Abstract:
In one embodiment, a cardiovascular condition of a subject is determined by capturing a three-dimensional electrocardiography image of the subject, generating a two-dimensional cardiac map from the electrocardiography image, and processing the cardiac map to determine the cardiovascular condition of the subject.

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application claims priority to U.S. Provisional Application Ser. No. 61/705,395, filed Sep. 25, 2012, which is hereby incorporated by reference herein in its entirety. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention was made with government support under 1266331 awarded by National Science Foundation. The government has certain rights in the invention. 
    
    
     BACKGROUND 
     Heart disease is the number one cause of death in the world. Cardiac events often occur in daily life and account for some 30% of mortalities in the U.S. Unfortunately, current medical technologies and procedures typically fail to prevent life-threatening acute cardiac events (e.g., heart attacks). This is because current technologies and procedures typically do not detect the risk precursors that can lead to such an event. 
     Two broad categories of tests are used in clinical practice to detect cardiac disorders, namely, “static” and “dynamic” tests. Static tests are essentially frozen snapshots of cardiac information, such as x-rays, computer images, and blood enzyme test results. This sort of testing is expensive and not always readily available. Dynamic tests are those that continuously monitor heart dynamics, such as when recording electrocardiograms (ECGs). There is an increasing appreciation for the benefits of continuously monitoring the dynamic details of cardiac functioning. If such monitoring were performed on an ongoing basis, for example, several times a day, each day, cardiac disorders could be detected earlier and acute cardiac events could be avoided. However, real-time ECG monitoring generates enormous amounts of data that are simply too large for humans to visually analyze. 
     Another limitation of current dynamic testing is that it generates relatively low-resolution information as to cardiac activity. Recent developments in electrocardiogram imaging (ECGI) promise to provide higher resolution sensing of cardiac electrical dynamics. Moreover, ECGI has been shown to substantially enhance the detection of certain cardiac disorders in their early stages. If ECGI could be continually performed and the collected data continually analyzed, physicians would have an unprecedented opportunity to observe high-risk subjects for cardiac disorders. 
     Recently, sensor-embedded “smart shirts” have been developed to monitor cardiac activity. Some smart shirts that include ECG electrodes have been proposed to collect a limited number of channels of ECG signals (i.e., &lt;12 leads). Further, an ECGI system has been proposed to include hundreds of small electrodes, but not in the form of smart shirt. Although the electrodes can be successfully used to collect ECGI data, each electrode must maintain strict contact with the skin surface, typically requiring the use of sticky gels, connectors, and/or hard plastic chest straps. As a result, such shirts are uncomfortable to wear and therefore create patient compliance issues. Furthermore, the compact representation and interpretation of large spatiotemporal data from ECGI, which is essential for a functional cyber-physical infrastructure, has not been developed. 
     The above-described issues pose critical scientific and technological barriers for improving the outcomes of cardiac care services. It can therefore be appreciated that it would be desirable to have a wearable ECGI system and method that could be used to monitor patients and detect cardiac disorders that pose a significant health risk to patients. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure may be better understood with reference to the following figures. Matching reference numerals designate corresponding parts throughout the figures, which are not necessarily drawn to scale. 
         FIG. 1  is a schematic diagram of an embodiment of an electrocardiogram imaging (ECGI) system. 
         FIG. 2  is a block diagram that illustrates an example configuration for a computing device shown in  FIG. 1 . 
         FIG. 3  is schematic diagram that illustrates a spatiotemporal estimation model for estimating missing ECG image data. 
         FIGS. 4A-4E  are time-varying ECG imaging surfaces at the locations of the (A) P wave, (B) Q wave, (C) R peak, (D) S wave, and (E) T wave of an ECGI signal. 
         FIG. 5  is a flow diagram that illustrates an embodiment of a method reconstructing missing ECG image data. 
         FIG. 6  is schematic diagram that illustrates a cardiac cartography process. 
         FIG. 7  is a schematic diagram that illustrates segmentation of time-varying cardiac maps resulting from cardiac cartography. 
         FIG. 8  is a flow diagram that illustrates an embodiment of a method for performing cardiac cartography. 
         FIG. 9  is a block diagram illustrating an embodiment of a hierarchical modeling structure that can be used to detect cardiac disorders. 
         FIG. 10  is a flow diagram that illustrates an embodiment of a method for detecting cardiac disorders from cardiac maps. 
     
