Abstract:
A physics-based mathematical model is used to estimate central pressure waveforms from measurements of a brachial pressure waveform measured using a supra-systolic cuff. The method has been tested in numerous subjects undergoing cardiac catheterisation. Central pressure agreement was within 11 mm Hg and as good as the published non-invasive blood pressure agreement between the oscillometric device in use and the so-called “gold standard.” It also exceeds international standards for the performance of non-invasive blood pressure measurement devices. The method has a number of advantages including simplicity of application, fast calculation and accuracy of prediction. Additionally, model parameters have physical meaning and can therefore be tuned to individual subjects. Accurate estimation of central waveforms also allow continuous measurement (with intermittent calibration) using other non-invasive sensing systems including photoplethysmography.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This present application claims benefit of priority from U.S. patent application Ser. No. 11/358,283, filed Feb. 21, 2006 (now U.S. Patent Publication No. 2006/0224070-A1, published Oct. 5, 2006); U.S. patent application Ser. No. 12/157,854, filed Jun. 13, 2008 (now U.S. Patent Publication No. 2009/0012411-A1, published Jan. 8, 2009); U.S. Provisional Application Ser. No. 61/127,436, filed May 15, 2008 and U.S. Provisional Application No. 61/194,193, filed Sep. 24, 2008. The invention disclosed and claimed herein is related in subject matter to that disclosed in U.S. Pat. No. 5,913,826, issued Jun. 22, 1999; U.S. Pat. No. 6,994,675, issued Feb. 7, 2006; and the aforementioned U.S. Patent Publication No. 2006/0224070-A1 and U.S. Patent Publication No. 2009/0012411-A1, all of which are incorporated herein by reference. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    The present invention relates to a method of measurement of suprasystolic waveforms from an upper-arm blood pressure cuff. The analysis and interpretation of these waveforms can be performed directly on the measured and processed signals. It has been demonstrated that the suprasystolic waveform changes significantly and predictably with the administration of vasoactive agents, physiological challenges, normal ageing processes and morbidities. 
         [0003]    Recent literature has noted the potential importance of central blood pressure (waveform and values such as systolic, diastolic and mean) in the management of cardiovascular risk. To that end, it would be advantageous to be able to estimate central pressures. 
         [0004]    More particularly, the invention relates to methods of physics-based modelling of the waveform measurement system and the arterial system being studied. One of the early models of this kind, constructed by Joe El-Aklouk at the Institute of Biomedical Technologies, Auckland University of Technology, was based on acoustic pressure wave propagation in tubes. 
         [0005]    El-Aklouk&#39;s work involved the development of models to simulate wave propagations given known material properties, geometry, end conditions and driving inputs. El-Aklouk also studied the transmission of pressure oscillations in an artery to an externally applied inflatable cuff. 
         [0006]    More recent models have been proposed by Berend Westerhof et. al. (Am J Physiol Heart Circ Physiol 292:800-807, 2007.) who examined the pressure transfer between the subclavian root and unoccluded brachial artery assuming that the more peripheral arteries present a known end-impedance. In another recent paper (J Appl Physiol 105:1858-1863, 2008), Westerhof et al. attempt to show that changes in impedance caused by changes in the peripheral circulation have a negligible effect on the central pressure prediction. Westerhof et al. do not consider the use of a suprasystolic cuff to isolate the brachial artery from the peripheral circulation. 
       SUMMARY OF THE INVENTION 
       [0007]    A principal object of the present invention is to improve the estimation of central pressure waveform by applying a suprasystolic cuff and using an inverse brachial-artery to cuff-pressure model. 
         [0008]    A more particular object of the present invention is to extend the theoretical work done by El-Aklouk and Westerhof et al. to include a derivation of an inverse model and specifically applies it to the subclavian-brachial arterial branch. This inverse model allows the prediction of the driving input pressure (in the aortic arch) from the measurement of a suprasystolic waveform. It has been found that the inverse model problem can be solved without resorting to computationally costly and iterative numerical methods. A solution has been derived with assumptions to allow presentation in a closed-form. The model utilises only physically meaningful parameters. 
         [0009]    This model according to the invention has been applied to clinical data collected in a study of subjects undergoing cardiac catheterisation at Auckland City Hospital, led by Dr. Wil Harrison. The results of this study, which validate the model, are set forth hereinbelow. 
         [0010]    Model Derivation 
         [0011]    In the arterial system under consideration, a pressure wave propagates through a volume of blood enclosed by the left subclavian and brachial arteries. At the brachial end, the artery is essentially closed by the application of a suprasystolic blood pressure cuff. 
         [0012]    A number of assumptions, along with their justifications, have been made, as follows:
       The artery is circular in cross section. MRI imaging has shown this to be essentially correct.   The artery has parallel sides. The radius change between the subclavian root and brachial artery is approximately 1.5 millimetres over a distance of 400 mm.   The arterial cylinder is thin walled, that is, the wall thickness is much less than the internal radius. The artery wall thickness reported in the literature is approximately ⅕ th  the radius.   The blood flow velocity is much less than the speed of sound. That is, kinetic-to-potential energy conversion is negligible. Also, the viscoelastic properties of blood flow can be ignored. Under conditions of a suprasystolic cuff with consequent artery occlusion, there is essentially no blood flow within the artery.   There are no bifurcations within the artery segment. The left subclavian-brachial conduit is essentially free from bifurcations (although there are a number of small branches). The next major bifurcation is the branching of the brachial artery in to the radial and ulnar arteries. This occurs more distally than the suprasystolic cuff.   The end conditions of the artery segment can be described as an abrupt change in impedance. Finite element models show the transition to the closed state under the suprasystolic cuff happens over the space of a few millimetres. Likewise, the subclavian root branches abruptly from the aortic arch, which is of much larger diameter.   There is no hydrostatic pressure differential along the artery. Medical practice advises that non-invasive measurements are taken with the cuff approximately level with the heart. This assumption therefore holds.       
 
