Patent Publication Number: US-9402549-B2

Title: Methods and apparatus to estimate ventricular volumes

Description:
FIELD OF THE DISCLOSURE 
     This disclosure relates generally to estimating ventricular volumes, and, more particularly, to methods and apparatus to estimate ventricular volumes. 
     BACKGROUND 
     Cardiovascular diseases are the leading cause of death in western countries. To diagnosis and treat cardiovascular diseases, the cardiac functions of the left ventricle and the right ventricle may be analyzed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a schematic illustration of a closed circulation heart system. 
         FIG. 2  illustrates a frame of magnetic resonance imaging (MRI) sequence showing an initial input, identification and/or selection of first and second landmarks in accordance with the teachings of this disclosure. 
         FIG. 3  shows a graph of estimated volumes of a left ventricle and a right ventricle over a cardiac cycle in accordance with the teaching of this disclosure. 
         FIG. 4  shows a frame in which a region of interest (ROI) has been selected that encloses both a left ventricle and a right ventricle in accordance with the teachings of this disclosure. 
         FIG. 5  shows a more detailed view of the region of interest of  FIG. 4 . 
         FIG. 6  shows a plot of an example blob based appearance model. 
         FIG. 7  shows a plot of an example homogeneity based appearance model. 
         FIG. 8  shows a plot of an example edge based appearance model. 
         FIG. 9  is an example blob mask associated with a blob based appearance model. 
         FIG. 10  illustrates an example homogeneity mask associated with a homogeneity based appearance model. 
         FIG. 11  shows an example edge mask associated with an example edge based appearance model. 
         FIG. 12  shows an example system in accordance with the examples disclosed herein. 
         FIG. 13  is a flowchart representative of machine readable instructions that may be executed to implement the system of  FIG. 12 . 
         FIG. 14  is a flow diagram illustrating some of the processes described in the flowchart of  FIG. 13 . 
         FIG. 15  is a graph showing the correlation between the left ventricle cavity area and the right ventricle cavity area. 
         FIG. 16  is a processor platform to execute the instructions of  FIG. 13  to implement the system of  FIG. 12 . 
     
    
    