    
    
     DETAILED DESCRIPTION 
     As described above, it would be desirable to have an electrocardiogram imaging (ECGI) system and method that could be used to monitor patients and detect cardiac disorders. Disclosed herein are examples of such systems and methods. In one embodiment, a smart shirt having many electrodes and a relaxed fit is used to measure electrical potentials from many spatial locations on a patient&#39;s torso over predetermined periods of time. Three-dimensional ECGIs can be generated from the electrical potentials, and spatiotemporal reconstruction can be performed to fill in the blanks created when electrodes lose contact with the skin because of the relaxed fit of the shirt. The ECGIs can then be computer analyzed to detect the presence of a cardiac disorder. In some embodiments, this can be achieved by first transforming the three-dimensional ECG images into two-dimensional cardiac maps using a cardiac cartography process. 
     In the following disclosure, various specific embodiments are described. It is to be understood that those embodiments are example implementations of the disclosed inventions and that alternative embodiments are possible. All such embodiments are intended to fall within the scope of this disclosure. 
     Recording ECG Images of a Subject 
       FIG. 1  illustrates an example ECGI system  10  that can be used to generate ECG images and detect cardiac disorders from the images. As shown in this figure, the system  10  generally comprises a smart shirt  12 , a local personal computing device  14 , and a remote computer  16  that can receive data from the personal computing device via a network  18 . 
     The smart shirt  12  generally comprises a shirt substrate  20  made of a flexible fabric to which are attached (e.g., embedded) many small electrodes  22  that can contact the skin surface of a patient&#39;s torso when the shirt is worn. The shirt substrate  20  can be made of natural and/or manmade fibers. In some embodiments, the shirt  12  has a relaxed fit and is comfortable when worn so as to increase the likelihood that a patient will wear the shirt and that valuable cardiac data will be collected. 
     By way of example, the shirt  12  can comprise hundreds of electrodes  22  that surround the torso so that a high-resolution image of cardiac activity can be obtained from all sides of the heart. To increase wearer comfort, the electrodes  22  can comprise soft nano-textile ECG sensors that are knitted into the shirt substrate  20 . Irrespective of their construction, the electrodes  22  are communicatively coupled to an integrated data acquisition device  24  that is configured to collect signals (i.e., the measured electrical potentials) from the electrodes and transmit them to the personal computing device  14 . The location of the electrodes  22  can be optimized to enable reconstruction of a complete picture of underlying cardiac electrical dynamics. In some embodiments, nonlinear regression models can be wrapped into an objective function to search the space of all lead subsets to optimize the signal information. Starting from an empty lead set, the additional lead L +  that maximizes the objective function J(L k +L + ) can be sequentially added into a lead subset L k  that has already been selected. These steps can be repeated until the optimal signal information is obtained. 
     In some embodiments, signals can be collected from the electrodes  22  for a time period of one or more seconds at a sample rate of approximately 1 to 2 kHz. Assuming that the patient wears the shirt  12  all day, signals can be collected in this manner several times each day, such as every few hours. Each time signals are collected, data for 1,000 or more images can be obtained. 
     The local personal computing device  14  is configured to receive the signals (i.e., ECGI data) from the smart shirt  12 . In some embodiments, the personal computing device  14  comprises a smart phone. Alternatively, the personal computing device  14  can comprise a tablet computer, a notebook computer, a desktop computer, or another computing device capable of receiving and transmitting the ECGI data. In some embodiments, the personal computing device  14  is configured to compress the ECGI data and periodically transmit it (e.g., over the network  18 ) to the remote computer  16  for processing and storage. In other embodiments, the personal computing device  14  is further configured to locally process the ECGI data. For example, one or more algorithms that execute on the personal computing device  14  can be used to reconstruct missing ECGI data that results from broken contact between electrodes  22  and the patient&#39;s skin surface. In addition, one or more algorithms can execute on the personal computing device  14  to analyze the ECGI data and detect cardiac disorders for the purpose of providing a warning to the patient and/or his physician. 