         [0020]    Note that many of these assumptions do not hold for other measurement methods. In particular, the use of an arterial line or tonometry method does not allow the assumption of a constant, abrupt change in impedance, nor of zero blood flow. Measurement at a radial site also introduces a significant bifurcation into the arterial system being studied, as well as further compromising the thin-walled tube assumption. Note also that the model is most correct for the left arm. The right subclavian artery is one branching generation removed from the aorta. 
         [0021]    Using the above assumptions, it can be demonstrated that pressure propagation in the system can be described by the acoustic wave equation in one dimension: 
         [0000]    
       
         
           
             
               
                 
                   
                     ∂ 
                     2 
                   
                    
                   
                     p 
                     t 
                   
                 
                 
                   ∂ 
                   
                     x 
                     2 
                   
                 
               
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                       p 
                       t 
                     
                   
                   
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             = 
             0 
           
         
       
     
         [0000]    where p t  is the acoustic pressure (local deviation from ambient pressure), c is the speed of sound, x is the spacial coordinate and t is time. 
         [0000]    
       
         
           
             c 
             = 
             
               
                 Eh 
                 
                   2 
                    
                   ρ 
                    
                   
                       
                   
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                   r 
                 
               
             
           
         
       
     
         [0000]    where E is the elastic modulus of the artery wall material, h is wall thickness, r is tube radius and ρ is blood density. 
         [0022]    Given a constant arterial cross section, the speed of sound is constant in time and space, and so the general solution can be described by 
         [0000]        p   t   =p   p ( x−c t )+ p   n ( x+c t ) 
         [0000]    where p p , p n  represent positive- and negative-going pressure waves respectively, the total pressure p t  being a superposition of the two component waves. 
         [0023]    It is also known that at an impedance change (causing a change in the speed of sound) a portion of a wave will be reflected, and a portion (the remainder) of the wave will be transmitted. 
         [0024]    Using this information, the following relationships between the total pressure in the aorta and the total pressure at the occlusion may be written, for the system depicted in  FIG. 1 : 
         [0000]    
       
         
           
             
               
