C.R. Johnson. Computational Methods and Software for Bioelectric Field Problems, In Biomedical Engineering Handbook, 4, Vol. 1, Ch. 43, Edited by J.D. Bronzino and D.R. Peterson, CRC Press, pp. 1--28. 2015.
Computer modeling and simulation continue to become more important in the field of bioengineering. The reasons for this growing importance are manyfold. First, mathematical modeling has been shown to be a substantial tool for the investigation of complex biophysical phenomena. Second, since the level of complexity one can model parallels the existing hardware configurations, advances in computer architecture have made it feasible to apply the computational paradigm to complex biophysical systems. Hence, while biological complexity continues to outstrip the capabilities of even the largest computational systems, the computational methodology has taken hold in bioengineering and has been used successfully to suggest physiologically and clinically important scenarios and results.
This chapter provides an overview of numerical techniques that can be applied to a class of bioelectric field problems. Bioelectric field problems are found in a wide variety of biomedical applications, which range from single cells, to organs, up to models that incorporate partial to full human structures. We describe some general modeling techniques that will be applicable, in part, to all the aforementioned applications. We focus our study on a class of bioelectric volume conductor problems that arise in electrocardiography (ECG) and electroencephalography (EEG).
We begin by stating the mathematical formulation for a bioelectric volume conductor, continue by describing the model construction process, and follow with sections on numerical solutions and computational considerations. We continue with a section on error analysis coupled with a brief introduction to adaptive methods. We conclude with a section on software.
Encyclopedia of Applied and Computational Mathematics, Edited by Björn Engquist, Springer, pp. 1537-1546. 2015.
CIBC. Note: map3d: Interactive scientific visualization tool for bioengineering data. Scientific Computing and Imaging Institute (SCI), Download from: http://www.sci.utah.edu/cibc/software.html, 2015.
Entropy-based particle correspondence for shape populations, In International Journal of Computer Assisted Radiology and Surgery, Springer, pp. 1-12. December, 2015.I. OguzI, J. Cates, M. Datar, B. Paniagua, T. Fletcher, C. Vachet, M. Styner, R. Whitaker.
Statistical shape analysis of anatomical structures plays an important role in many medical image analysis applications such as understanding the structural changes in anatomy in various stages of growth or disease. Establishing accurate correspondence across object populations is essential for such statistical shape analysis studies.
In this paper, we present an entropy-based correspondence framework for computing point-based correspondence among populations of surfaces in a groupwise manner. This robust framework is parameterization-free and computationally efficient. We review the core principles of this method as well as various extensions to deal effectively with surfaces of complex geometry and application-driven correspondence metrics.
We apply our method to synthetic and biological datasets to illustrate the concepts proposed and compare the performance of our framework to existing techniques.
Through the numerous extensions and variations presented here, we create a very flexible framework that can effectively handle objects of various topologies, multi-object complexes, open surfaces, and objects of complex geometry such as high-curvature regions or extremely thin features.
Poor scar formation after ablation is associated with atrial fibrillation recurrence, In Journal of Interventional Cardiac Electrophysiology, Vol. 44, No. 3, pp. 247-256. December, 2015.B.R. Parmar, T.R. Jarrett, E.G. Kholmovski, N. Hu, D. Parker, R.S. MacLeod, N.F. Marrouche, R. Ranjan.
Patients routinely undergo ablation for atrial fibrillation (AF) but the recurrence rate remains high. We explored in this study whether poor scar formation as seen on late-gadolinium enhancement magnetic resonance imaging (LGE-MRI) correlates with AF recurrence following ablation.
We retrospectively identified 94 consecutive patients who underwent their initial ablation for AF at our institution and had pre-procedural magnetic resonance angiography (MRA) merged with left atrial (LA) anatomy in an electroanatomic mapping (EAM) system, ablated areas marked intraprocedurally in EAM, 3-month post-ablation LGE-MRI for assessment of scar, and minimum of 3-months of clinical follow-up. Ablated area was quantified retrospectively in EAM and scarred area was quantified in the 3-month post-ablation LGE-MRI.
With the mean follow-up of 336 days, 26 out of 94 patients had AF recurrence. Age, hypertension, and heart failure were not associated with AF recurrence, but LA size and difference between EAM ablated area and LGE-MRI scar area was associated with higher AF recurrence. For each percent higher difference between EAM ablated area and LGE-MRI scar area, there was a 7–9 % higher AF recurrence (p values 0.001–0.003) depending on the multivariate analysis.