     The remote computer  16  can receive and process the ECGI data transmitted by the personal computing device  14 . The remote server computer  16  can also comprise one or more algorithms configured to reconstruct missing ECGI data and analyze the ECGI data to detect cardiac disorders. As described below, the analysis can comprise transforming three-dimensional ECG images into two-dimensional cardiac maps through a process called cardiac cartography. With such mapping, the cardiac activity of the patient can be compared with historical cardiac data collected from the patient or from other subjects and analyzed to diagnose particular cardiac disorders. This can entail performing long-term cardiac trend analysis and integrating prior knowledge from historical databases (e.g., PhysioNet). 
       FIG. 2  is a block diagram of a computing device  30 , whether it be the local personal computing device  14  or the remote computer  16  shown in  FIG. 1 , or some other computing device that can process the ECGI data collected by the smart shirt  12 . As shown in  FIG. 2 , the computing device  30  includes a processing device  32 , memory  34 , a user interface  36 , and at least one I/O device  38 , each of which is connected to a local interface  40 . The processing device  32  can include a central processing unit (CPU) or a semiconductor-based microprocessor (in the form of a microchip). The memory  34  includes any one of or a combination of volatile memory elements (e.g., RAM) and nonvolatile memory elements (e.g., hard disk, ROM, Flash, etc.). The user interface  36  comprises the components with which a user interacts with the computing device  30 , such as a keyboard, keypad, and display screen, and the I/O devices  38  are adapted to facilitate communications with other devices. 
     The memory  34  (a non-transitory computer-readable medium) comprises programs (logic) including an operating system  42  and an ECGI data processing system  44 . In the example of  FIG. 2 , the data processing system  44  includes one or more ECGI reconstruction algorithms  46  that are configured to estimate data missing from the measured ECGI data and one or more cardiac disorder detection algorithms  48  that are configured to perform spatiotemporal cardiac cartography and characterization. In addition, the memory  34  comprises a database  52  that can include historical ECGI data of the patient and/or one or more other subjects. 
     Reconstructing Missing ECG Image Data 
     As identified above, it is desirable to optimize the wearability of the smart shirt to increase wearer comfort and enable individuals to move around and interact freely because this will increase the likelihood of such individuals actually wearing the shirt. Given the aforementioned relaxed-fit design of the shirt, however, the electrodes may intermittently lose contact with the skin surface at dynamically varying locations of the body. This loss of contact has temporal and spatial aspects. Specifically, electrodes lose contact for discrete periods of time, thereby creating a temporal absence of signals, and lose contact at discrete spatial locations of the body, thereby creating a spatial absence of signals. These absences are illustrated in  FIG. 3 . In some embodiments, both temporal and spatial estimation can be used to reconstruct the missing ECGI data. In particular, a spatiotemporal model can be constructed that receives as input both temporal data in the form of temporal patterns from the electrodes that have lost contact and spatial data in the form of signals from neighboring electrodes (i.e., electrodes that are positioned near the electrodes that have lost contact). 
     As can be expected, two points on an ECG image have a stronger correlation when they are closer to each other. Therefore, the spatial correlation between neighboring electrodes is valuable to estimating the spatially absent values. As shown in  FIG. 4 , the ECG images in the front and back of the body vary with respect to time. At a given time point, the spatial correlation in the ECG images can be captured as a model of the form: 
                     Y   ⁡     (   s   )       =         M   ⁡     (     s   ;   β     )       +     ɛ   ⁡     (   s   )         =         ∑     i   =   1     N     ⁢           ⁢         w   i     ⁡     (   s   )       ⁢       f   i   ′     ⁡     (   s   )       ⁢     β   i         +     ɛ   ⁡     (   s   )                   [     Equation   ⁢           ⁢   1     ]               
where Y(s) is an observation taken at location s in the body surface, β i =(β i1 , . . . , β ip )′ is a vector of model parameters, N is the total number of components, and ε(s) is Gaussian random noise. The w i (s) is a non-negative weighting kernel function, i.e.,
 