     The figures are not to scale. Wherever possible, the same reference numbers will be used throughout the drawing(s) and accompanying written description to refer to the same or like parts. 
     DETAILED DESCRIPTION 
     Cardiovascular diseases are a leading cause of death in western countries. Determined ventricular volumes can be used to globally assess cardiac functions. To diagnose and treat these diseases, both the left and right ventricles are analyzed using ventricular volumes, ejection fraction (EF) and/or stroke volumes, etc. Some of these known estimating methods are limited to estimating the volume of the left ventricle using segmentation, which is computationally expensive, slow and tedious. In contrast to some known methods, the examples disclosed herein estimate the volume of the left ventricle and the right ventricle jointly and/or substantially simultaneously using an example segmentation-free method that uses an example adapted Bayesian formulation. Specifically, in some examples, the left and right ventricle volumes are determined using the Bayesian formulation that includes an example likelihood model and an example prior probability model where the likelihood model uses multiple appearance features and the prior probability model correlates the areas and/or other features between the left ventricular cavity and the right ventricular cavity. Thus, using the examples disclosed herein, a direct, efficient and accurate assessment of global cardiac functions can be determined. 
     In some of the illustrated examples, based on an initial input of manually or automatically identifying attachment locations between a right ventricle and a left ventricular septal wall, the bi-ventricular volumes can be estimated without manual and automatic contouring. The cavity areas (e.g., short-axis view cavity areas) can be estimated with a Bayesian framework and the bi-ventricular volume can be estimated by integrating the cavity areas along a sagittal direction. Thus, the bi-ventricular volumes can be estimated without manual and automatic contouring. Using the estimated bi-ventricular volumes, the cardiac functional parameters for both the left and right ventricles can be determined efficiently and simultaneously. In some examples, the estimated volumes can be used to estimate functional parameters of the heart such as end-systolic volume, end-diastolic volume, ejection fraction, cardiac output, peak ejection rate, filling rate, etc. 
       FIG. 1  illustrates a schematic illustration of a closed circulation heart system  100  including a heart  102  having a left ventricle  104 , a right ventricle  106 , a systemic circuit  108  and a pulmonary circuit  110 . Because the left ventricle  104  and the right ventricle  106  both belong to the closed circulation heart system  100  and are physically connected, the left and right ventricles  104 ,  106  share the same motion pattern of cyclically expanding during a diastolic period and contracting during a systolic period. Thus, the volumes of the left and right ventricles  104 ,  106  similarly change as the heart  102  transitions through the different phases. 
       FIG. 2  illustrates a frame  200  of an MRI sequence  200  showing an initial input, identification and/or selection of first and second landmarks  202 ,  204  on a frame  200  of the MRI sequence. 
     The first landmark  202  corresponds to a first attachment point between a left ventricular septal wall  208  and a right ventricular wall  210  and the second landmark  204  corresponds to a second attachment point between the right ventricular wall  210  and the left ventricular septal wall  208 . In the illustrate examples, the landmarks  202 ,  204  are used to automatically estimate the bi-ventricular volumes throughout a cardiac cycle in real time, the results of which are shown in  FIG. 3 .  FIG. 3  shows a graph  300  of the estimated volumes of the left ventricle and the right ventricle over a cardiac cycle where the x-axis  302  corresponds to a frame number, the y-axis  304  corresponds to an estimated volume, a first line  306  is associated with the left ventricle and a second line  308  is associated with the right ventricle. 
       FIG. 4  shows the frame  200  in which a region of interest (ROI)  402  has been selected that encloses both a left ventricle  404  and a right ventricle  406 . In the illustrated examples, the landmarks and/or the user selections  202 ,  204  enable consistency to be maintained between different potential regions of interest (ROIs) and/or between different frames and/or patients. Specifically, in the illustrated examples, the anatomical significance of the landmarks  202 ,  204  enables the ROI selections to be consistent and for the final estimated results to be robust to intra-user variability and/or inter-user variability. 
     Using the ROI selection  402  of  FIG. 4 , a central point  408  between the landmarks  202 ,  204  can be identified in the center of the squared ROI selection  402 . In the illustrated examples, the scale of the central point  408  is twice as large as a distance between the landmarks  202 ,  204 . In some examples, a central line  410  that couples and/or links the landmarks  202 ,  204  can be used to orient the ROI selection  402  as shown in  FIG. 5 . 
       FIG. 5  illustrates the ROI selection  402  having been rotated such that the central line  410  is vertical relative to the bottom of the ROI selection  402  and the central line  410  separates the left ventricle  404  and the right ventricle  406 . In the illustrated example of  FIG. 5 , the ROI selection  402  has been rescaled to 40×40 pixels. Using the illustrated examples of  FIGS. 4 and 5 , a single ROI selection can be used to analyze both the left ventricle  404  and the right ventricle  406 . Using the illustrated examples of  FIGS. 4 and 5  and correlation information of an example probability model, both the left ventricle  404  and the right ventricle  406  can be jointly examined within the ROI selection  402 . 
     In the illustrated examples, the cavity areas (Ai) of the left ventricle  404  and the right ventricle  406 , respectively, are determined using an example Bayesian formulation. The example Bayesian formulation may be used and/or adapted to incorporate different models and/or constraints related to appearance, motion, etc. In the example Bayesian framework, statistical pattern recognition includes estimating a posterior probability density of an object parameterized by X given a prior, p(X), and an observation, (Z). In some examples, Equation 1 represents the posterior probability of X given the observation, Z, where p(X|Z) is a likelihood function modeling a probability of observing Z given an object state, X, and p(X) is a prior probability of the object state.
 
 p ( X|Z )α p ( Z|X ) p ( X )  Equation 1
 
     Equation 2 is a modified example Bayesian formulation used to estimate bi-ventricle volumes and/or areas based at least in part on physical aspects of the heart and/or the left and right ventricles. Referring to Equation 2, the LV corresponds to the left ventricle, RV corresponds to the right ventricle and p(Z|X) corresponds to an example multi-feature likelihood function. In some examples, the connections are determined by P RV  (X) (e.g., an example right ventricle probability model; an example area correlation prior probability model), which is modeled as a function of P LV  (X|Z) (e.g., an example left ventricular posterior probability) and uses the estimated left ventricle area as a prior based on a correlation between the left ventricle and the right ventricle. In the illustrated example, the left ventricle issued as an estimate for the right ventricle because of the circular geometry of the left ventricle in the short-axis view. 
     
