Abstract:
The present invention, in one form, is a method for improving image reconstruction in computed tomography systems by using a reconstruction algorithm and a detector cell algorithm. In accordance with one embodiment of the present invention, the reconstruction algorithm generates fan-parallel data directly from projection data which is processed to generate image data. In particular and in one embodiment, after view to view rebinning of the projection data, the data is pre- and post-convolution weighted, filtered and backprojected to generate image data. In another embodiment, the detector cell algorithm is utilized to determine the shape of the detector to include an arc sin dependency to eliminate axial interpolation of the projection data.

Description:
BACKGROUND OF THE INVENTION 
     This invention relates generally to computed tomography (CT) imaging and more particularly, to reconstructing an image from CT scan data. 
     In at least one known CT system configuration, an x-ray source projects a fan-shaped beam which is collimated to lie within an X-Y plane of a Cartesian coordinate system and generally referred to as the “imaging plane”. The x-ray beam passes through the object being imaged, such as a patient. The beam, after being attenuated by the object, impinges upon an array of radiation detectors. The intensity of the attenuated beam radiation received at the detector array is dependent upon the attenuation of the x-ray beam by the object. Each detector element of the array produces a separate electrical signal that is a measurement of the beam attenuation at the detector location. The attenuation measurements from all the detectors are acquired separately to produce a transmission profile. 
     In known third generation CT systems, the x-ray source and the detector array are rotated with a gantry within the imaging plane and around the object to be imaged so that the angle at which the x-ray beam intersects the object constantly changes. A group of x-ray attenuation measurements, i.e., projection data, from the detector array at one gantry angle is referred to as a “view”. A “scan” of the object comprises a set of views made at different gantry angles during one revolution of the x-ray source and detector. In an axial scan, the projection data is processed to construct an image that corresponds to a two dimensional slice taken through the object. 
     One method for reconstructing an image from a set of projection data is referred to in the art as the filtered backprojection technique. This process converts the attenuation measurements from a scan into integers called “CT numbers” or “Hounsfield units”, which are used to control the brightness of a corresponding pixel on a cathode ray tube display. 
     To reduce the total scan time required for multiple slices, a “helical” scan may be performed. To perform a “helical” scan, the patient is moved while the data for the prescribed number of slices is acquired. Such a system generates a single helix from a one fan beam helical scan. The helix mapped out by the fan beam yields projection data from which images in each prescribed slice may be reconstructed. 
     At least one known filtered-backprojection image reconstruction technique comprises the steps of pre-processing, filtering and backprojection. In the fan-beam geometry, the backprojection process includes a computationally expensive pixel dependent weight factor. Accordingly, to obtain reasonable reconstruction times, it is necessary in the fan-beam geometry to design and develop an application specific integrated circuit (ASIC) board to perform the backprojection. 
     Alternatively, it is possible to rearrange the fan-beam data into parallel data, a process known as rebinning. In the parallel geometry, the pixel-dependent backprojection factor is eliminated. At least some known rebinning procedures include a two step process. In the first step, view data are interpolated view-to-view, azimuthally, to obtain projection data samples, identified as Radon samples, that lie on a radial line, intersecting the origin of Radon space. This geometry is referred to as fan-parallel. The second step in the rebinning procedure comprises a radial interpolation. However, in the reconstruction process, data points are filtered by a high-pass filter in the radial direction. Accordingly, radial interpolation, proceeding from non-evenly spaced, is computationally expensive and may compromise the view high-frequencies. 
     It would be desirable to provide a reconstruction algorithm that enables image reconstruction directly from fan parallel data. It would also be desirable to provide such a reconstruction algorithm that does not require rebinning of the fan beam data. Further, it would be desirable to provide a detector for direct generation of parallel data. 
     BRIEF SUMMARY OF THE INVENTION 
     These and other objects may be attained by a reconstruction algorithm which generates image data directly from projection data without requiring radial interpolation. The reconstruction algorithm defines fan beam parameterization for fan parallel reconstruction without radial interpolation of the projection data. Specifically, the reconstruction algorithm includes applying pre- and post convolution weights and filtering the fan-parallel projection data to generate a reconstructed image of the object. 
     In addition, a detector having variable length detector cells or variable distance gaps between the detector cells can be utilized to generate parallel data without radial interpolation. Specifically, a detector cell algorithm generates positions for locating the center, or locus, of each detector cell of the detector. In one embodiment, the length of each detector cell is altered so that the detector cells are positioned adjacent to one another. In an alternative embodiment, the gaps, or distances, between fixed length detector cells are altered so that parallel data is generated by the detector. In either of these embodiments, the view-to-view interpolation may be replaced by data acquisition system (DAS) channel dependent delays, thereby allowing direct generation of parallel projection data without rebinning or interpolation. 
     The above described reconstruction algorithm enables image reconstruction directly from fan parallel data. In addition, the reconstruction algorithm generates an image of the object without requiring interpolation of the fan beam data. Further, the above described detector directly generates parallel data. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a pictorial view of a CT imaging system. 
     FIG. 2 is a block schematic diagram of the system illustrated in FIG.  1 . 
     FIG. 3 is illustrates a fan-parallel geometry image in accordance with one embodiment of the present invention. 
     FIG. 4 illustrates a Cartesian coordinate system for a given fan vertex and a detector curve in accordance with one embodiment of the present invention. 