                 w   i     ⁡     (   s   )       ∝              ∑   i     ⁢                  1   2       ⁢   exp   ⁢     {       -       (     s   -     μ   i       )     ′       ⁢       ∑   i     -   1       ⁢           ⁢       (     s   -     μ   i       )     /   2.                   
The f i (S)=(f i1 (s), . . . , f ip (s))′ is a set of known basis functions. The spatial model is designed as a locally weighted mixture of basis function regressions. For one realization of the spatiotemporal process, it can be observed that Y=(Y(s 1 ), . . . , Y(s n )) at locations s 1 , . . . , s n . If one defines w i =(w i (s i ), . . . , w i (s n )) as the vector of weights for kernel i and X i ={f i1 (s), . . . , f ip (s)} as the design matrix for the ith mixture component, the spatial model can be written as a linear regression: Y=Xβ+ε, where X=(diag(w 1 )X 1 , . . . , diag(w N )X n ) and β=(β′ 1 , . . . , β′ N ). The spatially missing value Y({tilde over (s)}) can then be estimated as X{tilde over (β)} for the location {tilde over (s)}.
 
     This is a kernel-weighted regression model of an ECG image. Generally, the ECG image at a given time point is non-stationary. The same Gaussian kernel or different kernels can be used for w i (s) in Equation 1. It is clear that, for the spatial model in Equation 1, an adaptive kernel function can be chosen in w 1 (s), which could be different from that of w 2 (s) to obtain a better fit to the data. Thus, kernel functions can be adaptively matched to the data for increasing the model convergence. Also, if the kernel-weighted model converges faster, a finite number of terms N would be sufficient to obtain a good approximation, which reduces the computation. 
     The spatial model can be augmented to include temporal components, i.e., to define the time-varying model parameters as β t =(β t1 , . . . β tp )′ at time t. As shown in  FIG. 4 , as cardiac electrical activities vary in both space and time, the ECGI surfaces M(x;β t ),(x;β t+1 ) vary with respect to time. A Kalman filter ( FIG. 3 ) can be used to establish temporal correlation to recursively estimate the state of a discrete-time controlled process, i.e., to link the parameters β t  over time by the evolution equation:
 
β t   =G   t β t-1 +ω t ,ω t   ˜N (0 ,Z   t )  [Equation 2]
 
where G t  is the evolution matrix and ω t  is the process noise with zero mean and the covariance matrix Z t . Meanwhile, the spatial model at a given time is defined as:
 
 Y   t   =X   t β t +ε t ,ε t   ˜N (0 ,V   t )  [Equation 3]
 
where Y t  is the observed ECG image at time t and ε t  is the measurement noise. The Kalman filter estimates the state of model parameters β t  at some time and then obtains feedback in the form of (noisy) measurements. The temporal predictor equation (i.e., Equation 2) is responsible for projecting forward (in time) the current state and error covariance estimates to obtain the priori estimates for the next time step. The spatial update equation (i.e., Equation 3) is responsible for providing feedback, i.e., for incorporating a new measurement of the ECG image into the priori estimate to obtain an improved posteriori estimate. After each temporal predictor and spatial update, the process is repeated with the previous posteriori estimates used to project or predict the new priori estimates. This recursive estimation using the Kalman filter makes practical implementations more feasible for modeling the time-varying model parameters. This combination of a spatial model and a Kalman-filter-type model is attractive because it can be implemented to estimate not only the spatially-temporally missing electrode values but also to predict the ECG image in the next time step.
 
