other attachments that might hinder the patient&#39;s ability to draw the requested spirals. Further, the patient was not subject to any intimidating or invasive stimuli that would make him feel uneasy or uncomfortable while drawing the spirals. 
     FIGS. 23A-L through  25 A-L depict three spirals drawn by the subject using his right hand, and FIGS. 26A-L through  28 A-L depict three spirals drawn by the subject using his left hand, which are the first, fifth and tenth of the series of ten spirals drawn for each hand. The figures each have 12 subpart designated A-L, which depict, respectively, (A) the original spiral; (B) the radius—angle transform; (C) time vs. trace; (D) pressure vs. X; (E) pressure vs. Y; (F) pressure vs. Time; (G) X spectrum; (H) Y spectrum; (I) pressure spectrum; (J) speed; (K) speed spectrum; and (L) acceleration. In the upper right hand corner of each of FIGS. 23-28 is the degree of severity calculated using Equation (1) for that test. Various indices are set forth in each figure, as collected in Tables 5-7 below. In Table 5-7, right hand (e.g., “RH1”) and left hand (e.g., “LH1”) samples are provided along with statistical measures (e.g., mean, standard deviation, etc.) for each of the indicated indices or measured parameters. Columns labeled “(2)” in Tables 5-7 (e.g., “I 1 (2)”) indicate measurements wherein outliers, i.e., maximum and minimum data points, have been omitted. A summary of the results is presented in Table 4. 
     For three of the ten spirals drawn by the patient&#39;s right hand shown in FIGS. 23-25, the Clinical Rating Score (also referred to as the “degree of severity”) was calculated to be, respectively (rounded to three significant figures), 1.15, 1.20 and 1.65. For three of the ten spirals drawn by the patient&#39;s left hand shown in FIGS. 26-28, the Clinical Rating Scores were 1.44, 1.44, and 1.83. As shown in Table 4, the summary results for all trials performed by this patient include average Clinical Rating Scores of 1.230±0.089 for his right hand and 1.504±0.135 for his left hand. These scores indicate that the patient exhibits mildly abnormal motor function and are consistent with other features of the patient&#39;s clinical condition. The slightly poorer scores of spirals drawn by the patient&#39;s left hand is likely due in part to the fact that the patient is right-handed. Beyond this explanation, however, the results further show that the R/L hemi-pressure ratio is slightly favored towards the right side of each spiral drawn by the subject. This confirms that the subject has a slight relative weakness on the left side. This disparity in the pressure exerted by the subject on the right versus left half of the drawn spirals (“hemi-spirals”) was previously noted by the inventor as a distinguishing feature of Parkinson&#39;s Disease as opposed to other motor disorders such as essential tremor. Therefore, the fact that the patient suffers from left-sided weakness also probably contributed to the poorer execution of spirals drawn by his left hand. 
     
       
         
               
             
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Example of Spiral Analysis Summary 
               
               
                 Clinical Motor Physiology Laboratory 
               
               
                 SPIRAL ANALYSIS SUMMARY 
               
               
                 Date of study: xxxxxxxxx 
               
               
                 Patient name: xxxxxxxxx 
               
               
                 Dominant hand: Right 
               
               
                 Clinical: Tr × 3 yrs., worse in action 
               
             
          
           
               
                   
                 Dominant 
                 Non-dominant 
               
             
          
           
               
                 (Average ± SD) 
                 Patient 
                 Normal 
                 Patient 
                 Normal 
               
               
                   
               
               
                 Degree of Seventy: 
                 1.230 ± 
                 0.333 ± 
                 1.504 ± 
                 0.581 ± 
               
               
                   
                 0.089 
                 0.275 
                 0.135 
                 0.321 
               
               
                 Peak frequencies: 
               
               
                 X 
                 0.881 ± 
                 0.760 ± 
                 0.900 ± 
                 0.809 ± 
               
               
                   
                 0.163 
                 0.125 
                 0.234 
                 0.201 
               
               
                 Power 
                 0.001 ± 
                 0.002 ± 
                 0.001 ± 
                 0.002 ± 
               
               
                   
                 0.000 
                 0.001 
                 0.005 
                 0.001 
               
               
                 Y 
                 0.887 ± 
                 0.778 ± 
                 3.122 ± 
                 0.883 ± 
               
               
                   
                 0.228 
                 0.161 
                 1.859 
                 0.356 
               
               
                 Power 
                 0.001 ± 
                 0.002 ± 
                 0.007 ± 
                 0.003 ± 
               
               
                   
                 0.000 
                 0.001 
                 0.005 
                 0.002 
               
               
                 Pressure 
                 2.559 ± 
                 0.777 ± 
                 0.461 ± 
                 0.870 ± 
               
               
                   
                 2.270 
                 0.334 
                 0.095 
                 0.625 
               
               
                 Power 
                 0.035 ± 
                 0.017 ± 
                 0.014 ± 
                 0.029 ± 
               
               
                   
                 0.024 
                 0.015 
                 0.007 
                 0.040 
               
               
                 Speed average: 
                 5.580 ± 
                 8.954 ± 
                 5.276 ± 
                 8.821 ± 
               
