The magnetocardiogram.

The magnetic field produced by the heart's electrical activity is called the magnetocardiogram (MCG). The first 20 years of MCG research established most of the concepts, instrumentation, and computational algorithms in the field. Additional insights into fundamental mechanisms of biomagnetism were gained by studying isolated hearts or even isolated pieces of cardiac tissue. Much effort has gone into calculating the MCG using computer models, including solving the inverse problem of deducing the bioelectric sources from biomagnetic measurements. Recently, most magnetocardiographic research has focused on clinical applications, driven in part by new technologies to measure weak biomagnetic fields.

Depth-Dependent Strain Model (1D) for Anisotropic Fibrils in Articular Cartilage.

The mechanical response of articular cartilage (AC) under compression is anisotropic and depth-dependent. AC is osmotically active, and its intrinsic osmotic swelling pressure is balanced by its collagen fibril network. This mechanism requires the collagen fibers to be under a state of tensile pre-strain. A simple mathematical model is used to explain the depth-dependent strain calculations observed in articular cartilage under 1D axial compression (perpendicular to the articular surface). The collagen fibers are under pre-strain, influenced by proteoglycan concentration (fixed charged density, FCD) and collagen stiffness against swelling stress. The stiffness is introduced in our model as an anisotropic modulus that varies with fibril orientation through tissue depth. The collagen fibers are stiffer to stretching parallel to their length than perpendicular to it; when combined with depth-varying FCD, the model successfully predicts how tissue strains decrease with depth during compression. In summary, this model highlights that the mechanical properties of cartilage depend not only on proteoglycan concentration but also on the intrinsic properties of the pre-strained collagen network. These properties are essential for the proper functioning of articular cartilage.

The Electric Field Induced by a Microcoil During Magnetic Stimulation.

OBJECTIVE: The purpose of this study is to calculate the electric field produced by an implanted microcoil during magnetic stimulation of the brain. METHODS: The electric field of a microcoil was calculated numerically. RESULTS: The maximum value of the induced electric field is approximately 0.000026 V/m for a 1 mA, 3 kHz current passed through the coil. CONCLUSION: This electric field value is too small to cause neural stimulation. SIGNIFICANCE: Previous studies reporting magnetic stimulation using a microcoil must have been exciting neurons by some other mechanism.

Biomagnetism: The First Sixty Years.

Biomagnetism is the measurement of the weak magnetic fields produced by nerves and muscle. The magnetic field of the heart-the magnetocardiogram (MCG)-is the largest biomagnetic signal generated by the body and was the first measured. Magnetic fields have been detected from isolated tissue, such as a peripheral nerve or cardiac muscle, and these studies have provided insights into the fundamental properties of biomagnetism. The magnetic field of the brain-the magnetoencephalogram (MEG)-has generated much interest and has potential clinical applications to epilepsy, migraine, and psychiatric disorders. The biomagnetic inverse problem, calculating the electrical sources inside the brain from magnetic field recordings made outside the head, is difficult, but several techniques have been introduced to solve it. Traditionally, biomagnetic fields are recorded using superconducting quantum interference device (SQUID) magnetometers, but recently, new sensors have been developed that allow magnetic measurements without the cryogenic technology required for SQUIDs.

Can MRI Be Used as a Sensor to Record Neural Activity?

Magnetic resonance provides exquisite anatomical images and functional MRI monitors physiological activity by recording blood oxygenation. This review attempts to answer the following question: Can MRI be used as a sensor to directly record neural behavior? It considers MRI sensing of electrical activity in the heart and in peripheral nerves before turning to the central topic: recording of brain activity. The primary hypothesis is that bioelectric current produced by a nerve or muscle creates a magnetic field that influences the magnetic resonance signal, although other mechanisms for detection are also considered. Recent studies have provided evidence that using MRI to sense neural activity is possible under ideal conditions. Whether it can be used routinely to provide functional information about brain processes in people remains an open question. The review concludes with a survey of artificial intelligence techniques that have been applied to functional MRI and may be appropriate for MRI sensing of neural activity.

