Cardiac position sensitivity study in the electrocardiographic forward problem using stochastic collocation and boundary element methods.

The electrocardiogram (ECG) is ubiquitously employed as a diagnostic and monitoring tool for patients experiencing cardiac distress and/or disease. It is widely known that changes in heart position resulting from, for example, posture of the patient (sitting, standing, lying) and respiration significantly affect the body-surface potentials; however, few studies have quantitatively and systematically evaluated the effects of heart displacement on the ECG. The goal of this study was to evaluate the impact of positional changes of the heart on the ECG in the specific clinical setting of myocardial ischemia. To carry out the necessary comprehensive sensitivity analysis, we applied a relatively novel and highly efficient statistical approach, the generalized polynomial chaos-stochastic collocation method, to a boundary element formulation of the electrocardiographic forward problem, and we drove these simulations with measured epicardial potentials from whole-heart experiments. Results of the analysis identified regions on the body-surface where the potentials were especially sensitive to realistic heart motion. The standard deviation (STD) of ST-segment voltage changes caused by the apex of a normal heart, swinging forward and backward or side-to-side was approximately 0.2 mV. Variations were even larger, 0.3 mV, for a heart exhibiting elevated ischemic potentials. These variations could be large enough to mask or to mimic signs of ischemia in the ECG. Our results suggest possible modifications to ECG protocols that could reduce the diagnostic error related to postural changes in patients possibly suffering from myocardial ischemia.

Establishing multiscale models for simulating whole limb estimates of electric fields for osseointegrated implants.

Although the survival rates of warfighters in recent conflicts are among the highest in military history, those who have sustained proximal limb amputations may present additional rehabilitation challenges. In some of these cases, traditional prosthetic limbs may not provide adequate function for service members returning to an active lifestyle. Osseointegration has emerged as an acknowledged treatment for those with limited residual limb length and those with skin issues associated with a socket together. Using this technology, direct skeletal attachment occurs between a transcutaneous osseointegrated implant (TOI) and the host bone, thereby eliminating the need for a socket. While reports from the first 100 patients with a TOI have been promising, some rehabilitation regimens require 12-18 months of restricted weight bearing to prevent overloading at the bone-implant interface. Electrically induced osseointegration has been proposed as an option for expediting periprosthetic fixation and preliminary studies have demonstrated the feasibility of adapting the TOI into a functional cathode. To assure safe and effective electric fields that are conducive for osseoinduction and osseointegration, we have developed multiscale modeling approaches to simulate the expected electric metrics at the bone-implant interface. We have used computed tomography scans and volume segmentation tools to create anatomically accurate models that clearly distinguish tissue parameters and serve as the basis for finite element analysis. This translational computational biological process has supported biomedical electrode design, implant placement, and experiments to date have demonstrated the clinical feasibility of electrically induced osseointegration.

Spatiotemporal estimation of activation times of fractionated ECGs on complex heart surfaces.

Identification of electrical activation or depolarization times on sparsely-sampled complex heart surfaces is of importance to clinicians and researchers in cardiac electrophysiology. We introduce a spatiotemporal approach for activation time estimation which combines prior results using spatial and temporal methods with our own progress on gradient estimation on triangulated surfaces. Results of the method applied to simulated and canine heart data suggest that improvements are possible using this novel combined approach.

Developing a quantitative measurement system for assessing heterotopic ossification and monitoring the bioelectric metrics from electrically induced osseointegration in the residual limb of service members.

Poor prosthetic fit is often the result of heterotopic ossification (HO), a frequent problem following blast injuries for returning service members. Osseointegration technology offers an advantage for individuals with significant HO and poor socket tolerance by using direct skeletal attachment of a prosthesis to the distal residual limb, but remains limited due to prolonged post-operative rehabilitation regimens. Therefore, electrical stimulation has been proposed as a catalyst for expediting skeletal attachment and the bioelectric effects of HO were evaluated using finite element analysis in 11 servicemen with transfemoral amputations. Retrospective computed tomography (CT) scans provided accurate reconstructions, and volume conductor models demonstrated the variability in residual limb anatomy and necessity for patient-specific modeling to characterize electrical field variance if patients were to undergo a theoretical osseointegration of a prosthesis. In this investigation, the volume of HO was statistically significant when selecting the optimal potential difference for enhanced skeletal fixation, since higher HO volumes required increased voltages at the periprosthetic bone (p = 0.024, r = 0.670). Results from Spearman's rho correlations also indicated that the age of the subject and volume of HO were statistically significant and inversely proportional, in which younger service members had a higher frequency of HO (p = 0.041, r = -0.622). This study demonstrates that the volume of HO and age may affect the voltage threshold necessary to improve current osseointegration procedures.

Measurement of Defibrillator Surface Potentials for Simulation Verification.

