Workshop 3: Integrating Modalities and Scales in Life Science Imaging
Biofuel cell polarization estimation: inversion of electrochemical impedance spectroscopic measurements Importantance of Model FormulationRosemary Renaut
The inverse problem associated with electrochemical impedance spectroscopy requiring the solution of a Fredholm integral equation of the first kind is considered. If the underlying physical model is not clearly determined, the inverse problem needs to be solved using a regularized linear least squares problem that is obtained from the discretization of the integral equation. For this system, it is shown that the model error can be made negligible by a change of variables and by extending the effective range of quadrature. This change of variables serves as a right preconditioner that significantly improves the condition of the system. Still, to obtain feasible solutions the additional constraint of non-negativity is required. Simulations with artificial, but realistic, data demonstrate that the use of non-negatively constrained least squares with a smoothing norm provides higher quality solutions than those obtained without the non-negative constraint. Using higher-order smoothing norms also reduces the error in the solutions. The L-curve and residual periodogram parameter choice criteria, which are used for parameter choice with regularized linear least squares, are successfully adapted to be used for the non-negatively constrained problem. Although these results have been verified within the context of the analysis of electrochemical impedance spectroscopy, there is no reason to suppose that they would not be relevant within the broader framework of solving Fredholm integral equations for other applications.
Extensive genetic information and the expanding number of techniques available to manipulate the genome of the mouse have led to its widespread use in studies of brain development and to model human neurodevelopmental diseases. We are developing a combination of ultrasound and magnetic resonance micro-imaging approaches with sufficient resolution and sensitivity to provide noninvasive structural, functional and molecular data on developmental and disease processes in normal and genetically-engineered mice. Our efforts over the past decade have focused on in utero and early postnatal imaging and analysis of the developing brain and cerebral vasculature. The advantages and limitations of both ultrasound and MRI for imaging mouse development will be discussed, and examples provided to illustrate the utility of these approaches for 4D mutant phenotype analysis. Recent advances have also made in the area of molecular imaging, including the generation of novel reporter mice that enable cell-specific imaging with ultrasound and MRI contrast agents. Future directions for molecular imaging of mouse brain development will be discussed.
Mathematical modeling is of crucial importance for understanding the complexity of biological systems. Where biological experiments educate us about nature itself, mathematical models allow us to make prediction on the outcome of events based on current theories and hypotheses. In the field of cardiology, modeling has an important role in forward and inverse calculations between local cardiac events and the body surface ECG or the understanding complex atrial or ventricular arrhythmias. To develop and optimize an accurate mathematical model experimental data is required. Optical imaging has enabled the recording of epicardial, and also transmural, activation and repolarization patterns with a high spatial resolution. Also, optical imaging allows to relate the metabolic state and ionic homeostasis with cardiac electrophysiology by measuring simultaneously membrane voltage and Ca2+ and Na+ with fluorescent indicators or NADH, which has its own fluorescent spectrum. In this talk I will discuss several optical imaging modalities as they are applied to study human non-failing and failing hearts.
Both cardiac and brain bioelectric forward problems can be modeled accurately as quasi-static, implying that torso or scalp surface measurements depend on the spatial distribution of the respective sources independently at each time instant. However in both cases the time courses of the sources are in large part a function of intrinsic electrophysiological dynamics, and so exhibit strong and complex temporal correlations. This suggests that it would be advantageous to incorporate temporal models into inverse methods, especially in light of the ill-posed nature of both problems. This talk will present some ideas, results, and possibilities for dynamic modeling in inverse bioelectric problems, concentrating primarily on electrocardiography. We will review some standard methods and describe how three such approaches are related through their assumptions about spatiotemporal covariance structure. We will then present some recent results with clinically measured data using a new method which incorporates a non-linear temporal model. Finally we will illustrate manifold-inspired, non-linear dynamic structure in measured signals, suggesting the potential for even more powerful dynamic modeling in the near future. If time permits we will also show results of our dynamic modeling of EEG and pose some questions about their implications for brain source localization.