Bidomain modeling of electrical and mechanical properties of cardiac tissue.

Throughout the history of cardiac research, there has been a clear need to establish mathematical models to complement experimental studies. In an effort to create a more complete picture of cardiac phenomena, the bidomain model was established in the late 1970s to better understand pacing and defibrillation in the heart. This mathematical model has seen ongoing use in cardiac research, offering mechanistic insight that could not be obtained from experimental pursuits. Introduced from a historical perspective, the origins of the bidomain model are reviewed to provide a foundation for researchers new to the field and those conducting interdisciplinary research. The interplay of theory and experiment with the bidomain model is explored, and the contributions of this model to cardiac biophysics are critically evaluated. Also discussed is the mechanical bidomain model, which is employed to describe mechanotransduction. Current challenges and outstanding questions in the use of the bidomain model are addressed to give a forward-facing perspective of the model in future studies.

Mechanical bidomain model of cardiac muscle with unequal anisotropy ratios.

The properties of cardiac muscle are anisotropic, and the degree of anisotropy may be different in the intracellular and extracellular spaces. In the electrical bidomain model, such "unequal anisotropy ratios" of the conductivity lead to unanticipated behavior. In the mechanical bidomain model, unequal anisotropy ratios of the mechanical moduli might also result in unanticipated behavior. In this study, mathematical modeling based on the mechanical bidomain model is used to calculate the distribution of mechanotransduction in cardiac tissue when it is stretched. This analysis demonstrates that unexpected phenomena arise when the mechanical anisotropy ratios are unequal.

The mechanical bidomain model of cardiac muscle with curving fibers.

In the heart, cardiac muscle fibers curve creating zones of membrane forces resulting in regions of mechanotransduction. This study uses the finite difference method to solve the mechanical bidomain equations numerically for a complex fiber geometry. The magnitude of the active tension T is constant but its direction makes an angle with the x-axis that varies with position. Differences between the intracellular and extracellular displacements result from the bidomain behavior of the tissue that gives rise to forces on the integrin proteins in the membrane. The long-term goal is to use the mechanical bidomain model to suggest experiments and make predictions about growth and remodeling in the heart.

Modeling bipolar stimulation of cardiac tissue.

Unipolar stimulation of cardiac tissue is often used in the design of cardiac pacemakers because of the low current required to depolarize the surrounding tissue at rest. However, the advantages of unipolar over bipolar stimulation are not obvious at shorter coupling intervals when the tissue near the pacing electrode is relatively refractory. Therefore, this paper analyzes bipolar stimulation of cardiac tissue. The strength-interval relationship for bipolar stimulation is calculated using the bidomain model and a recently developed parsimonious ionic current model. The strength-interval curves obtained using different electrode separations and arrangements (electrodes placed parallel to the fibers versus perpendicular to the fibers) indicate that bipolar stimulation results in more complex activation patterns compared to unipolar stimulation. An unusually low threshold stimulus current is observed when the electrodes are close to each other (a separation of 1 mm) because of break excitation. Unlike for unipolar stimulation, anode make excitation is not present during bipolar stimulation, and an abrupt switch from anode break to cathode make excitation can cause dramatic changes in threshold with very small changes in the interval. These results could impact the design of implantable pacemakers and defibrillators.

Determining the light scattering and absorption parameters from forward-directed flux measurements in cardiac tissue.