                 P 
                 
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         [0000]    where subscripts 0, 1 and 2 respectively represent locations in the aorta outside the subclavian artery (source), the root of the subclavian artery and just before the occlusion. Factor a is the reflection coefficient at the cuff and is physically constrained to be in the range 0 to 1. Constant dt is the time taken for a wave to travel from the subclavian root to the cuff occlusion. 
         [0025]    It can be seen that under the conditions and assumptions described above, which are specific to suprasystolic measurement, theoretically, the aortic pressure waveform can be easily reconstructed from the occlusion pressure, using only two parameters, a and dt. 
         [0026]    Measurement Model 
         [0027]    The formulation thus far has considered only the internal physics of pressure wave propagation within the artery. The sensing system according to the invention is, however, non-invasive and relies on the transfer of internal pressure oscillations to an externally applied inflatable cuff. 
         [0028]    It has been reported in the literature that the amplitude of the transferred pressure oscillation is determined by a large number of factors. However, the critical parameter appears to be the transmural pressure—that is, the difference in pressure between the externally applied cuff pressure and the internal arterial pressure. This relationship is shown diagrammatically in  FIG. 2 , which shows that the maximum relative amplitude is transferred at zero transmural pressure. As absolute transmural pressure increases, less oscillation is observed at the cuff. Given an approximately constant cuff pressure, as is the case with suprasystolic measurement, it is seen that the transmural pressure will change over the cardiac cycle. 
         [0029]    This information permits compensation of the oscillometric waveform to estimate the arterial pressure. The procedure described herein is presented as a functional example, and may not be the only or even the best method of compensation. 
         [0030]    The suprasystolic waveform, after filtering, p osc , represents cuff pressure oscillations less than a few mmHg in amplitude. This waveform is rescaled to the measured systolic, SBP, and diastolic, DBP, pressures to generate p ss . 
         [0000]    
       
         
           
             
               p 
               SS 
             
             = 
             
               
                 
                   
                     
                       p 
                       Osc 
                     
                     - 
                     
                       Min 
                        
                       
                         ( 
                         
                           p 
                           Osc 
                         
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                       Max 
                        
                       
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         [0031]    The difference between p ss  and the cuff pressure, p Cuff , is calculated to be the transmural pressure, p tp . In the case of suprasystolic measurement the cuff pressure can be assumed to be a value 25 mmHg above SBP. 
         [0000]    
       
      
       p 
       TP 
       =p 
       Cuff 
       −p 
       ss  
      
     
         [0000]    A correction amount, p Δ  is calculated as a function of the transmural pressure. In order to match the relationship shown in  FIG. 2 , the correction amount should be zero at zero transmural pressure, and increase by increasing amounts as transmural pressure increases. These requirements can be met by a function of the form 
         [0000]        p   Δ =( d p   TP ) 4    
         [0000]    where d is a scaling factor. 
         [0032]    Other forms of correction may also be applied. It has been found from our analysis that the form of correction should be such that if the corrected and uncorrected waveforms are normalized, then the correction function should be monotonically increasing between zero and one, but proportionally greater for pressures between zero and one, as shown in  FIG. 12 . 
         [0033]    One function that satisfies this requirement is of the form 
         [0000]    
       
         
           
             
               p 
               Corr 
             
             = 
             
               
                 
                   - 
                   1 
                 
                 + 
                 d 
                 + 
                 
                   p 
                   SSnorm 
                 
               
               
                 1 
                 + 
                 d 
                 + 
                 
                   p 
                   SSnorm 
                 
               
             
           
         
       
     
         [0000]    where p SSnorm  is the uncorrected normalized waveform value, p Corr  is the corrected normalized waveform value and d is a control parameter that controls the amount of correction. 
         [0034]    Once the correction amount has been calculated, the estimated arterial pressure, p Art , can be rescaled as follows 
         [0000]    
       
         
           
             
               p 
               Corr 
             
             = 
             
               
                 p 
                 SS 
               
               + 
               
                 p 
                 Δ 
               
             
           
         
       
       
         
           
             
               P 
               Art 
             
             = 
             
               
                 