In medical imaging, the true underlying property of interest is unknown. A single image provides little to no insight into the impact of confounding factors such as: statistical noise, biological variability, scattered radiation, patient motion, deadtime in detectors and electronics, detector resolution, etc. Some of these physical factors can be quantified by scanning various configurations of test objects, often called phantoms. Physical phantoms, however, can not capture variability due to patient physiology and offer only mean performance characteristics of a limited set of objects.
Forward modeling of imaging systems provides an unparalleled window for examining and improving performance. For example, simulations using Monte Carlo photon tracking can be used to isolate a single factor of interest, for instance multiple i.i.d. realizations of the same imaging scenario can determine the effect of quantum noise or biological variability. Likewise, faster analytical models can be used to elucidate non-linear effects in the imaging chain. Accurate forward models also play a key role in improving iterative estimation of optimal images. Finally, forward models can be integrated into a feedback loop for optimization of a medical imaging tasks (not just images), that are not predictable a priori. We will give examples of the value of forward modeling in which an accurate model of the physics of the medical imaging system is an essential component to solving challenges in imaging research and healthcare.
Several mechanisms have been suggested to explain the increasing stability of atrial fibrillation (AF) over time. Disruption of electrical coupling between muscle bundles, resulting in narrower and thus more fibrillation waves, is considered as one of the main mechanisms contributing to AF stability in structurally remodeled atria. Also, the anatomy of the atrial wall has been demonstrated to significantly determine conduction patterns during AF. Most of these mechanisms have been studied in several in silico studies. But more than that, there are experimental studies suggesting that the development of the substrate for AF goes along with increasing incidence of conduction from the sub-epicardial layer to the endocardial bundle network and vice versa. While these studies conclusively demonstrate transmural conduction in the atrial wall, they leave open several important conceptual questions. In particular this talk focuses on in silico modeling of three-dimensional conductions during AF and its effect on AF stability.
Drug-resistant epilepsy occurs in over one third of epilepsy patients, and surgical excision of the affected brain region is often necessary to achieve seizure control. However, precise delineation of the seizure onset zone can be challenging, and can lead to poor surgical outcomes when incorrect. In many of these cases, the underlying pathology consists of subtle architectural abnormalities at the microscopic scale. Improved imaging of these lesions at a macroscopic scale thus requires integration of in-vivo MRI modalities that can probe the tissue microarchitecture, along with rigorous validation against histology. This talk will present our work on correlating quantitative relaxometry and diffusion imaging of temporal lobe epilepsy patients with histology of surgical specimens. I will highlight the challenges faced in spatial alignment of anatomy at vastly different scales, steps taken towards quantitative characterization of pathology in epilepsy, and how intrinsic MRI parameters can be used to improve our understanding of the excitotoxic effects of seizures.
Despite the overwhelming wealth of data available today, gaining mechanistic insight into cardiac function remains to be a challenging endeavour due to the multiscale/multiphysics nature of cardiac function, where complex interactions of processes arise within and across levels of organization, as well as between electrical, mechanical and fluidic systems. Computer simulation has become a powerful adjunct to experimental studies, but current modeling methodology imposes severe limitations, forcing research to resort to overly simplified modeling assumptions. This talk will highlight recent methodological advances in terms of modeling organ scale cardiac anatomy and electro-mechano-fluidic function at high spatial resolution. The presented methods aim at lifting many of the current modeling restrictions to enable computational studies where model complexity is chosen as a function of the question being addressed, and not based on feasibility constraints. The use of advanced numerical methods is of pivotal importance to reduce execution times, thus facilitating quick simulation-analysis cycles. Application examples will be presented including multiscale arrhythmogenic effects due to mitochondrial dysfunction and calcium handling, as well as clinical modeling studies which aim at optimization and outcome prediction due to interventions such as aortic valve replacement and repair of aortic coarctations.