     FIGS.  5   a - 5   f  illustrate various detector geometries for direct parallel data generation. 
     FIG. 6 illustrates a detector curve of an alternative embodiment of the detector shown in FIG.  4 . 
     FIG. 7 illustrates backprojection utilizing a reconstruction algorithm in accordance with one embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to FIGS. 1 and 2, a computed tomograph (CT) imaging system  10  is shown as including a gantry  12  representative of a “third generation” CT scanner. Gantry  12  has an x-ray source  14  that projects a beam of x-rays  16  toward a detector array  18  on the opposite side of gantry  12 . X-ray beam is collimated by a collimate (not shown) to lie within in an X-Y plane of a Cartesian coordinate system and generally referred to as an “imaging plane”. Detector array  18  is formed by detector elements  20  which together sense the projected x-rays that pass through a medical patient  22 . Each detector element  20  produces an electrical signal that represents the intensity of an impinging x-ray beam and hence the attenuation of the beam as it passes through patient  22 . During a scan to acquire x-ray projection data, gantry  12  and the components mounted thereon rotate about a center of rotation  24 . 
     Rotation of gantry  12  and the operation of x-ray source  14  are governed by a control mechanism  26  of CT system  10 . Control mechanism  26  includes an x-ray controller  28  that provides power and timing signals to x-ray source  14  and a gantry motor controller  30  that controls the rotational speed and position of gantry  12 . A data acquisition system (DAS)  32  in control mechanism  26  samples analog data from detector elements  20  and converts the data to digital signals for subsequent processing. In one embodiment, DAS  32  includes a plurality of channels and is referred to as a multiple channel DAS. An image reconstructor  34  receives sampled and digitized x-ray data from DAS  32  and performs high speed image reconstruction. The reconstructed image is applied as an input to a computer  36  which stores the image in a mass storage device  38 . 
     Computer  36  also receives commands and scanning parameters from an operator via console  40  that has a keyboard. An associated cathode ray tube display  42  allows the operator to observe the reconstructed image and other data from computer  36 . The operator supplied commands and parameters are used by computer  36  to provide control signals and information to DAS  32 , x-ray controller  28  and gantry motor controller  30 . In addition, computer  36  operates a table motor controller  44  which controls a motorized table  46  to position patient  22  in gantry  12 . Particularly, table  46  moves portions of patient  22  through gantry opening  48 . 
     The following discussion which describes a reconstruction algorithm which enables image reconstruction directly from fan parallel data sometimes refers specifically to an axial scan. The reconstruction algorithm, however, is not limited to practice in connection with only axial scans, and may be used with other scans, such as helical scans. It should be further understood that the algorithm described below may be implemented in computer  36  and would process, for example, reconstructed image data. Alternatively, the algorithm could be implemented in image reconstructor  34  and supply image data to computer  36 . Other alternative implementations are, of course, possible. 
     In accordance with one embodiment of the present invention, image reconstruction is completed directly from fan parallel data without radial rebinning of the data. More particularly, the reconstruction algorithm describes fan-parallel weighted-convolution reconstruction kernel decomposition. Specifically and referring to FIG. 3, the polar representation of the Radon transform of ƒ is:          p        (     s   ,   θ     )       =       ∫     -   ∞     ∞            ∫     -   ∞     ∞              f   _          (     x   ,   y     )            δ        (       x                 cos                 θ     +     y                 sin                 θ     -   s     )               x             y                                  
     where: ƒ(r, φ) is a polar representation of the x-ray attenuation coefficient distribution to be reconstructed and ƒ(x,y) is a Cartesian representation of the x-ray attenuation coefficient distribution to be reconstructed. 
     The reconstruction function is:          f        (     r   ,   φ     )       =       1     4        π   2                ∫   0     2      π              ∫     -   ∞     ∞            (       -   1     t     )          ∂     ∂   s            p        (     s   ,   θ     )               s             θ                                    
     with t=s−r cos(θ−φ). Interpreting the singular integral in its Cauchy principal value sense leads to:                f        (     r   ,   φ     )       =       1     4        π   2                ∫   0     2      π              lim     ε   →   0              ∫     -   ∞     ∞              F   ε          (   t   )            p        (     s   ,   θ     )               s             θ                       (   1   )                                
     with:                  F   ε          (   t   )       =     [               1     ε   2               t          ≤   ε                     -   1       t   2               t          ≥   ε           ]             (   2   )                                
     The Radon space parameterization (s, θ) is then changed into a fan-beam parameterization(a(u), η(ν)) to express the integral as a weighted convolution. Referring specifically to FIG. 3, projection data p(s, θ) is parameterized using the angle η from VO to VP where β is the angle from the y axis to the fan vertex V, S the distance from the vertex V to the origin O, and P the point sampled in Radon space by a single fan ray. The origin of the parameterization η is chosen to coincide with the line VO: η(0)=0. As the object to be reconstructed is assumed bounded, the angle η will be limited to [η min , η max ] so that the entire object cross-section is covered. 
     The parameters (u, ν) are the independent variables describing the system where, for example, u is a scan time and ν is a detector cell coordinate on the detector curve. Changing the variables (s, θ) to (u, ν) utilizing the parameterizations β(u), η(ν), and S(β) leads to:          [         θ           s         ]     =     [             β        (   u   )       +     η        (   v   )                     S        [     β        (   u   )       ]            sin        [     η        (   v   )       ]               ]                            
     The parameter limits are defined by u min , u max , ν min , and ν max  so that: 
     