                   
                     
                       p 
                       Corr 
                     
                     - 
                     
                       Min 
                        
                       
                         ( 
                         
                           p 
                           Corr 
                         
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         [0000]    An example of an estimated pressure wave (normalized to SBP=1, DBP=0) is shown in  FIG. 3 . 
         [0035]    Blood Pressure Scaling 
         [0036]    In the above discussion, p Art  was scaled to the measured systolic and diastolic pressures. In fact, the theory suggests that this is not a correct treatment. The arterial blood pressure is actually generated by wave reflections from the peripheral circulation. However, the arterial pressures estimated by suprasystolic measurement are a function of reflections from the cuff. The arterial pressures with a suprasystolic cuff will therefore likely be higher than the pressures without a suprasystolic cuff. The degree to which this is the case may depend on a number of factors. In this model, the scaling is treated as a constant factor, c. 
         [0000]        p   t2   =c  ( P   Art −Mean( p   Art )) 
         [0000]    Note once again that p t2  is the pressure perturbation about a mean pressure, not the gauge blood pressure. The assumptions infer that the mean pressure does not change along the length of the subclavian-brachial artery. Therefore the aortic blood pressure can be estimated by the equation: 
         [0000]        p   AO   =p   t0 +Mean( p   Art ) 
         [0037]    Model Summary 
         [0038]    In summary, the present invention is a model-based method of predicting central aortic pressures (specifically at the opening to the left subclavian artery). The input to the model is the suprasystolic, oscillometric waveform. The model has the following parameters:
       a: Absolute value of the reflection coefficient at the cuff. a ∈ (between 0 and 1);   dt: Time for the pressure wave to propagate from the subclavian root to the occluding cuff (greater than 0 seconds);   d: Scaling factor for transmural coupling correction; and   c: Scaling factor for suprasystolic pressure waveform.       
 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0043]      FIG. 1  is a diagram representing a model of an arterial system according to the present invention. 
           [0044]      FIG. 2  is a diagram showing oscillatory response of the model according to the invention. 
           [0045]      FIG. 3  is a time diagram showing a corrected pressure wave (upper line) and an original wave (lower line) in the model according to the invention. 
           [0046]      FIG. 4  presents a comparison of oscillometrically determined brachial systolic blood pressure (SBP), and measured aortic SBP.  FIG. 4A  is a Bland Altman Plot and  FIG. 4B  is an X-Y plot. 
           [0047]      FIG. 5  presents a comparison of oscillometrically determined brachial diastolic blood pressure (DBP), and measured aortic DBP.  FIG. 5A  is a Bland Altman Plot and  FIG. 5B  is an X-Y plot. 
           [0048]      FIG. 6  shows a correlation of a suprasystolically measured brachial Augmentation Index (AI), and invasively measured AI. 
           [0049]      FIG. 7  presents a prediction of central systolic blood pressure using the model according to the invention and measured central systolic blood pressure.  FIG. 7A  is a Bland Altman chart and  FIG. 7B  is an X-Y chart. 
           [0050]      FIG. 8  presents a prediction of central diastolic blood pressure using the model according to the invention and measured central diastolic blood pressure.  FIG. 8A  is a Bland Altman chart and  FIG. 8B  is an X-Y chart. 
           [0051]      FIG. 9  shows a prediction of central Augmentation Index (AI) using the model according to the invention and measured central Augmentation Index.  FIG. 9A  is a Bland Altman chart and  FIG. 9B  is an X-Y chart. 
           [0052]      FIG. 10  shows a correlation between first derivatives of measured and predicted waveforms as a function of model parameters. 
           [0053]      FIG. 11  shows a time series for the measured (solid line) and predicted (dashed line) pressure deviation from mean ( FIG. 11A ) and first derivative of pressure deviation ( FIG. 11B ). 
           [0054]      FIG. 12  shows a monotonically increasing relationship between the normalized, uncorrected cuff pressure waveform and the normalized, corrected, brachial artery waveform. 
           [0055]      FIG. 13  is a flow chart of a method for non-invasively calibrating the central pressure waveform. 
           [0056]      FIG. 14  is a time diagram of a single cardiac ejection cycle showing the timing of heart sounds, ECG pulses, central pressure and cuff oscillation waveforms. 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0057]    Clinical data collected in a study of subjects undergoing cardiac catheterisation at Auckland City Hospital, led by Dr. Wil Harrison, were used to experimentally verify the theory and model according to the present invention. 
         [0058]    Clinical Validation 