In AF ablation, poor scar formation as seen on LGE-MRI was associated with AF recurrence. Improved mapping and ablation techniques are necessary to achieve the desired LA scar and reduce AF recurrence.
SCI Institute. Note: SCIRun: A Scientific Computing Problem Solving Environment, Scientific Computing and Imaging Institute (SCI), Download from: http://www.scirun.org, 2015.
CIBC. Note: Seg3D: Volumetric Image Segmentation and Visualization. Scientific Computing and Imaging Institute (SCI), Download from: http://www.seg3d.org, 2015.
J.J.E. Blauer, D. Swenson, K. Higuchi, G. Plank, R. Ranjan, N. Marrouche,, R.S. MacLeod. Sensitivity and Specificity of Substrate Mapping: An In Silico Framework for the Evaluation of Electroanatomical Substrate Mapping Strategies, In Journal of Cardiovascular Electrophysiology, In Journal of Cardiovascular Electrophysiology, Vol. 25, No. 7, Note: Featured on journal cover., pp. 774--780. May, 2014.
Keywords: arrhythmia, computer-based model, electroanatomical mapping, voltage mapping, bipolar electrogram
Electrical activity of neuronal populations is a crucial aspect of brain activity. This activity is not measured directly but recorded as electrical potential changes using head surface electrodes (electroencephalogram - EEG). Head surface electrodes can also be deployed to inject electrical currents in order to modulate brain activity (transcranial electric stimulation techniques) for therapeutic and neuroscientific purposes. In electroencephalography and noninvasive electric brain stimulation, electrical fields mediate between electrical signal sources and regions of interest (ROI). These fields can be very complicated in structure, and are influenced in a complex way by the conductivity profile of the human head. Visualization techniques play a central role to grasp the nature of those fields because such techniques allow for an effective conveyance of complex data and enable quick qualitative and quantitative assessments. The examination of volume conduction effects of particular head model parameterizations (e.g., skull thickness and layering), of brain anomalies (e.g., holes in the skull, tumors), location and extent of active brain areas (e.g., high concentrations of current densities) and around current injecting electrodes can be investigated using visualization. Here, we evaluate a number of widely used visualization techniques, based on either the potential distribution or on the current-flow. In particular, we focus on the extractability of quantitative and qualitative information from the obtained images, their effective integration of anatomical context information, and their interaction. We present illustrative examples from clinically and neuroscientifically relevant cases and discuss the pros and cons of the various visualization techniques.
Keywords: Visualization, Bioelectric Field, EEG, tDCS, Human Brain
T. Fogal, F. Proch, A. Schiewe, O. Hasemann, A. Kempf, J. Krüger. Freeprocessing: Transparent in situ visualization via data interception, In Proceedings of the 14th Eurographics Conference on Parallel Graphics and Visualization, EGPGV, Eurographics Association, 2014.
In situ visualization has become a popular method for avoiding the slowest component of many visualization pipelines: reading data from disk. Most previous in situ work has focused on achieving visualization scalability on par with simulation codes, or on the data movement concerns that become prevalent at extreme scales. In this work, we consider in situ analysis with respect to ease of use and programmability. We describe an abstraction that opens up new applications for in situ visualization, and demonstrate that this abstraction and an expanded set of use cases can be realized without a performance cost.
Y. Gur, C.R. Johnson. Generalized HARDI Invariants by Method of Tensor Contraction, In Proceedings of the 2014 IEEE International Symposium on Biomedical Imaging (ISBI), pp. 718--721. April, 2014.
We propose a 3D object recognition technique to construct rotation invariant feature vectors for high angular resolution diffusion imaging (HARDI). This method uses the spherical harmonics (SH) expansion and is based on generating rank-1 contravariant tensors using the SH coefficients, and contracting them with covariant tensors to obtain invariants. The proposed technique enables the systematic construction of invariants for SH expansions of any order using simple mathematical operations. In addition, it allows construction of a large set of invariants, even for low order expansions, thus providing rich feature vectors for image analysis tasks such as classification and segmentation. In this paper, we use this technique to construct feature vectors for eighth-order fiber orientation distributions (FODs) reconstructed using constrained spherical deconvolution (CSD). Using simulated and in vivo brain data, we show that these invariants are robust to noise, enable voxel-wise classification, and capture meaningful information on the underlying white matter structure.