       
         
           
             
               
                 
                   
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     In the illustrated example, based on the example Bayesian equation as described in Equation 2, an object state can be defined as X=[X 1 , . . . X Q ] where X q ε{0, 1} is a label assigned to the qth pixel in the input image and qε{1, . . . , Q} and where {0, 1} corresponds to a background, the left ventricle and the right ventricle, respectively. In this example, X labels and partitions the image into the cavity and the background (e.g., into two segments). To determine an area of the cavity, in some examples, the posterior probability of the object state, X, is estimated using an example Bayesian inference method and the cavity area is determined based on a function of X. Using an estimation of the posterior probability, p(X|Z), Equation 3 can be used to determine the mean cavity area of the left ventricle and the right ventricle as a function of the posterior where A(X)=Σ q δ(X q , 1) and δ(a, b) is a Kronecker delta function. In the examples disclosed herein, A(X) determines the left ventricle cavity area and the right ventricle cavity area by counting the pixels labeled as 1.
 
ε[ A ( X )| Z]=Σ   Xε{0,1}     Q     A ( X ) p ( X|Z )  Equation 3
 
     Equation 4 describes a likelihood function, p(Z|X), that uses a blob based appearance model, p b (Z|X), a homogeneity based appearance model, p h (Z|X), and an edge based appearance model, p e (Z|X) where α and β are used to adjust the relative importance of each of the models. In the illustrated examples, the blob, homogeneity and edge based appearance models are assumed to be conditionally independent of each other given an object state, X, which is an assumption for integrating multiple features and/or models.
 
 p ( Z|X )= p   b ( Z|X ) p   h ( Z|X ) α   p   e ( Z|X ) β   Equation 4
 
       FIGS. 6, 7 and 8  show plots of the blob based appearance model, the homogeneity based appearance model and the edge based appearance model, respectively, based on an input image and hypothesized object states (e.g., approximately 3300) collected from manual segmenting data. A comparison between the blob based appearance model of  FIG. 6  and the edge based appearance model of  FIG. 8  shows a low degree of correlation. In some examples, the blob based appearance model is useful in medical imaging when objects have a blob-like appearance (e.g., an inside area is brighter or darker than a surrounding area). Because in an MRI, the left ventricle cavity and the right ventricle cavity may be brighter than neighboring structures, the blob based appearance model is advantageous when extracting cavity regions. 
       FIG. 9  is associated with a blob based appearance model and illustrates an example mask  900  that captures blob features by determining the dot product with an input image. In the illustrated example of  FIG. 9 , fb(X) is the mask  900  constructed based on the object state, X, and fb q (X) is the qth pixel in the mask. As shown in  FIG. 9 , the mask  900  includes a cavity region (e.g., a white region)  902 , a narrow band region (e.g., a black band or region)  904  and remaining and/or surrounding pixels (e.g., a grey region)  906 . In the illustrated example, the pixel weight of the cavity region  902  is approximately 1, the pixel weight of the narrow band region  904  is approximately −1 and the pixel weight of the remaining pixels is approximately 0. Equation 5 describes a process of constructing the mask  900  of  FIG. 9 , where d is the width of the band, A(X) is the area of the left ventricle and the right ventricle, Ω c (X) and Ω b (X) are the cavity region  902  and the surrounding narrow band region  904 . In the illustrated examples, the cavity region  902  and the surrounding narrow band region  904  are determined by the object state, X, and δ(•) 
     
       
         
           
             
               
                 
                   
                     
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       FIG. 10  illustrates an example homogeneity mask  1000  used to specify a cavity region within which homogeneity is computed. When the left ventricle and the right ventricle are filled with blood, except for a papillary muscle region, the left ventricle and the right ventricle may have a bright and homogeneous appearance in an MRI. The papillary muscle region provides for a homogeneity constraint in the object state, X (e.g., having low intensity variance in a specified cavity region). Even with possible disturbances from papillary muscles, homogeneity can provide for a complementary constraint for cavity estimation problems. Equation 6 is an example appearance model that captures the homogeneity feature, where μ(Z, X) is a mean intensity with the cavity region, Ω C (X), specified by the object state, X, as shown in the example mask  1000  of  FIG. 10 . Equation 7 defines a mean intensity within the cavity region, Ω C (X), specified by the object state, X.
 