               
                   
                 0.504 
                 3.014 
                 0.262 
                 2.831 
               
               
                 Pressure-time res.: 
                 11.027 ±  
                 10.307 ±  
                 13.261 ±  
                 12.212 ±  
               
               
                   
                 1.199 
                 4.336 
                 2.340 
                 5.520 
               
               
                 Tightness: 
                 1.977 ± 
                 1.266 ± 
                 1.676 ± 
                 1.140 ± 
               
               
                   
                 0.224 
                 0.332 
                 0.195 
                 0.299 
               
               
                 R/L hemi-pres. ratio 
                 1.196 ± 
                 1.052 ± 
                 1.225 ± 
                 0.906 ± 
               
               
                   
                 0.031 
                 0.179 
                 0.038 
                 0.132 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
               
                   
               
             
             
               
                   
                 DOS (1) 
                 DOS (2) 
                 I 1  (1) 
                 I 1  (2) 
                 I 2  (1) 
                 I 2  (2) 
                 I 1  (1) 
                 I 1  (2) 
                 I 1  (1) 
               
               
                   
               
               
                 RH1 
                 1.1548 
                 1.1548 
                 −0.8619 
                 −0.8619 
                 −0.62683 
                   
                 1.5914 
                   
                 24.9778 
               
               
                 RH2 
                 1.1778 
                 1.1778 
                 −0.64614 
                 −0.64614 
                 −1.2811 
                 −1.2811 
                 2.1588 
                 2.1588 
                 12.6984 
               
               
                 RH3 
                 1.2008 
                 1.2008 
                 −0.90647 
                 −0.90647 
                 −1.8008 
                 −1.8008 
                 2.143 
                 2.143 
                 16.5195 
               
               
                 RH4 
                 1.3396 
                 1.3396 
                 −0.10198 
                 −0.10198 
                 −1.3518 
                 −1.3518 
                 1.7449 
                 1.7449 
                 10.4053 
               
               
                 RH5 
                 1.2053 
                 1.2053 
                 −0.45788 
                 −0.45788 
                 −1.7007 
                 −1.7007 
                 1.7114 
                 1.7114 
                 14.2282 
               
               
                 RH6 
                 1.2777 
                 1.2777 
                 −0.36082 
                 −0.36082 
                 −1.932 
                   
                 2.4627 
                   
                 12.0101 
               
               
                 RH7 
                 1.1161 
                 1.1161 
                 −0.59165 
                 −0.59165 
                 −1.3798 
                 −1.3798 
                 2.0819 
                 2.0819 
                 14.788 
               
               
                 RH8 
                 1.3663 
                 1.3663 
                 −0.022792 
                   
                 −1.5042 
                 −1.5042 
                 1.7992 
                 1.7992 
                 9.5672 
               
               
                 RH9 
                 .82955 
                   
                 −1.3055 
                   
                 −1.5806 
                 −1.5806 
                 2.3095 
                 2.3095 
                 20.2222 
               
               
                 RH10 
                 1.6518 
                   
                 −0.042043 
                 0.042043 
                 −1.388 
                 −1.388 
                 1.8641 
                 1.8641 
                 11.9734 
               
               
                 Mean 
                 1.232 
                 1.2298 
                 −0.5297 
                 −0.4961 
                 −1.4546 
                 −1.4984 
                 0.9867 
                 1.9766 
                 14.739 
               
               
                 SD 
                 0.2092 
                 0.0892 
                 0.4194 
                 0.3196 
                 0.3594 
                 0.1829 
                 0.2857 
                 0.2229 
                 4.7507 
               
               
                 Coef var 
                 0.1698 
                 0.0725 
                 0.7917 
                 0.6443 
                 0.2471 
                 0.1221 
                 0.1438 
                 0.1133 
                 0.3223 
               
               
                 LH11 
                 1.4443 
                 1.4443 
                 −0.38157 
                 −0.38157 
                 −1.2773 
                 −1.2773 
                 1.5822 
                 1.5822 
                 15.9812 
               
               
                 LH12 
                 1.5165 
                 1.5165 
                 −0.40719 
                 −0.4.719 
                 −0.75933 
                 −0.75933 
                 1.5381 
                 1.5381 
                 13.4771 
               
               
                 LH13 
                 .94823 
                   
                 −0.90461 
                   
                 −1.6843 
                   
                 1.9825 
                 1.9825 
                 17.6334 
               
               
                 LH14 
                 1.2864 
                 1.2864 
                 −0.71565 
                 −0.71565 
                 −1.1411 
                 −1.411 
                 2.06 
                   
                 17.6471 
               
               
                 LH15 
                 1.4382 
                 1.4382 
                 −0.58282 
                 −0.58282 
                 −0.3704 
                 −0.3704 
                 1.9812 
                 1.9812 
                 13.7858 
               
               
                 LH16 
                 1.4118 
                 1.4118 
                 −0.39302 
                 −0.39302 
                 −1.5575 
                 −1.5575 
                 1.6768 
                 1.6768 
                 13.8736 
               