         [0059]    Data for clinical validation was collected under the leadership of Dr. Wil Harrison from the cardiac investigation laboratories at Auckland City Hospital. Twenty-seven subjects were recruited from consecutive cases, with the exclusion of those with known, severe aneurysms, moderate to severe arrhythmias, or abnormal subclavian/brachial anatomy. Suprasystolic, oscillometric waveforms were collected non-invasively using a blood pressure cuff and analyzed using the model according to the present invention. Concurrently, ten seconds of invasive pressure waveforms were collected with the catheter tip near the aortic root. The non-invasive blood pressure (NIBP) was measured with a monitor using its internal, Welch Allyn oscillometric NIBP module. NIBP was determined approximately thirty seconds prior to the collection of waveform data. 
         [0060]    Of the twenty-seven subjects recruited, technical difficulties prevented measurements from being taken on two of the first subjects. Poor quality catheter tracings were recorded on a further two subjects. Catheter tracings for one additional subject were not available at the time of this analysis. Waveform measurements were obtained from the remaining twenty-two subjects with a mean (sd) signal to noise ratio, SNR, of 13.4 (3.06) dB. This represents very good signal quality. 
         [0061]    Non-Invasive vs. Invasive Measurements 
         [0062]    As a point of reference, the statistics derived directly from the non-invasive and invasive measurements were compared. 
         [0063]      FIG. 4  shows agreement and correlation between oscillometric systolic pressure and measured invasive systolic pressure. Pearson&#39;s correlation coefficient, r, was 0.88. However, the limits of agreement (twice the standard deviation of the difference between paired measurements) are 5.9±24.2 mm Hg. This means that approximately 95% of measurements will be accurate within these limits. Clinically, such wide limits of agreement and significant bias indicate that non-invasive systolic pressure is a poor estimator of the central systolic pressure. 
         [0064]    In the case of diastolic pressure, as shown in  FIG. 5 , the limits of agreement are somewhat tighter being 10.7±11.0 mmHg. However, the average bias is large. Correlation is comparable, with r=0.84. 
         [0065]    Direct comparison between suprasystolic augmentation index as calculated by the R6.5 device (AI SS ) and central Augmentation Index AI is not justifiable due to the different method of calculation. However, if performed, it gives very poor limits of agreement of 57±94% and r of 0.56. The X-Y plot is shown in  FIG. 6 . 
         [0066]    Model-Predicted vs. Measured Invasive Measurements 
         [0067]    The model described above was applied to the clinical data in an investigation into the feasibility of predicting central pressures. Model parameters were set as follows: a=0.7, c=1.25, dt=0.045 seconds and d=0.045. 
         [0068]    As can be seen in  FIG. 7 , central systolic pressures show much better agreement than directly comparing non-invasive pressures. The limits of agreement are 0.2±8.7 mmHg, with correlation coefficient r of 0.98. These limits of agreement should be considered in light of results published by Welch Allyn on the accuracy of the NIBP module being used, for which the limits of agreement are 2±11 mmHg. 
         [0069]    Similar results were obtained for diastolic blood pressure as shown in  FIG. 8 . The limits of agreement for the prediction are −0.3±10.6 mmHg. For comparison, the limits of agreement for Welch Allyn non-invasive diastolic pressure are −0.5±11 mmHg. 
         [0070]    The invasive and predicted augmentation indices were also compared. The relevant charts are shown in  FIG. 9 . The limits of agreement are 4.1±24.6% and the correlation coefficient is 0.54. 
         [0071]    Results of Clinical Study 
         [0072]    It may be seen that the prediction of the central pressures using the model and method according to the present invention closely matches the actual values that were measured invasively. The method according to the invention does not require any calibration to central waveform parameters (such as diastolic and mean pressures). In view of the documented inaccuracies of the NIBP estimation, it appears that the central pressure variations cannot be significantly improved. Indeed, the blood pressure predictions easily pass the international standards for the accuracy of blood pressure devices (although this standard does not strictly apply to central pressure estimation). 
         [0073]    There are a few methodological shortcomings to the current study, which are described below.
       Central pressures were measured at the aortic root, whereas the model predicts pressures at the entrance to the left subclavian artery, which is situated near the top of the aortic arch.   A single NIBP determination was used for each patient. An idea of the variability introduced could be obtained by multiple, consecutive measurements, or by invasive measurement.   Model parameters were determined somewhat arbitrarily. A better approach would have been to estimate them from an independent set of data, or through mathematical modelling.   Identification of the anacrotic notch on measured invasive waveforms was open to debate in seven of the twenty-two subjects. This may explain some of the variability in agreement between model-predicted and measured augmentation index.       
 