 p   h ( Z|X )=1−Σ qεΩ     C     (x) ( z   q −μ( Z,X )) 2   /A ( X )  Equation 6
 
μ( Z,X )=Σ zεΩ     C     (x)   Z   q   /A ( X )  Equation 7
 
       FIG. 11  shows an example edge mask  1100  used to capture edge features by determining the dot product with an edge image. Edge features may be used in active contour based segmentation because edge features popularly exist and are efficiently computable. In the illustrated examples, edge features are used in both spatial and temporal domains. Edges in the spatial domain may correspond to high gradients along boundaries between the cavity and the myocardium. Edges in the temporal domain may correspond to motion of the cavity boundary during diastolic and systolic periods. Equation 8 is an example edge based appearance model where f e (X) represents the edge mask  1100  constructed based on Z and f q   e (X) is the qth pixel in the mask  1100 . Equation 9 shows a formal construction of the mask  1100  where Ω e (X) is the boundary of the cavity determined by the object state, X. In this example, an edge image, Z e , is defined by Equation 10, where δ r Z, δ C Z and δ t Z are the first derivative in the row, column and temporal directions, respectively. 
     
       
         
           
             
               
                 
                   
                     
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     In the illustrated examples, an example prior probability model uses joint information between the left ventricle and the right ventricle that results from motion similarity. Equation 11 shows how the joint information between the left ventricle and the right ventricle can be expressed as a linear correlation between the cavity areas where A R (t) and A L (t), respectively, represent the cavity areas of the right and left ventricles at a certain time, tε{1, . . . , T}, during a cardiac cycle of T frames, and N(0, σ) represents Gaussian noise. The correlation between the left ventricle area and the right ventricle area, as shown in Equation 11, has been confirmed by manually segmented cavities in a dataset.
 
 A   R ( t )=α* A   L ( t )+ b+N (0,σ)  Equation 11
 
     In the illustrated examples, the estimated area of the left ventricle cavity over a cardiac cycle obtained using Equation 11 can be used to predict the right ventricle area over the same cycle (e.g., a first prior or first right ventricle cavity area estimation). The first prior can be used to obtain a more accurate right ventricle posterior probability estimation. Equation 12 shows an example prior probability model that can be used to formulate and/or use the first prior by correlating the prior term, f L⊕R (X, a, b, t), where p S X is an underlying prior distribution embedded in a training set and f L⊕R (X, a, b, t) is determined and/or derived using Equation 13. 
     
       
         
           
             
               
                 
                   
                       
                   
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     Referring to Equation 13, the parameter, t, indicates the frame index of the current object state, X, during a cardiac circle. Thus, a current right ventricle cavity area, A(X) or A R (t) of Equation 11, is linearly correlated to the left ventricle cavity area, (A L (t)), in the same frame. 
     The example prior probability model of Equation 12 is configured to determine the right ventricle area using the corresponding left ventricle area information. For the left ventricle area information, the prior probability model uses the underlying distribution embedded in the training set described in Equation 14.
 
 P   LV ( X )= p   S ( X )  Equation 14
 
     Equation 15 shows a maximum posterior estimation (MAP) method for estimating the parameters, a, b, given all the images (e.g., an MRI sequence) during a cardiac cycle.
 
[ â,{circumflex over (b)}]   MAP   =arg  max [a,b]   p ( a,b|Z   1:T )  Equation 15
 
     Equations 16-19 are processes to determine a posterior distribution, p(a, b|Z 1:T ), in which the prior distribution of [a, b] is assumed to be uniform, p(Z 1:T ) and constant, and equations 3 and 11 are defined in p(Z t |X t ) and p(X t |a, b)=p (X|a, b, t). When determining Equations 16-19, the following assumptions may be made including that the observation image at time, t, Z t  is independent given the object state at the time, t, Z t  and X t  is independent provided the parameters a and b. 
     