       
         β( u   max )−β( u   min )=2π, η(ν min )=η min η(ν max )=η max   (3) 
       
     
     The Jacobian of the transformation with S(β)=S constant is: 
     
       
         J=β′( u )×η′( v )×S×COS[η( v )]  (4) 
       
     
     The transformation of t with the argument of F ε  is: 
     
       
           t=s−r  cos(θ−φ) 
       
     
     so: 
     
       
           t =S×sin[η(ν)]− r  cos(θ−φ)  (5) 
       
     
     In fan-parallel reconstruction as in parallel reconstruction, the angle θ is constant for one fan-parallel view. As a result, the fan angle for the ray passing through the point ƒ(r, φ) to be reconstructed where {overscore (η)}=η({overscore (ν)}), is: 
     
       
         S×sin({overscore (η)})= r  cos(θ−φ) 
       
     
     As a result, the argument t is:                    t   =     S   ×     {       sin        [     η        (   v   )       ]       -     sin        [     η        (     v   _     )       ]         }                   =       {         sin        [     η        (   v   )       ]       -     sin        [     η        (     v   _     )       ]           v   -     v   _         }     ×   S   ×     (     v   -     v   _       )                     (   6   )                                
     where:            lim                 ɛ     →     0          ∫     -   ∞     ∞          F                   ɛ        (     λ                   b        (   λ   )         )            a        (   λ   )               λ             =       lim                 ɛ     →     0          ∫     -   ∞     ∞          F                   ɛ        (   λ   )              a        (   λ   )           b   2          (   λ   )                   λ     .                                    
     Using the expression for t from above, the under the summation sign is:          F                   ɛ        (   t   )         =     F                   ɛ        (     v   -     v   _       )       ×     1     S   2                {       v   -     v   _           sin        [     η        (   v   )       ]       -     sin        [     η        (     v   _     )       ]           }     2     .                              
     Let K be defined as:                K        (     v   ,     v   _       )       =         sin        [     η        (   v   )       ]       -     sin        ⌊     η        (     v   _     )       ⌋           v   -     v   _                 (   7   )                                
     Writing K(η,{overscore (η)}) as a weighted convolution kernel: 
     