               
                 LH17 
                 1.5916 
                 1.5916 
                 −0.24714 
                 −0.24714 
                 −0.94846 
                 −0.94846 
                 1.5831 
                 1.5831 
                 13.029 
               
               
                 LH18 
                 1.655 
                 1.655 
                 −0.11493 
                 −0.11493 
                 −0.74297 
                 −0.74297 
                 1.5469 
                 1.5469 
                 10.9925 
               
               
                 LH19 
                 1.686 
                 1.686 
                 0.10461 
                   
                 −0.02371 
                   
                 1.5185 
                 1.5185 
                 14.0015 
               
               
                 LH20 
                 1.8317 
                   
                 0.062897 
                 0.062897 
                 −0.42992 
                 −0.42992 
                 1.4456 
                   
                 12.6316 
               
               
                 Mean 
                 1.481 
                 1.5037 
                 −0.3579 
                 −0.3474 
                 −0.8935 
                 −0.9034 
                 1.6915 
                 1.6762 
                 14.3063 
               
               
                 SD 
                 0.2446 
                 0.135 
                 0.3239 
                 0.2479 
                 0.5337 
                 0.4107 
                 0.2269 
                 0.1946 
                 2.1521 
               
               
                 Coef var 
                 0.1652 
                 0.0897 
                 0.9048 
                 0.7136 
                 0.5973 
                 0.4547 
                 0.1341 
                 0.1161 
                 0.1504 
               
               
                 R-1 
                 −0.249 
                 −0.274 
                 −0.1718 
                 −0.1487 
                 −0.5611 
                 −0.595 
                 0.2952 
                 0.3004 
                 0.4327 
               
               
                 (R-1)/min 
                 −20% 
                 −22% 
                 32% 
                 30% 
                 39% 
                 40% 
                 17% 
                 18% 
                 3% 
               
               
                 avg 
               
               
                 R 1 
                 0.8319 
                 0.8138 
                 1.4799 
                 1.628 
                 1.628 
                 1.6586 
                 1.1745 
                 1.1792 
                 1.0302 
               
               
                   
               
             
          
           
               
                   
                   
                 I 2  (2) 
                 I 2  (1) 
                 I 1  (2) 
                 I 2  (1) 
                 I 2  (2) 
                 I 2  (1) 
                 I 2  (2) 
                 I 3  (1) 
               
               
                   
                   
               
               
                   
                 RH1 
                   
                 51.0222 
                 51.0222 
                 0.38106 
                 0.38106 
                 8.098 
                   
                 0.038298 
               
               
                   
                 RH2 
                 12.6984 
                 53.869 
                 53.869 
                 0.30373 
                 0.30373 
                 10.6044 
                 10.6044 
                 0.038016 
               
               
                   
                 RH3 
                 16.5193 
                 50.6936 
                 50.6936 
                 0.29748 
                 0.29748 
                 8.9082 
                 8.9082 
                 0.045505 
               
               
                   
                 RH4 
                 10.4053 
                 53.7788 
                 53.7788 
                 0.30648 
                 0.30648 
                 11.0235 
                 11.0235 
                 0.048276 
               
               
                   
                 RH5 
                 14.2282 
                 53.9597 
                 53.9397 
                 0.20716 
                   
                 13.9784 
                   
                 0.049109 
               
               
                   
                 RH6 
                 12.6101 
                 52.086 
                 52.086 
                 0.72075 
                 0.72075 
                 10.5863 
                 10.5863 
                 0.050588 
               
               
                   
                 RH7 
                 14.788 
                 55.4292 
                   
                 0.83008 
                   
                 11.0729 
                 11.0729 
                 0.049743 
               
               
                   
                 RH8 
                   
                 52.8474 
                 52.8474 
                 0.64191 
                 0.64191 
                 10.7624 
                 10.7624 
                 0.054327 
               
               
                   
                 RH9 
                 20.2222 
                 53.7778 
                 53.7778 
                 0.71368 
                 0.71368 
                 12.6562 
                 12.6562 
                 0.038887 
               
               
                   
                 RH10 
                 11.9734 
                 46.5632 
                   
                 0.74962 
                 0.74962 
                 12.6003 
                 12.6003 
                 0.045247 
               
               
                   
                 Mean 
                 14.1056 
                 52.4027 
                 52.7543 
                 0.5152 
                 0.5143 
                 11.0291 
                 11.0268 
                 0.0458 
               
               
                   
                 SD 
                 3.1244 
                 2.5109 
                 1.336 
                 0.2358 
                 0.2092 
                 1.7433 
                 1.199 
                 0.0057 
               
               
                   
                 Coef var 
                 0.2215 
                 0.0479 
                 0.0253 
                 0.4577 
                 0.4067 
                 0.1581 
                 0.1087 
                 0.1246 
               
               
                   
                 LH11 
                 15.9812 
                 50.2938 
                 50.2938 
                 0.56805 
                 0.56805 
                 13.5407 
                 13.5407 
                 0.038145 
               
               
                   
                 LH12 
                 13.4771 
                 48.9218 
                 48.9218 
                 0.31959 
                   
                 10.6127 
                 10.6127 
                 0.037592 
               
               
                   