We describe a method to accurately measure the light scattering model parameters from forward-directed flux (FDF) measurements carried out with a fiber-optic probe (optrode). Improved determination of light scattering parameters will, in turn, permit better modeling and interpretation of optical mapping in the heart using voltage-sensitive dyes. Using our optrode-based system, we carried out high spatial resolution measurements of FDF in intact and homogenized cardiac tissue, as well as in intralipid-based tissue phantoms. The samples were illuminated with a broad collimated beam at 660 and 532 nm. Measurements were performed with a plunge fiber-optic probe (NA=0.22) at a spatial resolution of up to 10 µm. In the vicinity of the illuminated surface, the FDF consistently manifested a fast decaying exponent with a space constant comparable with the decay rate of ballistic photons. Using a Monte Carlo model, we obtained a simple empirical formula linking the rate of the fast exponent to the scattering coefficient, the anisotropy parameter g, and the numerical aperture of the probe. The estimates of scattering coefficient based on this formula were validated in tissue phantoms. Potential applications of optical fiber-based FDF measurements for the evaluation of optical parameters in turbid media are discussed.

Cardiac strength-interval curves calculated using a bidomain tissue with a parsimonious ionic current.

The strength-interval curve plays a major role in understanding how cardiac tissue responds to an electrical stimulus. This complex behavior has been studied previously using the bidomain formulation incorporating the Beeler-Reuter and Luo-Rudy dynamic ionic current models. The complexity of these models renders the interpretation and extrapolation of simulation results problematic. Here we utilize a recently developed parsimonious ionic current model with only two currents-a sodium current that activates rapidly upon depolarization INa and a time-independent inwardly rectifying repolarization current IK-which reproduces many experimentally measured action potential waveforms. Bidomain tissue simulations with this ionic current model reproduce the distinctive dip in the anodal (but not cathodal) strength-interval curve. Studying model variants elucidates the necessary and sufficient physiological conditions to predict the polarity dependent dip: a voltage and time dependent INa, a nonlinear rectifying repolarization current, and bidomain tissue with unequal anisotropy ratios.

Heterogeneous anisotropic magnetic susceptibility of the myelin-water layers causes local magnetic field perturbations in axons.

One goal of MRI is to determine the myelin water fraction in neural tissue. One approach is to measure the reduction in T2 * arising from microscopic perturbations in the magnetic field caused by heterogeneities in the magnetic susceptibility of myelin. In this paper, analytic expressions for the induced magnetic field distribution are derived within and around an axon, assuming that the myelin susceptibility is anisotropic. Previous models considered the susceptibility to be piecewise continuous, whereas this model considers a sinusoidally varying susceptibility. Many conclusions are common in both models. When the magnetic field is applied perpendicular to the axon, the magnetic field in the intraaxonal space is uniformly perturbed, the magnetic field in the myelin sheath oscillates between the lipid and water layers, and the magnetic field in the extracellular space just outside the myelin sheath is heterogeneous. These field heterogeneities cause the spins to dephase, shortening T2 *. When the magnetic field is applied along the axon, the field is homogeneous within water-filled regions, including between lipid layers. Therefore the spins do not dephase and the magnetic susceptibility has no effect on T2 *. Generally, the response of an axon is given as the superposition of these two contributions. The sinusoidal model uses a different set of approximations compared with the piecewise model, so their common predictions indicate that the models are not too sensitive to the details of the myelin-water distribution. Other predictions, such as the sensitivity to water diffusion between myelin and water layers, may highlight differences between the two approaches. Copyright © 2016 John Wiley & Sons, Ltd.

A numerical solution of the mechanical bidomain model.

INTRODUCTION: The mechanical bidomain model predicts forces on integrin proteins in the membrane. It has been solved analytically for idealized examples, but a numerical algorithm is needed to address realistic problems. METHODS: The bidomain equations are approximated using finite differences. An ischemic region is modeled as a circular area having no active tension, surrounded by normal tissue. RESULTS: The membrane force is large in the ischemic border zone, but is small elsewhere. Strain is distributed widely throughout the ischemic region and surrounding tissue. CONCLUSION: This calculation provides a testable prediction for the mechanism of mechanotransduction and remodeling in cardiac tissue.

The Mechanism of Reflection Type Reentry: A Simulation Study.