       
         
           
             
               
                 
                   
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     To determine the cavity area of the right ventricle and the left ventricle, a sample set, {S 1 , . . . , S N }, is created from a training set in which, during a training phase, each input image is manually segmented into the left ventricle, the right ventricle and the background. In the illustrated example, the training set is produced using Equation 20 in which all left ventricle and right ventricle images are collected together to naturally embed different prior information about the shape, location and scale in the training set.
 
 P   S ( X )≈Σ i=1   N δ( X,s   i )/ N   Equation 20
 
ε[ A ( X )| Z]≈Σ   i=1   N   A ( s   i )π i   Equation 21
 
     To incorporate additional priors and/or information into the training set, in the illustrated examples, the sample weight may be modified to include prior terms such as the mutual information term, f L⊕R (X, a, b, t), determined using Equation 12 and/or by computing the sample weight as a product of f L⊕R (X, a, b, t) and the example likelihood function, p(Z|X) and/or other correlation information between the left ventricle and the right ventricle. 
     In some examples, each sample within the sample set is assigned a weight, π i , based on the likelihood function described in Equation 4 where the weighting for the left ventricle is described in Equation 22 and the weighting for the right ventricle is described in Equation 23. Equation 24 is used to normalize the weighted sample set, {S i , π i } i=1   N , which can be used to approximate the posterior density, p(X|Z). Equation 21 can be used to estimate the cavity area, ε[A(X)|Z].
 
π i   =p ( Z   t   |X=s   i )  Equation 22
 
π i   =p ( Z   t   |X=s   i )* f   L⊕R ( X,a,b,t )  Equation 23
 
{π i } i=1   N  to {{tilde over (π)} i } i=1   N   Equation 24
 
     In the illustrated examples, to determine the ventricular volumes of the left ventricle and the right ventricle, the cavity areas are integrated in short-axis view slices along a sagittal direction by summing the volume of each slice. Equation 25 can be used to determine the volume of the ventricles by summing the product of the corresponding cavity area, A i , and slice thickness, h.
 