Keywords: Diffusion MRI, HARDI, invariants
Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization, Mathematics and Visualization, Springer, 2014.
Reflectance confocal microscopy (RCM) images skin non-invasively, with optical sectioning and nuclear-level resolution comparable to that of pathology. Based on assessment of the dermal-epidermal junction (DEJ) and morphologic features in its vicinity, skin cancer can be diagnosed in vivo with high sensitivity and specificity. However, the current visual, qualitative approach for reading images leads to subjective variability in diagnosis. We hypothesize that machine learning-based algorithms may enable a more quantitative, objective approach. Testing and validation was performed with two algorithms that can automatically delineate the DEJ in RCM stacks of normal human skin. The test set was composed of 15 fair and 15 dark skin stacks (30 subjects) with expert labellings. In dark skin, in which the contrast is high due to melanin, the algorithm produced an average error of 7.9±6.4 μm. In fair skin, the algorithm delineated the DEJ as a transition zone, with average error of 8.3±5.8 μm for the epidermis-to-transition zone boundary and 7.6±5.6 μm for the transition zone-to-dermis. Our results suggest that automated algorithms may quantitatively guide the delineation of the DEJ, to assist in objective reading of RCM images. Further development of such algorithms may guide assessment of abnormal morphological features at the DEJ.
Although catheter ablation therapy for atrial fibrillation (AF) is becoming more common, results vary widely, and patient selection criteria remain poorly defined. We hypothesized that late gadolinium enhancement MRI (LGE-MRI) can identify left atrial (LA) wall structural remodeling (SRM) and stratify patients who are likely or not to benefit from ablation therapy.
A widely used approach to solving the inverse problem in electrocardiography involves computing potentials on the epicardium from measured electrocardiograms (ECGs) on the torso surface. The main challenge of solving this electrocardiographic imaging (ECGI) problem lies in its intrinsic ill-posedness. While many regularization techniques have been developed to control wild oscillations of the solution, the choice of proper regularization methods for obtaining clinically acceptable solutions is still a subject of ongoing research. However there has been little rigorous comparison across methods proposed by different groups. This study systematically compared various regularization techniques for solving the ECGI problem under a unified simulation framework, consisting of both 1) progressively more complex idealized source models (from single dipole to triplet of dipoles), and 2) an electrolytic human torso tank containing a live canine heart, with the cardiac source being modeled by potentials measured on a cylindrical cage placed around the heart. We tested 13 different regularization techniques to solve the inverse problem of recovering epicardial potentials, and found that non-quadratic methods (total variation algorithms) and first-order and second-order Tikhonov regularizations outperformed other methodologies and resulted in similar average reconstruction errors.
B.R. Parmar, T.R. Jarrett, N.S. Burgon, E.G. Kholmovski, N.W. Akoum, N. Hu, R.S. Macleod, N.F. Marrouche, R. Ranjan.
Comparison of Left Atrial Area Marked Ablated in Electroanatomical Maps with Scar in MRI, In Journal of Cardiovascular Electrophysiology, 2014.
Three-dimensional electroanatomic mapping (EAM) is routinely used to mark ablated areas during radiofrequency ablation. We hypothesized that, in atrial fibrillation (AF) ablation, EAM overestimates scar formation in the left atrium (LA) when compared to the scar seen on late-gadolinium enhancement magnetic resonance imaging (LGE-MRI).
Methods and Results
Of the 235 patients who underwent initial ablation for AF at our institution between August 2011 and December 2012, we retrospectively identified 70 patients who had preprocedural magnetic resonance angiography merged with LA anatomy in EAM software and had a 3-month postablation LGE-MRI for assessment of scar. Ablated area was marked intraprocedurally using EAM software and quantified retrospectively. Scarred area was quantified in 3-month postablation LGE-MRI. The mean ablated area in EAM was 30.5 ± 7.5% of the LA endocardial surface and the mean scarred area in LGE-MRI was 13.9 ± 5.9% (P < 0.001). This significant difference in the ablated area marked in the EAM and scar area in the LGE-MRI was present for each of the 3 independent operators. Complete pulmonary vein (PV) encirclement representing electrical isolation was observed in 87.8% of the PVs in EAM as compared to only 37.4% in LGE-MRI (P < 0.001).
In AF ablation, EAM significantly overestimates the resultant scar as assessed with a follow-up LGE-MRI.
Keywords: atrial fibrillation, magnetic resonance imaging, radiofrequency ablation