Despite the growing use of implantable cardioverter defibrillators (ICDs) in adults and children, there has been little progress in optimizing device and electrode placement. To facilitate effective placement of ICDs, especially in pediatric cases, we have developed a predictive model that evaluates the efficacy of a delivered shock. Most recently, we have also developed an experimental validation approach based on measurements from clinical cases. The approach involves obtaining body surface potential maps of ICD discharges during implantation surgery and comparing these measured potentials with simulated surface potentials to determine simulation accuracy. Comparison of the simulated and measured potentials yielded very similar patterns and a typical correlation greater than 0.9, suggesting that the predictive simulation generates realistic potential values. Ongoing sensitivity studies will determine the robustness of the results and pave the way for use of this approach for assisting optimization of ICD use.

Bioelectric analyses of an osseointegrated intelligent implant design system for amputees.

The projected number of American amputees is expected to rise to 3.6 million by 2050. Many of these individuals depend on artificial limbs to perform routine activities, but prosthetic suspensions using traditional socket technology can prove to be cumbersome and uncomfortable for a person with limb loss. Moreover, for those with high proximal amputations, limited residual limb length may prevent exoprosthesis attachment all together. Osseointegrated implant technology is a novel operative procedure which allows firm skeletal attachment between the host bone and an implant. Preliminary results in European amputees with osseointegrated implants have shown improved clinical outcomes by allowing direct transfer of loads to the bone-implant interface. Despite the apparent advantages of osseointegration over socket technology, the current rehabilitation procedures require long periods of restrictive load bearing prior which may be reduced with expedited skeletal attachment via electrical stimulation. The goal of the osseointegrated intelligent implant design (OIID) system is to make the implant part of an electrical system to accelerate skeletal attachment and help prevent periprosthetic infection. To determine optimal electrode size and placement, we initiated proof of concept with computational modeling of the electric fields and current densities that arise during electrical stimulation of amputee residual limbs. In order to provide insure patient safety, subjects with retrospective computed tomography scans were selected and three dimensional reconstructions were created using customized software programs to ensure anatomical accuracy (Seg3D and SCIRun) in an IRB and HIPAA approved study. These software packages supported the development of patient specific models and allowed for interactive manipulation of electrode position and size. Preliminary results indicate that electric fields and current densities can be generated at the implant interface to achieve the homogenous electric field distributions required to induce osteoblast migration, enhance skeletal fixation and may help prevent periprosthetic infections. Based on the electrode configurations experimented with in the model, an external two band configuration will be advocated in the future.

Effect of nonuniform interstitial space properties on impulse propagation: a discrete multidomain model.

This work presents a discrete multidomain model that describes ionic diffusion pathways between connected cells and within the interstitium. Unlike classical models of impulse propagation, the intracellular and extracellular spaces are represented as spatially distinct volumes with dynamic/static boundary conditions that electrically couple neighboring spaces. The model is used to investigate the impact of nonuniform geometrical and electrical properties of the interstitial space surrounding a fiber on conduction velocity and action potential waveshape. Comparison of the multidomain and bidomain models shows that although the conduction velocity is relatively insensitive to cases that confine 50% of the membrane surface by narrow extracellular depths (> or =2 nm), the action potential morphology varies greatly around the fiber perimeter, resulting in changes in the magnitude of extracellular potential in the tight spaces. Results also show that when the conductivity of the tight spaces is sufficiently reduced, the membrane adjacent to the tight space is eliminated from participating in propagation, and the conduction velocity increases. Owing to its ability to describe the spatial discontinuity of cardiac microstructure, the discrete multidomain can be used to determine appropriate tissue properties for use in classical macroscopic models such as the bidomain during normal and pathophysiological conditions.

Evaluation of different meshing algorithms in the computation of defibrillation thresholds in children.

In this paper we evaluate different meshing schemes to solve for the bioelectric fields that arise in the human body due to the defibrillation shock generated by an Implantable Cardiac Defibrillator, with particular emphasis on implantation in children. For children, the question of relative performance of different electrode locations remains open. Computational simulation is a critical tool to address this question, and mesh design is a critical component of such simulations. We use the SCIRun software package to address this simulation problem because it combines the powerful numeric tools required with interactive flexibility allowing easy comparison of both algorithms and electrode orientation. We describe a pipeline that starts with segmented CT-images and produces clinically useful parameters. Using this framework we report below that a meshing scheme using regularly spaced hexahedral elements which are locally refined around the electrodes constitute a quick and relatively accurate way of solving this problem.

The effect of conductivity on ST-segment epicardial potentials arising from subendocardial ischemia.