       
         K(ν, {overscore (ν)})=E(ν)H(ν−{overscore (ν)})G(ν) 
       
     
     where H is a convolution kernel, and E and G are pre- and post-convolution weights, then:                F                   ε        (   t   )         =       F                   ε        (     v   -     v   _       )               S   2          [       E        (   v   )            H        (     v   -     v   _       )            G        (     v   _     )         ]       2               (   8   )                                
     As a result of equation 4 being a function of η, the reconstruction equation is written in the form of a weighted convolution-backprojection as:                f        (     r   ,   φ     )       =         1     4        π   2          S   2                ∫     u   inf       u   sup            lim                 ε         →     o          ∫     v   inf       v   sup                F                   ε        (     v   -     v   _       )                 J        (     u   ,   v     )                    u             v           [       E        (   v   )            H        (     v   -     v   _       )            G        (     v   _     )         ]     2            Xp        [       β        (   u   )       ,     η        (   v   )         ]                     9                              
     For a given projection, a pre-convolution weighting is applied to the projection data utilizing the E and Jacobian functions. The pre-convolution weights are independent of the image point described by (r, θ). Convolution kernels F and H are then performed. Prior to backprojecting, a post-convolution weighting G, independent of the image point, is applied. 
     By following the method described below for the fan-beam reconstruction kernel, a necessary condition for the fan-parallel kernel K to be decomposed is:                K        (     v   ,     v   _       )       =           sin        ⌊     η        (   v   )       ⌋       -     sin        ⌊     η        (     v   _     )       ⌋           v   -     v   _         =       E        (   v   )            H        (     v   -     v   _       )            G        (   v   )                   (   10   )                                
     The necessary condition can be expressed in term of the fan-beam parameterization η as:                      K        (     v   ,     v   _       )       =         sin        [     η        (   v   )       ]       -     sin        [     η        (     v   _     )       ]           v   -     v   _                     =         {           η   ′          (   v   )            cos        [     η        (   v   )       ]              η   ′          (     v   _     )            cos        [     η        (     v   _     )       ]               η   ′          (   0   )              η   ′          (     v   -     v   _       )            cos        [     η        (     v   -     v   _       )       ]           }       1   /   2                sin        [     η        (     v   -     v   _       )       ]         v   -     v   _         .                     (   11   )                                
     The necessary condition for η is:                  sin        [     η        (   v   )       ]       -     sin        [     η        (     v   _     )       ]         =         {           η   ′          (   v   )            cos        [     η        (   v   )       ]              η   ′          (     v   _     )            cos        [     η        (     v   _     )       ]               n   ′          (   0   )              η   ′          (     v   -     v   _       )            cos        [     η        (     v   -     v   _       )       ]           }       1   /   2              sin        [     η        (     v   -     v   _       )       ]       .               (   12   )                                
     Utilizing equation 7 it is clear that η(ν)=Arc sin (a×ν) is solution. 
     To avoid interpolation, the solution η(ν)=Arc sin(a×ν) requires either a specific “Arc sin” detector as described below or detector cells having centers distributed along the arc of a circle centered on fan-vertex according to the Arc sin parameterization. Utilizing either of these detector geometries, the reconstruction algorithm reduces to a parallel reconstruction: 
     
       
         K(ν, {overscore (ν)})= a,   
       
     
     with the Jacobian given by: 
     