INTRODUCTION: Reflection is a special type of reentry in which an electrical wave front travels in a forward direction through tissue that is then re-excited by a wave front that propagates backward. This type of reentry has been studied computationally in 1-dimensional fibers and verified experimentally. Different hypotheses explaining reflected reentry have been proposed based on the structure and heterogeneity of the tissue properties, but the mechanism remains uncertain. METHODS AND RESULTS: We used the bidomain model to represent cardiac tissue and the Luo-Rudy model to describe the active membrane properties. We consider an ischemic region in a volume of ventricular myocardium. Our results show that a slow depolarization in the ischemic border zone caused by electrotonic coupling to depolarized tissue in the normal region creates a delay between proximal and distal regions that produces enough electrotonic current in the distal region to re-excite the proximal region. CONCLUSION: Our simulation shows that an early afterdepolarization (EAD) is not the source of the reflection. It depends on the pacing interval and stimulus strength necessary to maintain enough time delay between proximal and distal regions.

Electrical Pacing of Cardiac Tissue Including Potassium Inward Rectification.

In this study cardiac tissue is stimulated electrically through a small unipolar electrode. Numerical simulations predict that around an electrode are adjacent regions of depolarization and hyperpolarization. Experiments have shown that during pacing of resting cardiac tissue the hyperpolarization is often inhibited. Our goal is to determine if the inward rectifying potassium current (IK1) causes the inhibition of hyperpolarization. Numerical simulations were carried out using the bidomain model with potassium dynamics specified to be inward rectifying. In the simulations, adjacent regions of depolarization and hyperpolarization were observed surrounding the electrode. For cathodal currents the virtual anode produces a hyperpolarization that decreases over time. For long duration pulses the current-voltage curve is non-linear, with very small hyperpolarization compared to depolarization. For short pulses, the hyperpolarization is more prominent. Without the inward potassium rectification, the current voltage curve is linear and the hyperpolarization is evident for both long and short pulses. In conclusion, the inward rectification of the potassium current explains the inhibition of hyperpolarization for long duration stimulus pulses, but not for short duration pulses.

Using the mechanical bidomain model to analyze the biomechanical behavior of cardiomyocytes.

The mechanical bidomain model provides a macroscopic description of cardiac tissue biomechanics and also predicts the microscopic coupling between the extracellular matrix and the intracellular cytoskeleton of cardiomyocytes. The goal of this chapter is to introduce the mechanical bidomain model, to describe the mathematical methods required to solve the model equations, and to predict where the membrane forces acting on integrin proteins coupling the intracellular and extracellular spaces are large.

ELECTRICAL INSTABILITY DUE TO REGIONAL INCREASE IN EXTRACELLULAR POTASSIUM ION CONCENTRATION.

INTRODUCTION: Ventricular tachycardia and ventricular fibrillation are the two most dangerous arrhythmias. Both are related to reentrant electrical activity in the ventricles. Many studies of arrhythmias consider a homogeneous sheet of cardiac tissue. Since normal ventricular myocardium is inhomogeneous and inhomogeneities play an important role in the induction of reentry, we investigate the effect of a localized inhomogeniety developed at the border between normal and ischemic region. METHODS: We used the bidomain model to represent the electrical properties of cardiac tissue and a modified version of the dynamic Luo-Rudy (LRd) model to represent the active properties of the membrane. To investigate the effect of a localized inhomogeneity, the extracellular potassium [K]e concentration is raised to 10 mM from normal [K]e (4 mM) on the right half of the tissue. RESULTS AND DISCUSSION: A train of cathodal stimuli are applied from the lower left corner of the tissue with different basic cycle lengths (BCL). At certain BCL, the spatial heterogeneity created with regional elevation of [K]e can lead to action potential instability (alternans) in the normal and border regions, and 2:1 conduction block in the ischemic region. We observed the reentry when local heterogeneity in [K]e is changed from 10 to 12 mM on the right half of the virtual ventricular myocardium sheet. CONCLUSION: Electrical alternans occur during high heart rates and are observed in patients suffering from ventricular tachycardia. It is an early indication of left ventricular systolic impairment. This study will help to evaluate alternans as a predictor and guide for antiarrhythmic therapy.