We quantify and provide biophysical explanations for some aspects of the relationship between the bidomain conductivities and ST-segment epicardial potentials that result from subendocardial ischemia. We performed computer simulations of ischemia with a realistic whole heart model. The model included a patch of subendocardial ischemic tissue of variable transmural thickness with reduced action potential amplitude. We also varied both intracellular and extracellular conductivities of the heart and the conductivity of ventricular blood in the simulations. At medium or high thicknesses of transmural ischemia (i.e., at least 40% thickness through the heart wall), a consistent pattern of two minima of the epicardial potential over opposite sides of the boundary between healthy and ischemic tissue appeared on the epicardium over a wide range of conductivity values. The magnitude of the net epicardial potential difference, the epicardial maximum minus the epicardial minimum, was strongly correlated to the intracellular to extracellular conductivity ratios both along and across fibers. Anisotropy of the ischemic source region was critical in predicting epicardial potentials, whereas anisotropy of the heart away from the ischemic region had a less significant impact on epicardial potentials. Subendocardial ischemia that extends through at least 40% of the heart wall is manifest on the epicardium by at least one area of ST-segment depression located over a boundary between ischemic and healthy tissue. The magnitude of the depression is a function of the bidomain conductivity values.

On the passive cardiac conductivity.

In order to relate the structure of cardiac tissue to its passive electrical conductivity, we created a geometrical model of cardiac tissue on a cellular scale that encompassed myocytes, capillaries, and the interstitial space that surrounds them. A special mesh generator was developed for this model to create realistically shaped myocytes and interstitial space with a controlled degree of variation included in each model. In order to derive the effective conductivities, we used a finite element model to compute the currents flowing through the intracellular and extracellular space due to an externally applied electrical field. The product of these computations were the effective conductivity tensors for the intracellular and extracellular spaces. The simulations of bi-domain conductivities for healthy tissue resulted in an effective intracellular conductivity of 0.16S/m (longitudinal) and 0.005 S/m (transverse) and an effective extracellular conductivity of 0.21S/m (longitudinal) and 0.06 S/m (transverse). The latter values are within the range of measured values reported in literature. Furthermore, we anticipate that this method can be used to simulate pathological conditions for which measured data is far more sparse.

Mechanism for ST depression associated with contiguous subendocardial ischemia.

INTRODUCTION: A mechanism for ST depression arising on the epicardial surface over the border between normal and ischemic tissue is proposed. Depression is caused by current flowing in a transmural loop that begins and ends at the lateral boundary between healthy and ischemic tissue and passes through the transmural boundary between healthy and ischemic tissue. The result is ST depression at the epicardium over the lateral boundary. The size and direction of current flow are dictated by differences in the magnitude and orientation of anisotropic conductivity between those boundaries. METHODS AND RESULTS: Computer simulations verified and quantified the relationship between ST depression and conductivity differences. We used computer simulations based on an anatomically accurate, anisotropic model of canine ventricles and a bidomain representation of the effects of ischemia to verify the biophysical basis of this mechanism. CONCLUSION: ST depression at the epicardium appears over a lateral boundary between healthy and ischemic tissue.

Using models of the passive cardiac conductivity and full heart anisotropic bidomain to study the epicardial potentials in ischemia.

In this paper we present a multi-scale approach for cardiac modeling. Based on the histology of cardiac tissue we created a geometrical model at a cellular scale to compute the effective conductivity of a piece of cardiac tissue. In turn, the conductivity values obtained from this cellular scale model were used in a whole heart model in which we simulated regional, subendocardial ischemia. Histological changes at a cellular level led to changes in the effective conductivity tensor of the tissue, which in turn resulted in changes in the epicardial potential patterns during the ST-interval. Two effects were studied using this multi-scale approach: (1) the influence of a dynamically growing ischemic region on the epicardial potentials, and (2) the influence of a dynamically changing conductivity in the ischemic zone due to changes in the underlying pathology. One specific finding was the presence of epicardial patterns consisting of a central elevation and two opposite depressions at the edges of the ischemic zone which rotated as the ischemia became more transmural. In addition, the epicardial potentials decreased in magnitude with the duration of the ischemia due to changes in the effective conductivity of the ischemic tissue predicted by the cellular level model.

A study of the dynamics of cardiac ischemia using experimental and modeling approaches.

The dynamics of cardiac ischemia was investigated using experimental studies and computer simulations. An experimental model consisting of an isolated and perfused canine heart with full control over blood flow rate to a targeted coronary artery was used in the experimental study and a realistically shaped computer model of a canine heart, incorporating anisotropic conductivity and realistic fiber orientation, was used in the simulation study. The phenomena investigated were: (1) the influence of fiber rotation on the epicardial potentials during ischemia and (2) the effect of conductivity changes during a period of sustained ischemia. Comparison of preliminary experimental and computer simulation results suggest that as the ischemic region grows from the endocardium towards the epicardium, the epicardial potential patterns follow the rotating fiber orientation in the myocardium. Secondly, in the experimental studies it was observed that prolonged ischemia caused a subsequent reduction in the magnitude of epicardial potentials. Similar results were obtained from the computer model when the conductivity of the tissue in the ischemic region was reduced.