       
         J=β′( u )×η′(ν)×S×cos[η(ν)]=β′( u )×α×S 
       
     
     As a result, the reconstruction equation is:                        f        (     r   ,   φ     )       =         1     4      aS                   π   2                ∫     u   inf       u   sup            lim                 ɛ         →     0          ∫     v   inf       v   sup            F                   ɛ        (     v   -     v   _       )              β   ′          (   u   )       ×                        p        [       β        (   u   )       ,     arcsin        (   v   )         ]               u             v             (   13   )                                
     so that the Radon samples lie equidistant on radial lines through the origin of Radon space. Using known methods of image reconstruction following either known view-to-view data interpolation, or direct fan-parallel data acquisition via DAS delays, the image is reconstructed. 
     On a typical third generation CT scanner, η(ν)=a×ν. Substituting into the necessary condition described in equation 11 above, provides:                      K        (     v   ,     v   _       )       =                    sin        (     a   ×   v     )       -     sin        (     a   ×     v   _       )           v   -     v   _                     ≈                    {         cos        (     a   ×   v     )            cos        (     a   ×     v   _       )           cos        [     a   ×     (     v   -     v   _       )       ]         }       1   /   2              sin   [     a   ×     (     v   -     v   _       )           v   -     v   _                         (   14   )                                
     and accordingly to the following image reconstruction algorithm:                4        S   2          π   2     ×     f        (     r   ,   φ     )         =         ∫     u   inf       u   sup            lim                 ɛ       →     0          ∫     v   inf       v   sup                F                   ɛ        (     v   -     v   _       )            cos        [     a   ×     (     v   -     v   _       )       ]              {       v   -     v   _         sin   [     a   ×     (     v   -     v   _       )           }     2               J        (     u   ,   v     )                    u             v           cos        (     a   ×   v     )            cos        (     a   ×     v   _       )           ×       p        [       β        (   u   )       ,     η        (   v   )         ]       .                     (   15   )                                
     Utilizing equation 4 for the Jacobian, the expression for the pre-convolution weights is equal to 1.0, and the filter expression is:          F                   ɛ        (     v   -     v   _       )            cos        [     a   ×     (     v   -     v   _       )       ]              {       v   -     v   _         sin   [     a   ×     (     v   -     v   _       )           }     2       =     F                   ɛ        (     v   -     v   _       )       ×       {         v   -     v   _       2       sin        [       a   ×     (     v   -     v   _       )       2     ]         }     2     ×       {     1   -       tan   2          [     a   ×     (       v   -     v   _       2     )       ]         }     .                              
     The post-convolution weights are:          1     cos        (     a   ×     v   _       )         .                          
     Equation 14 is exact for any ν when {overscore (ν)}=0 and the reconstruction equation 15 is exact at the isocenter. Image reconstruction proceeds according to known fan beam geometry reconstruction algorithms except the pre-filtering weights are 1.0, the filtering kernel does not include multiplying by a cosine factor and the post-convolution weights are 1/cos(fan-angle). Additionally, in the backprojection, the inverse square distance from the fan-vertex to the pixel factor is eliminated, and the arctangent function is replaced by an arcsine function. 
     Alternatively to this “Arc sin” algorithm for direct reconstruction of fan-parallel data, the Arc sin parameterization described above may be used to generate detector cell position information. These new detector geometries, when combined with DAS-dependent channel delays, allow direct parallel reconstruction on a third generation CT scanner. Specifically, position of detector cells along a detector curve can be determined wherein the loci of the detector cells are found for the Arc sin parameterizations utilizing the assumption that the detector cells are equidistant on the detector curve. Alternatively, utilizing the parameterization the detector cell locations can be mapped onto a third-generation detector having an arc of a circle centered on the fan-vertex. Fixed length detector cells are positioned on the arc with the gap, or distance between the detector cells being altered so that the detector generates equispaced parallel data after either view-to-view rebinning or direct DAS delays. The equispaced parallel data is generated from the parallel projection rays which result from the location of the detector cells. 
     More particularly and with respect to FIG. 4, a detector cell D is positioned at a Cartesian coordinate (x,y) where the Cartesian coordinate system is centered on the fan vertex V and the x axis passes through the scanner isocenter O. A DL curve describing the locus of points D(x,y) is parameterized by ν: (x,y)=(x(ν),y(ν)), so that:              y        (   v   )         x        (   v   )         =     tan        [     η        (   v   )       ]         ;       η        (   v   )       =       atan        [       y        (   v   )         x        (   v   )         ]       .                              
     The condition of cell equidistance translates as:              [            x        (   v   )              v       ]     2     +       [            y        (   v   )              v       ]     2       =   1.                          
     Substituting, and with η(ν)=Arc sin (a×ν):          y        (   v   )       =         x        (   v   )       ×     tan        [     η        (   v   )       ]         =         x        (   v   )       ×   a   ×   v         1   -       (     a   ×   v     )     2                                    
     the differential equation is:                 x        (   v   )              v       =       M        (     x   ,   v     )       .                            
     The second degree equation relating x′(ν) to x(ν) and ν is: 
     