 V=Σ   i   A   i   *h   Equation 25
 
       FIG. 12  depicts an example system  1200  for estimating (e.g., automatically estimating) ventricular volumes. In some examples, the system  1200  includes a computer  1202  and a generator  1204  communicatively coupled to the computer  1202 . In this example, the computer  1202  includes a user interface  1206  and a data input (e.g., a keyboard, mouse, microphone, etc.)  1208  and the generator  1204  includes a processor  1210  and a database or other data store  1212 . 
     In some examples, the user interface  1206  displays data such as images (e.g., MRI sequence, frames, etc.) received from the generator  1204 . In some examples, the user interface  1206  receives commands and/or input from a user  1214  via the data input  1208 . For example, in examples in which the system  1020  is used to determine the areas and/or volumes of the left ventricle or the right ventricle, the user interface  1206  displays a frame(s) of cardiac MRI images in a short-axis view and the user  1214  provides an initial input identifying, for example, a location(s) on a basal slice of the intersection between the left ventricular septal wall and a right ventricular wall. In the illustrated example, the initial input includes selecting two points on the frame. 
     In other examples, the initial input may be performed automatically. In some such examples, a region of interest (e.g., a course ROI) may be identified and/or extracted by identifying moving parts in the MRI sequence and/or scene (e.g., the left ventricle and the right ventricle move significantly during a cardiac cycle). In some examples, the ROI includes fitting a bounding box over and/or to a region having high intensity variance over a cardiac cycle. In some example, within the region of interest, the left ventricle can be detected and/or identified using a Hough circle transform and the right ventricle may be detected and/or identified by template matching the regions geometrically constrained by the detected left ventricle. After the right ventricle is identified, the initial input of the intersections between the left and right ventricles are identified (e.g., automatically identified) by mapping two corresponding landmarks of a template in an original image coordinate. 
     In the illustrated example, based on the initial input, the processor  1210  automatically identifies and extracts a region of interest in each slice and/or frame of the MRI sequence that includes and/or encompasses both the left ventricle and the right ventricle. In the illustrated examples, the processor  1210  automatically determines the area(s) of the right ventricle and the left ventricle by generating a sample set using an example prior probability model for the right and left ventricles and assigning a weight to each sample within the set based on an example likelihood function. Additionally, in the illustrated examples, to determine the area(s) of the right ventricle and the left ventricle, the weighted sample set is normalized and then used to approximate the posterior density and the area of the left ventricle and right ventricle. In the illustrated examples, the processor  1210  automatically determines the volume(s) of the right ventricle and left ventricle by summing the volume of each slice (e.g., product of the cavity area (Ai) and the slice thickness (h). 
     In the illustrated examples, using determined area(s) and/or volume(s) and/or other information stored in the data  1212 , the processor  1210  may generate a figure and/or chart to assist in assessing cardiac functionality. These generated figures and/or charts can be displayed at the user interface  1206 . In the illustrated examples, using the determined area(s) and/or volume(s) and/or other information stored in the data  1212 , the processor  1210  may generate and cause the display of an overlay of the identified left ventricle and the right ventricle over the corresponding MRI sequence and/or one or more frames of the MRI sequence to enable visual validation. In the illustrated examples, using the determined area(s) and/or volume(s) and/or other information stored in the data  1212 , the processor  1210  may automatically insert into and/or generate a report using functional parameters as disclosed herein. 
     While an example manner of implementing the system  1200  of  FIG. 12  is illustrated in  FIG. 13 , one or more of the elements, processes and/or devices illustrated in  FIG. 13  may be combined, divided, re-arranged, omitted, eliminated and/or implemented in any other way. Further, the computer  1202 , the generator  1204 , the user interface  1206  the data input  1208  and/or, more generally, the example system  1200  of  FIG. 12  may be implemented by hardware, software, firmware and/or any combination of hardware, software and/or firmware. Thus, for example, any of the example, the computer  1202 , the generator  1204 , the user interface  1206 , the data input  1208  and/or, more generally, the example system  1200  could be implemented by one or more analog or digital circuit(s), logic circuits, programmable processor(s), application specific integrated circuit(s) (ASIC(s)), programmable logic device(s) (PLD(s)) and/or field programmable logic device(s) (FPLD(s)). When reading any of the apparatus or system claims of this patent to cover a purely software and/or firmware implementation, at least one of the example, the computer  1202 , the generator  1204 , the user interface  1206 , the data input  1208  and/or, more generally, the example system  1200  is/are hereby expressly defined to include a tangible computer readable storage device or storage disk such as a memory, a digital versatile disk (DVD), a compact disk (CD), a Blu-ray disk, etc. storing the software and/or firmware. Further still, the example system of  FIG. 12  may include one or more elements, processes and/or devices in addition to, or instead of, those illustrated in  FIG. 13 , and/or may include more than one of any or all of the illustrated elements, processes and devices. 