       FIG. 5  is a flow diagram that summarizes an example method for reconstructing missing ECG image data that is consistent with the above discussion. Beginning with block  60 , ECGI data is recorded in the manner described above using a smart shirt. Because some of the electrodes of the shirt will not be in contact at the instant in time in which the ECGI data is recorded, spatial and temporal image data will be missing. 
     With reference to block  62 , the spatial morphology of an ECG image recorded at the given time instance can be modeled. As described above, the spatial morphology can be modeled using a parametric model, such as a kernel-weighted regression model. 
     Referring next to block  64 , a temporally evolving morphology of the ECG image can be predicted by recursively estimating time-varying parameters in the spatial model. When this is performed, a complete ECG image can be obtained, as indicated in block  66 . At this point, flow can return to block  62  and the process can be repeated for the next ECG image, if desired (block  68 ). 
     Performing Cardiac Cartography 
     Once the ECGI data has been reconstructed, the data can be analyzed to detect cardiac disorders. Cardiac electrical dynamics are initiated and propagated in space and time, and these dynamics can be shifted because of the spatial localization and temporal deterioration of cardiac disorders, such as myocardial infarctions. It would therefore be desirable to have new mathematical models that identify real-time biomarkers from ECG images that are sensitive to the spatiotemporal disease process. Methods discussed below include spatial mapping, cartography, and multi-level factorial analysis. Using such methods, regions of interest can be quantified and related to spatial (i.e., anterior, posterior, inferior, superior, septal, and lateral, etc.) and temporal (i.e., ischemia, injury, necrosis) factors of cardiac disorders. 
     By using algorithms that can extract hidden knowledge in space-time ECGI data, one can study specific regions of interest that are related to spatial location and temporal progression of cardiac pathological behaviors for real-time diagnostic applications. Most existing medical devices utilize simple time-domain ECG metrics (e.g., heart rate, ST segment, QT interval) for monitoring purposes. However, cardiac electrical dynamics are initiated and propagated spatiotemporally. Such space-time activities are inevitably shifted by the spatial location and temporal progression of cardiovascular diseases. The approach described below utilizes cardiac cartography, which normalizes and maps the ECGIs onto unit spheres around the heart, as illustrated in  FIG. 6 . As is further depicted in  FIG. 6 , the unit spheres can be transformed into two-dimensional cardiac maps, in similar manner to projecting a globe&#39;s surface onto a two-dimensional plane to obtain a two-dimensional geographic map. The normalization addresses the issues of thorax inhomogeneity because of subject differences. In cardiac cartography, normalization factors can be calculated by minimizing the squared errors between the estimated ECGI datasets Ê i (t) and the actual datasets E i (t) using the following equation: 
                     min   ⁢       ∫   0   T     ⁢         [         E   i     ⁡     (   t   )       -         E   ^     i     ⁡     (   t   )         ]     2     ⁢           ⁢     ⅆ   t     ⁢           ⁢   and   ⁢           ⁢     n   i           =         ∫   0   T     ⁢           E   i     ⁡     (   t   )       ·     [       V   ⁡     (   t   )       ·     L   i       ]       ⁢           ⁢     ⅆ   t             ∫   0   T     ⁢         [       V   ⁡     (   t   )       ·     L   i       ]     2     ⁢           ⁢     ⅆ   t                   [     Equation   ⁢           ⁢   4     ]               
where Ê i (t)=V(t)·L i ·n i , L i  is the directional vector of i th  electrode, n i  is the i th  normalization factor, V(t) is the 3-lead VCG, and Ê 1 (t) T is the total time. Cardiac vectors can, therefore, be normalized by multiplying with the factor n as V N (t)=V (t)·n, where
 
             n   =         ∑     i   =   1     N     ⁢     n   i       N           
and N is the total number of electrodes. The normalized cardiac vector is then mapped onto a unit sphere as the inner product with a unit vector u ij  on the sphere:
 
 I   ij ( t )=( V   N     X   ( t ), V   N     Y   ( t ), V   N     Y   ( t )·( u   x     ij     ,u   Y     ij     ,u   z     ij   )  [Equation 5]
 