                 LH13 
                 17.6334 
                 55.9165 
                   
                 0.37699 
                 0.37699 
                 10.3387 
                   
                 0.042021 
               
               
                   
                 LH14 
                   
                 50.8824 
                 50.8824 
                 0.77406 
                 0.77406 
                 10.5926 
                 10.5926 
                 0.048177 
               
               
                   
                 LH15 
                 13.7858 
                 48.0382 
                 48.0382 
                 0.56693 
                 0.56693 
                 12.1393 
                 12.1393 
                 0.044442 
               
               
                   
                 LH16 
                 13.8736 
                 50.2747 
                 50.2747 
                 0.58609 
                 0.58609 
                 15.1891 
                 15.1891 
                 0.042006 
               
               
                   
                 LH17 
                 13.029 
                 48.441 
                 48.441 
                 0.52291 
                 0.52291 
                 11.9951 
                 11.9951 
                 0.050465 
               
               
                   
                 LH18 
                   
                 48.3458 
                 48.3458 
                 0.59228 
                 0.59228 
                 17.1123 
                 17.1123 
                 0.041822 
               
               
                   
                 LH19 
                 14.0115 
                 50.4798 
                 50.4798 
                 0.85511 
                   
                 14.9071 
                 14.9071 
                 0.041647 
               
               
                   
                 LH20 
                 12.6316 
                 45.7895 
                   
                 0.53129 
                 0.53129 
                 19.4151 
                   
                 0.045579 
               
               
                   
                 Mean 
                 14.3029 
                 49.7383 
                 49.4597 
                 0.5693 
                 0.5648 
                 13.5843 
                 13.2611 
                 0.0432 
               
               
                   
                 SD 
                 1.6709 
                 2.6541 
                 1.1347 
                 0.1589 
                 0.109 
                 3.0496 
                 2.3401 
                 0.0041 
               
               
                   
                 Coef var 
                 0.1168 
                 0.0534 
                 0.0229 
                 0.02792 
                 0.193 
                 0.2245 
                 0.1765 
                 0.0942 
               
               
                   
                 R-1 
                 −0.1973 
                 2.6643 
                 3.2946 
                 −0.0541 
                 −0.0505 
                 −2.5552 
                 −2.2343 
                 0.0026 
               
               
                   
                 (R-1)/min 
                 −1% 
                 5% 
                 7% 
                 −11% 
                 −10% 
                 −23% 
                 −20% 
                 6% 
               
               
                   
                 avg 
               
               
                   
                 R 1 
                 0.9862 
                 1.0536 
                 1.0666 
                 0.9049 
                 0.9106 
                 0.8119 
                 0.8315 
                 1.0604 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
             
             
               
                   
                   
                   
                   
                   
                   
                 R/L 
                 R-1 hemi- 
                 R-1 hemi- 
                   
                   
               
               
                 I 9  (2) 
                 R hemi-pr 
                 R hemi-pr 
                 L hemi-pr 
                 L hemi-pr 
                 R/L hemi-pr 
                 hemi-pr 
                 pr 
                 pr 
                 L 9  (1) 
                 L 9  (2) 
               
               
                   
               
             
          
           
               
                 0.038298 
                 52.0065 
                   
                 46.6814 
                   
                 1.1141 
                   
                 6.2649 
                   
                 .73242 
                 0.73242 
               
               
                   
                 64.5163 
                 64.5163 
                 55.1889 
                 55.1889 
                 1.169 
                 1.169 
                 9.9227 
                 9.9227 
                 .64453 
               
               
                 0.045505 
                 76.9135 
                 76.1935 
                 63.7189 
                 63.7189 
                 1.2071 
                 1.2071 
                 14.1878 
                 14.1878 
                 .89355 
                 0.89355 
               
               
                 0.048276 
                 95.8088 
                 95.8088 
                 76.1316 
                 76.1316 
                 1.2585 
                   
                 18.5634 
                 18.5634 
                 .99609 
                 0.99609 
               
               
                 0.049109 
                 99.1634 
                 99.1634 
                 79.9005 
                 79.9005 
                 1.2411 
                 1.2411 
                 17.8361 
                 17.8361 
                 1.1865 
               
               
                 0.050588 
                 99.6287 
                 99.6287 
                 80.3297 
                 80.3297 
                 1.2402 
                 1.2402 
                 19.203 
                   
                 1.0254 
                 1.0254 
               
               
                 0.049743 
                 103.9507 
                 103.9507 
                 88.9418 
                 88.9418 
                 1.1687 
                 1.1687 
                 12.6125 
                 12.6125 
                 .65918 
                 0.65918 
               
               
                   
                 121.2796 
                 121.2796 
                 103.8818 
                 103.8818 
                 1.1675 
                 1.1675 
                 14.2604 
                 14.2604 
                 .99609 
                 0.99609 
               
               
                 0.038887 
                 110.1692 
                 110.1692 
                 92.0322 
                 92.0322 
                 1.1971 
                 1.1971 
                 12.8632 
                 12.8632 
                 1.0547 
                 1.0547 
               