     A flowchart representative of example machine readable instructions for implementing the example system  13  is shown in  FIG. 13 . In this example, the machine readable instructions comprise a program for execution by a processor such as the processor  1612  shown in the example processor platform  1600  discussed below in connection with  FIG. 16 . The program may be embodied in software stored on a tangible computer readable storage medium such as a CD-ROM, a floppy disk, a hard drive, a digital versatile disk (DVD), a Blu-ray disk, or a memory associated with the processor  1612 , but the entire program and/or parts thereof could alternatively be executed by a device other than the processor  1612  and/or embodied in firmware or dedicated hardware. Further, although the example program is described with reference to the flowchart illustrated in  FIG. 16 , many other methods of implementing the example system  1600  may alternatively be used. For example, the order of execution of the blocks may be changed, and/or some of the blocks described may be changed, eliminated, or combined. 
     As mentioned above, the example processes of  FIG. 12  may be implemented using coded instructions (e.g., computer and/or machine readable instructions) stored on a tangible computer readable storage medium such as a hard disk drive, a flash memory, a read-only memory (ROM), a compact disk (CD), a digital versatile disk (DVD), a cache, a random-access memory (RAM) and/or any other storage device or storage disk in which information is stored for any duration (e.g., for extended time periods, permanently, for brief instances, for temporarily buffering, and/or for caching of the information). As used herein, the term tangible computer readable storage medium is expressly defined to include any type of computer readable storage device and/or storage disk and to exclude propagating signals and to exclude transmission media. As used herein, “tangible computer readable storage medium” and “tangible machine readable storage medium” are used interchangeably. Additionally or alternatively, the example processes of  FIG. 12  may be implemented using coded instructions (e.g., computer and/or machine readable instructions) stored on a non-transitory computer and/or machine readable medium such as a hard disk drive, a flash memory, a read-only memory, a compact disk, a digital versatile disk, a cache, a random-access memory and/or any other storage device or storage disk in which information is stored for any duration (e.g., for extended time periods, permanently, for brief instances, for temporarily buffering, and/or for caching of the information). As used herein, the term “non-transitory computer readable medium” is expressly defined to include any type of computer readable storage device and/or storage disk and to exclude propagating signals and to exclude transmission media. As used herein, when the phrase “at least” is used as the transition term in a preamble of a claim, it is open-ended in the same manner as the term “comprising” is open ended. 
     With reference to  FIGS. 13 and 14 , the program of  FIG. 13  begins at block  1300  where the user interface  1206  receives commands and/or input from a user  1214  via the data input  1208  (block  1302 ). For example, the user interface  1206  displays a frame(s) of a cardiac MRI image(s) (in a short-axis view) ( 1402  of  FIG. 14 ) and the user  1214  provides an initial input identifying, for example, a location(s) on a basal slice of the intersection between the left ventricular septal wall and a right ventricular wall ( 1404  of  FIG. 14 ). In the illustrated example, the initial input includes selecting two points on the frame. In other examples, the initial input may be performed automatically. Based on the initial input, a region of interest (ROI) ( 1406  of  FIG. 14 ) is automatically identified and/or extracted that encloses both the left ventricle and the right ventricle. 
     In the illustrated example, the bi-ventricular regions are automatically estimated using the examples disclosed herein ( 1408   FIG. 14 ). Specifically, the processor  1210  automatically determines the area(s) of the right ventricle and the left ventricle by generating a sample set using an example prior probability model for the right and left ventricles. (block  1304 ). The program then determines a likelihood function (block  1306 ). Using the likelihood function, a weight is assigned to each sample within the set (block  1308 ). At block  1310 , the sample set is normalized (block  1310 ). In the illustrated examples, the normalized sample set is used to approximate posterior density, which is used to determine the area of the left ventricle and the right ventricle and/or the area of the cavities (block  1312 ). In the illustrated examples, the processor  1210  automatically determines the volume(s) of the right ventricle and the left ventricle by summing the volume of each slice (e.g., product of the cavity area (Ai) and the slice thickness (h) (block  1314 ). At block  1316 , the program generates an output (block  1314 ). In the illustrated examples, the output may include displaying figures and/or charts on a user display to assist in cardiac functional assessment ( 1410  of  FIG. 14 ). In the illustrated examples, the output may include displaying an MRI with a visual marker overlaid on a user display for manual validation ( 1412  of  FIG. 14 ). In the illustrated examples, the output may include automatically inserting machine extracted functional parameters into a patient report ( 1414  of  FIG. 14 ). 
       FIG. 15  shows an example plot  1500  of left ventricular area and the right ventricular area of a first subject and/or individual  1502 , a second subject and/or individual  1504  and a third subject and/or individual  1506 . The plots lying in a straight line demonstrate the linear correlation between right ventricular area at a time, A_R (t) and the left ventricular area at the time A_L (t) with different slopes (α) and RV-axis intercept (b). 