       
         A(ν) x   ′2 (ν)+B(ν, x ) x   ′ (ν)+C(ν, x )=0 
       
     
     with:            A        (   v   )       =     1     1   -       a   2     ×     v   2             ,       B        (     v   ,   x     )       =       2        a   2          vx        (   v   )            (     1   +       a   2          v   2         )           [     1   -       a   2     ×     v   2         ]     2         ,   and             C        (     v   ,   x     )       =           a   2            x   2          (   v   )            (     1   +       a   2          v   2         )           [     1   -       a   2     ×     v   2         ]     3       -   1.                            
     The function M relating x′ to x and ν is therefore the algebraic expression for the roots of a second degree polynomial. Using the Runge-Kutta method, a numerical solution is calculated so that as x′(v) is given by the expression for the roots of a second degree equation, there exists two detector geometry classes. Each geometry class represents a root. To obtain a curve that is symmetric with respect to the x axis, the condition x′(−ν)=−x′(ν) is imposed by switching roots at ν=0. Further, x(0)=x 0  is fixed to 1.0, and the solutions are calculated starting from ν=0 to ν=ν min  and then starting again from ν=0 to ν=ν max . 
     To obtain a detector curve with a continuous derivative on the x axis for ν=0, it is necessary that x′(0)=0. This requires x(0)×a=1.0, and it can be shown that under that condition the discriminant becomes negative in the neighborhood of ν=0. Accordingly, the x-axis symmetric solutions all have an inflexion point at the origin. Six solutions corresponding to the values of three different parameters and their associated two detector geometries are given in FIG.  5   a  through  5   f . In FIGS.  5   a  and  5   b , a=0.8, starting with first and second solutions respectively and switching roots at 0, ν max =0.32. In FIGS.  5   c  and  5   d , a=0.95, ν max =0.35 (c) and ν max =0.131(d). In FIGS.  5   e  and  5   f , a=0.7, ν max =0.455, first and second solutions shown without switching roots at ν=0. 
     In an alternative embodiment, the detector cells of a detector are arranged on the traditional third generation detector geometry curve, with variable gaps, or distances between the cells. Specifically and referring to FIG. 6, utilizing a Cartesian coordinate system centered on the fan vertex V and the x-axis passing through the scanner isocenter O, detector cell d is positioned at the Cartesian coordinates of (x, y). S and D are respectively the vertex-to-isocenter and isocenter-to-detector distances. As above, the DL curve describing the locus of points d(x,y) is parameterized by ν: (x,y)=(x(ν),y(ν)), and the geometric constraint is:              [     x        (   v   )       ]     2     +       [     y        (   v   )       ]     2       =       (     S   +   D     )     2                            
     Substituting, 
     
       
         η(ν)=arc sin( a ×ν) 
       
     
     the following parameterization is obtained: 
     
       
         ( x (ν), y (ν))=(S+D)([1 −a   2 ×ν 2 ] ½   ,a ×ν). 
       
     
     The locations of the detector cell centers are determined by stepping on this parameterized curve at equal increments of the parameter v. In one embodiment, for example, the detector includes detector cells having variable lengths and being coupled to an arc shaped detector housing (not shown). The detector cells are positioned adjacent to one another. In an alternative embodiment, the detector includes detector cells of constant cell length and are coupled to the detector housing with varying distances, or gaps, between the cells. 
     Utilizing the variable length detector cells or variable gap size detector, as determined by the detector cell algorithm, the detector generates parallel data directly from the projection data with either view-to-view rebinning or DAS delays. 
     The above described algorithms allow images to be reconstructed directly from fan parallel data. Specifically, utilizing a detector having detector cells located in positions determined by the detector cell algorithm, the reconstruction algorithm allows direct parallel reconstruction of fan-beam data without interpolation. As a result, the computationally intensive step of radial interpolation with its associated resolution degradation can be eliminated. In addition, the reconstruction algorithm eliminates the backprojection pixel-dependent weight. Utilizing the two algorithms provides increased image quality by reducing aliasing and maintaining resolution, while reducing the number of calculations for image reconstruction. 
     From the preceding description of various embodiments of the present invention, it is evident that the objects of the invention are attained. Although the invention has been described and illustrated in detail, it is to be clearly understood that the same is intended by way of illustration and example only and is not to be taken by way of limitation. Accordingly, the spirit and scope of the invention are to be limited only by the terms of the appended claims.