               
                 0.045247 
                 122.4027 
                   
                 104.4259 
                   
                 1.1733 
                 1.1733 
                 16.2855 
                 16.2855 
                 .68848 
                 0.68848 
               
               
                 0.0457 
                 94.5839 
                 96.4288 
                 79.1133 
                 80.0157 
                 1.1937 
                 1.1955 
                 14.1999 
                 14.5664 
                 0.8877 
                 0.8807 
               
               
                 0.0848 
                 23.3196 
                 18.0487 
                 19.3931 
                 15.5417 
                 0.0441 
                 0.0314 
                 4.0444 
                 2.882 
                 0.1929 
                 0.163 
               
               
                 0.1016 
                 0.2465 
                 0.1872 
                 0.2451 
                 0.1942 
                 0.0369 
                 0.0263 
                 0.2848 
                 0.1979 
                 0.2173 
                 0.1851 
               
               
                 0.038145 
                 72.5222 
                   
                 53.9127 
                   
                 1.3452 
                   
                 15.7708 
                 15.7708 
                 1.04 
                 1.04 
               
               
                   
                 76.3246 
                 76.3246 
                 59.6489 
                 59.6489 
                 1.2796 
                 1.2796 
                 16.3487 
                 16.3487 
                 .64453 
                 0.64453 
               
               
                 0.042021 
                 76.4277 
                 76.4277 
                 62.4038 
                 62.4038 
                 1.2247 
                 1.2247 
                 16.4023 
                 16.4023 
                 .55664 
               
               
                 0.048177 
                 83.76 
                 83.76 
                 80.8509 
                 80.8509 
                 1.036 
                   
                 2.238 
                   
                 .81299 
                 0.81299 
               
               
                 0.044442 
                 96.7673 
                 96.7673 
                 79.8378 
                 79.8378 
                 1.212 
                 1.212 
                 15.3905 
                 15.3905 
                 .98145 
                 0.98145 
               
               
                 0.042006 
                 118.085 
                 118.085 
                 94.5711 
                 94.5711 
                 1.2486 
                 1.2486 
                 17.5477 
                 17.5477 
                 1.2012 
                 1.2012 
               
               
                   
                 128.5904 
                 128.5904 
                 110.7784 
                 110.7784 
                 1.1608 
                 1.1608 
                 15.095 
                 15.095 
                 .64453 
                 0.64453 
               
               
                 0.041822 
                 128.3619 
                 128.3619 
                 102.0986 
                 102.0986 
                 1.2573 
                 1.2573 
                 19.4558 
                   
                 .68848 
                 .68848 
               
               
                 0.041647 
                 138.5198 
                 138.5198 
                 116.0474 
                 116.0474 
                 1.1936 
                 1.1936 
                 12.6962 
                 12.6962 
                 3.3105 
               
               
                 0.045579 
                 153.1476 
                   
                 125.2732 
                   
                 1.225 
                 1.225 
                 15.6597 
                 15.6597 
                 1.1865 
                 1.1865 
               
               
                 0.043 
                 107.2509 
                 105.8548 
                 88.5423 
                 88.2796 
                 1.218 
                 1.2249 
                 14.6605 
                 15.6138 
                 1.1067 
                 0.9 
               
               
                 0.003 
                 29.5843 
                 25.492 
                 25.1052 
                 21.1239 
                 0.0813 
                 0.0375 
                 4.6945 
                 1.402 
                 0.8085 
                 0.2336 
               
               
                 0.0705 
                 0.2758 
                 0.2408 
                 0.2835 
                 0.2393 
                 0.0668 
                 0.0306 
                 0.3202 
                 0.0898 
                 0.7306 
                 0.2595 
               
               
                 0.0027 
                 −12.6669 
                 −9.4261 
                 −9.429 
                 −8.2639 
                 −0.0244 
                 −0.0294 
                 −0.4605 
                 −1.0474 
                 −0.219 
                 −0.0192 
               
             
          
           
               
                 6% 
                 −13% 
                 −10% 
                 −12% 
                 −10% 
                 −2% 
                 −2% 
                 −3% 
                 −7% 
                 −25% 
                 −2% 
               
             
          
           
               
                 1.0634 
                 0.8819 
                 0.911 
                 0.8935 
                 0.9064 
                 0.98 
                 0.976 
                 0.9686 
                 0.9329 
                 0.8021 
                 0.9786 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                 Pressure 
               
               
                   
                 I 10  (1) 
                 I 10  (2) 
                 I 11  (1) 
                 I 11  (2) 
                 I 12  (1) 
                 I 12  (2) 
                 Freq 
               
               
                   
                   
               
             
          
           
               
                   
                 0.0019174 
                   
                 0.71045 
                 0.71045 
                 0.0098593 
                 0.0098593 
                 3.3325 
               
               
                   
                 0.0088205 
                 0.008205 
                 0.65186 
                 0.63186 
                 0.0076059 
                 0.0076059 
                 5.2881 
               
               
                   
                 0.0057855 
                 0.0057855 
                 0.68848 
                 0.68848 
                 0.0042904 
                 0.0042904 
                 0.5127 
               
               
                   