     The ECG potentials on the unit sphere can then be normalized and projected on a two-dimensional surface (i.e., cartography) with map projections (e.g., cylinder, cone, plane, azimuthal projections), thereby accounting for the variation of torso morphology. As shown in  FIG. 7 , the two-dimensional cardiac maps vary spatiotemporally {V(s,t):sεR⊂R d ,tεT}, where s represents the spatial location, and t is the time. 
     Spatial regions of interest of the cardiac maps can be investigated during a particular time period in the time-varying cardiac cartography for purposes of identifying cardiac disorders. As shown in  FIG. 7 , each cardiac map at a given instant in time can be spatially partitioned into multiple uniform row-by-column sections (e.g., rows=2, 3, . . . , 6 and cols=2, 3, . . . , 6) so that the location of a cardiac disorder, such as a myocardial infarction, can be optimally searched. Temporally, the period t i ≦T≦(t i +Δt) will also be segmented to track the heart&#39;s sequential functioning for diagnostic clues. However, the uniform segmentation of the two-dimensional cardiac maps may roughly divide the area of myocardial infarction into several blocks (i.e., discrete bins). In an alternative approach, detection in neighboring areas can be repeatedly refined or adaptive segmentation (i.e., non-uniform) can be used to increase precision. 
       FIG. 8  is a flow diagram that summarizes an example method for performing cardiac cartography that is consistent with the above discussion. Beginning with block  70 , the torso geometry of the subject under evaluation is recorded. Next, a complete ECG image for the subject can be obtained, as indicated in block  72 . By way of example, the ECG image is one that resulted from the image reconstruction described above. 
     With reference to block  74 , the three-dimensional ECG image is normalized from the torso to a unit sphere to minimize the differences (size, shape, etc.) between subjects. Once this normalization has been performed, the normalized image can be projected onto a two-dimensional surface to create a cardiac map, as indicated in block  76 . Again, this process is similar to projecting the surface of a globe onto a two-dimensional geographical map. 
     Next, the cardiac map can be segmented into one or more local heart domains, as indicated in block  78 , so that the activity illustrated in the map can be associated with particular parts of the subject&#39;s heart. At this point, flow can return to block  72  and the above-described process can be performed on the next ECG image, if desired (block  80 ). 
     Determining Cardiovascular Conditions 
     A Bayesian hierarchical framework can be used to predict the spatiotemporal variations of cardiac electric events accounting for uncertainties, such as respiration and muscular activities. As shown in  FIG. 9 , a hierarchical model separates the ECG image V(s t) into a hierarchical structure of three components:
 
 V ( s,t )= P ( s,t )+φ( s )+ε( s,t )  [Equation 6]
 
where P(s,t) is the dominant morphology accounting for cardiac electric events. If the basis function α k (s ij ,t) is chosen to be a Mexican hat function, P(s,t) at location s ij  will be:
 
     
       
         
           
             
               
                 
                   
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     In addition, φ(s) accounts for the local variability (e.g., brody effects, intracardiac blood mass, respiration, and muscular activities) and is modeled as: 
                     f   ⁡     (     φ   ⁡     (   s   )       )       =         (     2   ⁢   π     )         -     (     n   -   m     )       2       ⁢       (          Q        *     )       1   2       ⁢       exp   ⁡     [       -     1   2       ⁢     (       φ   ⁡     (   s   )       -   μ     )       ]       T     ⁢     Q   ⁡     (       φ   ⁡     (   s   )       -   μ     )                 [     Equation   ⁢           ⁢   8     ]               
using the intrinsic Gaussian Markov random field (IGMRF), where μ is the mean of φ(s), m is the dimension of null space, Q is precision matrix with rank n−m, and |Q|* denotes the product of the nonzero eigenvalues of Q. The function ε(s,t) is an uncorrelated random process with mean 0 and variance σ ε   2 . The model can be generalized with optimal parameter settings. For example, an optimal model can be identified with the minimal hypothetic units but sufficient explanatory power. The Bayesian framework and Markov chain Monte Carlo (MCMC) simulation can be utilized to avoid the limitation of maximum likelihood based point estimate by marginalizing over the model parameters.
 
       FIG. 10  is a flow diagram that summarizes an example method for determining a cardiovascular condition, such as detecting a cardiac disorder from the two-dimensional cardiac maps. Beginning with block  82 , a cardiac map for the subject under evaluation is obtained. Next, the cardiac map is decomposed into a hierarchical structure of multiple components, as indicated in block  84 . As described above, these components can comprise global morphology, local variability, and noise. 
     With reference to block  86 , the parameters in the hierarchical modeling structure can then be estimated. At this point, model-based prediction of cardiac events can be performed based upon the cardiac map, as indicated in block  88 , and the cardiovascular condition of the subject can be evaluated with the global morphology and local variability in the model, as indicated in block  90 . 
     Once this evaluation has been performed, flow can return to block  82  and a similar process can be performed on the next cardiac map, if desired (block  92 ).