       FIG. 16  is a block diagram of an example processor platform  1000  capable of executing the instructions of  FIG. 13  to implement the system  1200  of  FIG. 12 . The processor platform  1600  can be, for example, a server, a personal computer, a mobile device (e.g., a cell phone, a smart phone, a tablet such as an IPAD™), a personal digital assistant (PDA), an Internet appliance, or any other type of computing device. 
     The processor platform  1600  of the illustrated example includes a processor  1652 . The processor  1612  of the illustrated example is hardware. For example, the processor  1612  can be implemented by one or more integrated circuits, logic circuits, microprocessors or controllers from any desired family or manufacturer. 
     The processor  1612  of the illustrated example includes a local memory  1613  (e.g., a cache). The processor  1612  of the illustrated example is in communication with a main memory including a volatile memory  1614  and a non-volatile memory  1616  via a bus  1618 . The volatile memory  1614  may be implemented by Synchronous Dynamic Random Access Memory (SDRAM), Dynamic Random Access Memory (DRAM), RAMBUS Dynamic Random Access Memory (RDRAM) and/or any other type of random access memory device. The non-volatile memory  1616  may be implemented by flash memory and/or any other desired type of memory device. Access to the main memory  1614 ,  1616  is controlled by a memory controller. 
     The processor platform  1600  of the illustrated example also includes an interface circuit  1020 . The interface circuit  1620  may be implemented by any type of interface standard, such as an Ethernet interface, a universal serial bus (USB), and/or a PCI express interface. 
     In the illustrated example, one or more input devices  1622  are connected to the interface circuit  1620 . The input device(s)  1622  permit(s) a user to enter data and commands into the processor  1612 . The input device(s) can be implemented by, for example, a keyboard, a button, a mouse, a touchscreen, a track-pad, a trackball, isopoint and/or a voice recognition system. 
     One or more output devices  1624  are also connected to the interface circuit  1620  of the illustrated example. The output devices  1624  can be implemented, for example, by display devices (e.g., a light emitting diode (LED), an organic light emitting diode (OLED), a liquid crystal display, a cathode ray tube display (CRT), a touchscreen, a tactile output device, a light emitting diode (LED)). The interface circuit  1620  of the illustrated example, thus, typically includes a graphics driver card, a graphics driver chip or a graphics driver processor. 
     The interface circuit  1620  of the illustrated example also includes a communication device such as a transmitter, a receiver, a transceiver, a modem and/or network interface card to facilitate exchange of data with external machines (e.g., computing devices of any kind) via a network  1626  (e.g., an Ethernet connection, a digital subscriber line (DSL), a telephone line, coaxial cable, a cellular telephone system, etc.). 
     The processor platform  1600  of the illustrated example also includes one or more mass storage devices  1628  for storing software and/or data. Examples of such mass storage devices  1028  include floppy disk drives, hard drive disks, compact disk drives, Blu-ray disk drives, RAID systems, and digital versatile disk (DVD) drives. 
     The coded instructions  1632  of  FIG. 13  may be stored in the mass storage device  1328 , in the volatile memory  1314 , in the non-volatile memory  1316 , and/or on a removable tangible computer readable storage medium such as a CD or DVD. 
     From the foregoing, it will appreciate that the above disclosed methods, apparatus and articles of manufacture enable automated right ventricle functional assessments, processing of the left and right ventricles substantially simultaneously and/or simultaneously and/or the direct performance of inter-ventricular analysis and/or regurgitant valvular disease detection. 
     The disclosed examples enable enhanced usability with little if any human interaction (e.g., two manual clicks) to perform bi-ventricular functional assessments. The disclosed examples enable improved efficiencies by removing tedious human interactions and inefficient segmentation steps, thereby providing real-time functional assessment tools and/or processing-time efficiencies. The disclosed examples provide advanced functionalities including an automated too for bi-ventricular functional assessment, comprehensive parameter estimation in each frame (e.g., instead of just end-systolic and end-diastolic frames) and/or direct inter-ventricular analysis by jointly investigating the bi-ventricular parameters (e.g., diagnosis of regurgitant valvular disease or intra-cardiac shunts, etc.). 
     The examples disclosed herein relate to an example method for estimating the volume of both the left ventricle and the right ventricle jointly without segmentation, an example likelihood function that uses multiple appearance features and/or an example probability model that uses area correlation information. 
     Methods and apparatus to estimate Cardiac biventricular volumes jointly are disclosed. An example computer-implemented method includes preparing a sample set, computing a prior probability model for a left ventricle and a right ventricle and using a likelihood function to assign a weight to each sample within the sample set. The example method includes, based on the weighted sample set, determining a cavity area of the right ventricle and the left ventricle in a slice. The example method includes integrating the determined areas over slices covering the whole heart to obtain the biventricular volumes. 
     Although certain example methods, apparatus and articles of manufacture have been disclosed herein, the scope of coverage of this patent is not limited thereto. On the contrary, this patent covers all methods, apparatus and articles of manufacture fairly falling within the scope of the claims of this patent.