                 0.0076752 
                 0.0076752 
                 0.55664 
                   
                 0.0047153 
                 0.047153 
                 5.4199 
               
               
                   
                 0.0081621 
                 0.0081621 
                 0.62988 
                 0.62988 
                 0.0053581 
                 0.0053581 
                 0.54199 
               
               
                   
                 0.0048277 
                   
                 1.1719 
                 1.1719 
                 0.0025282 
                   
                 0.55664 
               
               
                   
                 0.0073768 
                 0.0073768 
                 0.99609 
                 0.99609 
                 0.0059338 
                 0.059338 
                 0.38086 
               
               
                   
                 0.012387 
                 0.012387 
                 1.0547 
                 1.0547 
                 0.0072785 
                 0.0072785 
                 0.46875 
               
               
                   
                 0.0053825 
                 0.0053825 
                 1.1133 
                 1.1133 
                 0.0046343 
                 0.0046341 
                 5.5957 
               
               
                   
                 0.0076754 
                 0.0076754 
                 3.9111 
                   
                 0.01191 
                   
                 4.3506 
               
               
                   
                 0.0009 
                 0.0008 
                 1.1484 
                 0.8771 
                 0.0016 
                 0.0006 
                 2.6448 
               
               
                   
                 0.0004 
                 0.0002 
                 0.9964 
                 0.2279 
                 0.0033 
                 0.0002 
                 2.3563 
               
               
                   
                 0.4861 
                 0.2714 
                 0.8676 
                 0.2598 
                 2.0415 
                 0.308 
                 0.8909 
               
               
                   
                 0.0078855 
                 0.0078855 
                 4.0723 
                 4.0723 
                 0.011312 
                 0.011312 
                 5.1855 
               
               
                   
                 0.0094965 
                 0.0094965 
                 4.8193 
                 4.8193 
                 0.010443 
                 0.010443 
                 0.46875 
               
               
                   
                 0.0053134 
                 0.0053134 
                 .64453 
                   
                 0.007945 
                 .0007945 
                 0.57129 
               
               
                   
                 0.0056247 
                 0.0056247 
                 3.4937 
                 3.4937 
                 0.012812 
                   
                 0.39551 
               
               
                   
                 0.0079653 
                 0.0079653 
                 0.68848 
                 0.68848 
                 0.0056112 
                 .00056112 
                 0.39551 
               
               
                   
                 0.0027589 
                   
                 5.1562 
                   
                 0.011253 
                 0.011253 
                 0.4248 
               
               
                   
                 0.013553 
                 .0013553 
                 4.8779 
                 4.8779 
                 0.011633 
                 0.11663 
                 0.62988 
               
               
                   
                 0.0046506 
                 0.0046506 
                 0.99609 
                 0.99609 
                 0.0052555 
                   
                 0.4541 
               
               
                   
                 0.011848 
                   
                 1.1792 
                 1.1792 
                 0.0057202 
                 0.0057202 
                 0.28564 
               
               
                   
                 0.0062246 
                 0.0062246 
                 4.8486 
                 4.8486 
                 0.098915 
                 0.098915 
                 0.35156 
               
               
                   
                 0.0018 
                 0.0008 
                 3.0776 
                 3.1219 
                 0.007 
                 0.0071 
                 0.9163 
               
               
                   
                 0.0035 
                 0.0003 
                 1.9567 
                 1.8594 
                 0.0055 
                 0.0053 
                 1.5034 
               
               
                   
                 1.9434 
                 0.3825 
                 0.6358 
                 0.5956 
                 0.7925 
                 0.7567 
                 1.6408 
               
               
                   
                 −0.0009 
                 0 
                 −1.9292 
                 −2.2449 
                 −0.0053 
                 −0.0064 
                 1.7285 
               
             
          
           
               
                   
                 −108% 
                 4% 
                 −168% 
                 −256% 
                 −328% 
                 −1036% 
                 189% 
               
             
          
           
               
                   
                 0.4796 
                 1.042 
                 0.3732 
                 0.2809 
                 0.2337 
                 0.0088 
                 2.8865 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 7 
               
               
                   
               
             
             
               
                   
                   
                   
                   
                   
                   
                 Speed 
                 Speed 
                   
               
               
                 Pressure Freq 
                 Pressure Power 
                 Pressure Power 
                 Speed peak 
                 Speed peak 
                 Speed mean 
                 mean 
                 mean s 
                 Speed mean s 
               
               
                   
               
             
          
           
               
                 3.3325 
                 0.096296 
                   
                 8.3495 
                   
                 4.0833 
                   
                 0.007768 
                   
               
               
                 5.2881 
                 0.061731 
                 0.061731 
                 9.5933 
                 9.5933 
                 4.8141 
                 4.8141 
                 0.057164 
                 0.057164 
               
               
                 0.5127 
                 0.0044982 
                   
                 12.2647 
                 12.2647 
                 6.1768 
                 6.1768 
                 0.050443 
                 0.050443 
               
               
                 5.44199 
                 0.05208 
                 0.05208 
                 11.6228 
                 11.6228 
                 5.8715 
                 5.8715 
                 0.12527 
                 0.12527 
               