         [0078]    Ideally, parameters to the model would be determined by measurement of each individual subject. In the case of dt, this could be determined relatively easily using additional, non-invasive sensors, or possibly estimated from demographic information such as age, height, weight and sex. An analysis of the correlation between the derivative of the predicted waveform and the derivative of the measured waveform shows that this correlation is far more sensitive to parameter dt than to a. This is shown in  FIG. 10  for a specific subject, but the overall shape of this surface is typical. 
         [0079]    Note that the correlation shown in  FIG. 10  is for the first derivative of the waveform. The correlation between predicted and measured waveforms was greater than 0.97. The corresponding time series are shown in  FIG. 11 . 
         [0080]    Conclusions 
         [0081]    The method according to the invention advantageously includes the steps of:
       Non-invasive measurement of pressure waveforms;   The use of a suprasystolic blood pressure cuff;   The blood pressure measurement from the left brachial artery; and   The specific mathematical model presented above.       
 
         [0086]    The method thus estimates central artery pressures and pressure waveforms from measurement of pressure pulse wave signals at a peripheral location using a blood pressure cuff. 
         [0087]    The basic applications of this method are:
       The imposition of known impedance end-conditions on a section of an artery downstream of a central artery. In this example, the suprasystolic cuff causes an occlusion, and isolates the section of artery on the distal side of the cuff.   The measurement of a heart-pulse synchronous signal from the section of artery between the known end condition and the central artery.   A method of calculation based on a mathematical model relating the heart-pulse synchronous signal and central pressure at the root of the peripheral artery.   A method of estimating the parameters to the mathematical model. These may be estimated based on previously measured data, characteristics of the patient (such as age, weight, height) and/or measurements taken from the subject. For example, with reference to  FIG. 14 :
           A heart-sounds sensor may be used to estimate the time of entry of a pressure pulse into the subclavian artery. By assuming the systolic ejection period as measured on the cuff pressure wave is the same as for the central waveform, the time of entry of the pressure pulse is estimated by subtracting the systolic ejection period from the time of the heart sound corresponding to aortic valve closure.   The R-wave of an ECG can be assumed to occur a constant increment of time before the ejection of stroke volume, and therefore estimate the time of the foot of the central pressure wave.   If the left carotid artery is applanated concurrently with one suprasystolic cuff measurement, the time of the foot of the applanation wave can be considered to be nearly synchronous with the entry of the pressure wave into the subclavian artery.   
           A method of applying the mathematical model to estimate the central pressure from measured waveforms.       
 
         [0096]    There has thus been shown and described a novel method for estimating a central pressure waveform obtained with a blood pressure cuff, which method fulfils all the objects and advantages sought therefor. Many changes, modifications, variations and other uses and applications of the subject invention will, however, become apparent to those skilled in the art after considering this specification and the accompanying drawings which disclose the preferred embodiments thereof. All such changes, modifications, variations and other uses and applications which do not depart from the spirit and scope of the invention are deemed to be covered by the invention, which is to be limited only by the claims which follow. 
         [0097]    For example, additional aspects of the invention may include:
       The estimated central waveform can be used to calculate a transfer function between estimated central pressure and another heart pulse synchronous signal. This second signal (for example, a finger photoplethysmograph or PPG) could be measured from another section of a peripheral artery with or without the imposition of the known impedance end-condition. In this way, the PPG signal could be used to continuously estimate central or peripheral pressure waveforms. Recalibration by the central-pressure waveform estimating means can occur at preset intervals, triggered by the clinician, or when characteristics of the measured waveform change. This algorithm is illustrated in  FIG. 13 .   The estimated central waveform can be used in conjunction with another heart pulse synchronous signal and a further mathematical model or transfer function to estimate characteristics of blood flow, including cardiac output.