               
                 0.54199 
                 0.027901 
                 0.027901 
                 15.0426 
                   
                 6.0457 
                 6.0457 
                 0.1517 
                 0.1517 
               
               
                 0.55664 
                 0.0082316 
                 0.0082316 
                 13.3404 
                 13.3404 
                 6.012 
                 6.012 
                 0.16833 
                 0.16833 
               
               
                   
                 0.0052711 
                 0.0052711 
                 10.7915 
                 10.7915 
                 5.2681 
                 5.2681 
                 0.094529 
                 0.094529 
               
               
                 0.46875 
                 0.012483 
                 0.012483 
                 14.1176 
                 14.1176 
                 6.1778 
                   
                 0.17908 
               
               
                   
                 0.058576 
                 0.058576 
                 10.161 
                 10.161 
                 5.2236 
                 5.2236 
                 0.13968 
                 0.13968 
               
               
                 4.3506 
                 0.05491 
                 0.05491 
                 10.8455 
                 10.8455 
                 5.2258 
                 5.2258 
                 0.059048 
                 0.059048 
               
               
                 2.5589 
                 0.0382 
                 0.0351 
                 11.6129 
                 11.5921 
                 5.4899 
                 5.5797 
                 0.1033 
                 0.1058 
               
               
                 2.2762 
                 0.0311 
                 0.0242 
                 2.0962 
                 1.5643 
                 0.691 
                 0.5044 
                 0.0579 
                 0.0467 
               
               
                 0.8872 
                 0.814 
                 0.6889 
                 0.1805 
                 0.1349 
                 0.1259 
                 0.0904 
                 0.5608 
                 0.4418 
               
               
                   
                 0.061452 
                   
                 9.9972 
                   
                 6.1496 
                   
                 0.17253 
                 0.17253 
               
               
                 0.86875 
                 0.0094384 
                 0.0094384 
                 10.7797 
                 10.7797 
                 5.3819 
                 5.3819 
                 0.10134 
                 0.10134 
               
               
                 0.57129 
                 0.0073217 
                 0.0073217 
                 11.0506 
                 11.0506 
                 5.5366 
                 5.5366 
                 0.17892 
                 0.17892 
               
               
                 0.39551 
                 0.0051118 
                   
                 10.7443 
                 10.7443 
                 4.9679 
                 4.9679 
                 0.19278 
                 0.19278 
               
               
                 0.39551 
                 0.0077278 
                 0.6077278 
                 10.1037 
                 10.1037 
                 5.272 
                 5.272 
                 −0.02886 
               
               
                 0.4248 
                 0.02284 
                 0.02284 
                 12.7809 
                   
                 5.4773 
                 5.4773 
                 0.22708 
               
               
                 0.62906 
                 0.0082204 
                 0.0082204 
                 12.735 
                 12.735 
                 5.5803 
                 5.5803 
                 0.061202 
                 0.061202 
               
               
                 0.4541 
                 0.012612 
                 0.012612 
                 10.1842 
                 10.1842 
                 5.0876 
                 5.0876 
                 0.10128 
                 0.10128 
               
               
                   
                 0.015209 
                 0.015209 
                 11.3279 
                 11.3279 
                 4.204 
                   
                 0.062106 
                 .0062106 
               
               
                 0.35156 
                 0.025622 
                 0.025622 
                 11.4363 
                 11.4363 
                 4.903 
                 4.903 
                 0.020919 
                 0.020919 
               
               
                 0.4614 
                 0.0176 
                 0.0136 
                 11.114 
                 11.0452 
                 5.256 
                 5.2758 
                 0.1033 
                 0.1044 
               
               
                 0.0945 
                 0.0169 
                 0.0071 
                 0.9967 
                 0.8347 
                 0.5153 
                 0.2623 
                 0.0877 
                 0.0722 
               
               
                 0.205 
                 0.9605 
                 0.5217 
                 0.0897 
                 0.0756 
                 0.098 
                 0.0497 
                 0.8491 
                 0.6917 
               
               
                 2.0975 
                 0.0206 
                 0.0215 
                 0.4989 
                 0.5469 
                 0.2338 
                 0.3039 
                 0 
                 0.0014 
               
             
          
           
               
                 455% 
                 118% 
                 158% 
                 4% 
                 5% 
                 4% 
                 6% 
                 0% 
                 1% 
               
             
          
           
               
                 5.5456 
                 2.1758 
                 2.5799 
                 1.0449 
                 1.0495 
                 1.0445 
                 1.0576 
                 0.9996 
                 1.0132 
               
               
                   
               
             
          
           
               
                   
                 I 13  (1) 
                 I 13  (2) 
                 I 14  (1) 
                 I 14  (2) 
                 I 15  (1) 
                 I 15  (2) 
                 I 16  (1) 
                 I 16  (2) 
               
               
                   
                   
               
             
          
           
               
                   
                 0.21973 
                 0.21973 
                 0.051075 
                 1.1133 
                 1.1133 
                 2.88106 
                   
                   
               
               
                   
                 0.50537 
                 0.50537 
                 0.047243 
                   
                 0.65918 
                 0.63918 
                 1.39E.05 
                 1.39E.05 
               
               
                   
                 0.4834 
                 0.4834 
                 0.19419 
                 0.19419 
                 0.74707 
                 0.74707 
                 8.73E.06 
                 8.73E.06 
               
               
                   
                 0.9668 
                   
                 0.076818 
                 0.076818 
                 0.71777 
                 0.71777 
                 2.56E.05 
                 2.56E.05 
               
               
                   
                 0.54199 
                 0.54199 
                 0.26958 
                   
                 0.38086 
                 0.38086 
                 1.13E.05 
                 1.13E.05 
               
               
                   
                 0.11719 
                   
                 0.14149 
                 0.14149 
                 1.0986 
                 1.0986 
                 5.90E.05 
               
               
                   
                 0.36621 
                 0.36621 
                 0.25658 
                 0.25658 
                 0.82031 
                 0.82031 
                 1.08E.05 
                 1.08E.05 
               
               
                   
                 0.4541 
                 0.4541 
                 0.22589 
                 0.22589 
                 0.80566 
                 0.80566 
                 1.08E.05 
                 1.08E.05 
               
               
                   
                 0.41016 
                 0.41016 
                 0.086152 
                 0.086152 
                 0.10254 
                   
                 1.76E.05 
                 1.76E.05 
               
               
                   
                 0.32227 
                 0.32227 
                 0.1218 
                 0.1218 
                 1.1372 
                   
                 2.05E.05 
                 2.05E.05 
               
               
                   
                 0.4387 
                 0.4129 
                 0.1471 
                 0.1442 
                 0.7603 
                 0.7928 
                 0 
                 0 
               
               
                   
                 0.2278 
                 0.1066 
                 0.0843 
                 0.0745 
                 0.3318 
                 0.2368 
                 0 
                 0 
               
               
                   
                 0.5193 
                 0.2583 
                 0.573 
                 0.5167 
                 0.4365 
                 0.2986 
                 0.8231 
                 0.3591 
               
               
                   
                 0.39551 
                 0.39551 
                 0.045468 
                 0.045468 
                 0.64453 
                 0.64453 
                 1.08E.05 
               
               
                   
                 0.27832 
                 0.27832 
                 0.11044 
                 0.11044 
                 0.82031 
                 0.82031 
                 3.06E.05 
                 3.03E.05 
               
               
                   
                 0.35156 
                 0.35156 
                 0.088712 
                 0.088712 
                 1.0693 
                   
                 1.51E.05 
                 1.51E.05 
               
               
                   
                 1.1719 
                   
                 0.09231 
                 0.09321 
                 0.32959 
                   
                 5.31E.05 
               
               
                   
                 0.13184 
                   
                 0.044955 
                   
                 0.83496 
                 0.83496 
                 1.34E.05 
                 1.34E.05 
               
               
                   
                 0.41016 
                 0.41016 
                 0.069383 
                 0.069383 
                 0.76172 
                 0.76172 
                 2.03E.05 
                 2.03E.05 
               
               
                   
                 0.16113 
                 0.16113 
                 0.11091 
                   
                 0.33691 
                 0.33691 
                 2.03E.05 
                 2.03E.05 
               
               
                   
                 0.38086 
                 0.38086 
                 0.0719 
                 0.0719 
                 0.67383 
                 0.67383 
                 2.27E.05 
                 2.27E.05 
               
               
                   
                 0.16113 
                 0.16113 
                 0.059927 
                 0.059927 
                 0.37354 
                 0.37354 
                 1.12E.05 
                 1.12E.05 
               
               
                   
                 0.32227 
                 0.32227 
                 0.081702 
                 0.081702 
                 0.68848 
                 0.68848 
                 2.17E.05 
                 2.17E.05 
               
               
                   
                 0.3765 
                 0.3076 
                 0.0776 
                 0.0775 
                 0.6533 
                 0.6418 
                 0 
                 0 
               
               
                   
                 0.2981 
                 0.0997 
                 0.0237 
                 0.0203 
                 0.2428 
                 0.1896 
                 0 
                 0 
               
               
                   
                 0.7919 
                 0.324 
                 0.3055 
                 0.2618 
                 0.3717 
                 0.2955 
                 0.5714 
                 0.3177 
               
               
                   
                 0.0623 
                 0.1053 
                 0.0695 
                 0.0668 
                 0.1069 
                 0.1511 
                 0 
                 0 
               
             
          
           
               
                   
                 17% 
                 34% 
                 90% 
                 86% 
                 16% 
                 24% 
                 16% 
                 23% 
               
             
          
           
               
                   
                 1.1654 
                 1.3423 
                 1.8961 
                 1.8618 
                 1.1637 
                 1.2354 
                 0.8593 
                 0.8146 
               
               
                   
                   
               
             
          
         
       
     
     Although the present invention has been described in connection with particular embodiments thereof, it is to be understood that various modifications, alterations and adaptions may be made by those skilled in the art without departing from the spirit and scope of the invention. It is intended that the invention be limited only by the appended claims. 
     Various publications are cited herein, the contents of which are hereby incorporated by reference in their entireties.