Pattern selection in a biomechanical model for the growth of walled cells

In this paper, we analyse a model for the growth of three-dimensional walled cells. In this model the biomechanical expansion of the cell is coupled with the geometry of its wall. We consider that the density of building material depends on the curvature of the cell wall, thus yield-ing possible anisotropic growth. The dynamics of the axisymmetric cell wall is described by a system of nonlinear PDE including a nonlin-ear convection-diffusion equation coupled with a Poisson equation. We develop the linear stability analysis of the spherical symmetric config-uration in expansion. We identify three critical parameters that play a role in the possible instability of the radially symmetric shape, namely the degree of nonlinearity of the coupling, the effective diffusion of the building material, and the Poisson's ratio of the cell wall. We also investigate numerically pattern selection in the nonlinear regime. All the results are also obtained for a simpler, but similar, two-dimensional model

Multiscale Modeling of Cardiac Electrophysiology: Adaptation to Atrial and Ventricular Rhythm Disorders and Pharmacological Treatment

Multiscale modeling of cardiac electrophysiology helps to better understand the underlying mechanisms of atrial fibrillation, acute cardiac ischemia and pharmacological treatment. For this purpose, measurement data reflecting these conditions have to be integrated into models of cardiac electrophysiology. Several methods for this model adaptation are introduced in this thesis. The resulting effects are investigated in multiscale simulations ranging from the ion channel up to the body surface

Exploring the landscapes of "computing": digital, neuromorphic, unconventional -- and beyond

The acceleration race of digital computing technologies seems to be steering toward impasses -- technological, economical and environmental -- a condition that has spurred research efforts in alternative, "neuromorphic" (brain-like) computing technologies. Furthermore, since decades the idea of exploiting nonlinear physical phenomena "directly" for non-digital computing has been explored under names like "unconventional computing", "natural computing", "physical computing", or "in-materio computing". This has been taking place in niches which are small compared to other sectors of computer science. In this paper I stake out the grounds of how a general concept of "computing" can be developed which comprises digital, neuromorphic, unconventional and possible future "computing" paradigms. The main contribution of this paper is a wide-scope survey of existing formal conceptualizations of "computing". The survey inspects approaches rooted in three different kinds of background mathematics: discrete-symbolic formalisms, probabilistic modeling, and dynamical-systems oriented views. It turns out that different choices of background mathematics lead to decisively different understandings of what "computing" is. Across all of this diversity, a unifying coordinate system for theorizing about "computing" can be distilled. Within these coordinates I locate anchor points for a foundational formal theory of a future computing-engineering discipline that includes, but will reach beyond, digital and neuromorphic computing.Comment: An extended and carefully revised version of this manuscript has now (March 2021) been published as "Toward a generalized theory comprising digital, neuromorphic, and unconventional computing" in the new open-access journal Neuromorphic Computing and Engineerin

Flexible Two-point Selection Approach for Characteristic Function-based Parameter Estimation of Stable Laws

Stable distribution is one of the attractive models that well describes fat-tail behaviors and scaling phenomena in various scientific fields. The approach based upon the method of moments yields a simple procedure for estimating stable law parameters with the requirement of using momental points for the characteristic function, but the selection of points is only poorly explained and has not been elaborated. We propose a new characteristic function-based approach by introducing a technique of selecting plausible points, which could bring the method of moments available for practical use. Our method outperforms other state-of-art methods that exhibit a closed-form expression of all four parameters of stable laws. Finally, the applicability of the method is illustrated by using several data of financial assets. Numerical results reveal that our approach is advantageous when modeling empirical data with stable distributions.Comment: 15 pages, 7 figure

New Tools for Viscoelastic Spectral Analysis, with Application to the Mechanics of Cells and Collagen across Hierarchies

Viscoelastic relaxation spectra are essential for predicting and interpreting the mechanical responses of materials and structures. For biological tissues, these spectra must usually be estimated from viscoelastic relaxation tests. Interpreting viscoelastic relaxation tests is challenging because the inverse problem is expensive computationally. We present here (1) an efficient algorithm and (2) a quasi-linear model that enable rapid identification of the viscoelastic relaxation spectra of both linear and nonlinear materials. We then apply these methods to develop fundamental insight into the mechanics of collagenous and fibrotic tissues. The first algorithm, which we term the discrete spectral approach, is fast enough to yield a discrete spectrum of time constants that is sufficient to fit a measured relaxation spectrum with an accuracy insensitive to further refinement. The algorithm fits a discrete spectral generalized Maxwell (Maxwell-Wiechert) model, which is a linear viscoelastic model, to results from a stress-relaxation test. The discrete spectral approach was tested against trial data to characterize its robustness and identify its limitations and strengths. The algorithm was then applied to identify the viscoelastic response of reconstituted collagen and engineered fibrosis tissues, revealing that cells actively adapted the ECM, and that cells relax at multiple timescales, including one that is fast compared to those of the ECM. The second algorithm, which we term the discrete quasi-linear viscoelastic (DQLV) approach, is a spectral extension of the Fung quasi-linear viscoelastic (QLV) model, a standard tool for characterizing biological materials. The Fung QLV model provides excellent fits to most stress-relaxation data by imposing a simple form upon a material\u27s temporal relaxation spectrum. However, model identification is challenging because the Fung QLV model\u27s “box” shaped relaxation spectrum, predominant in biomechanics applications, because it can provide an excellent fit even when it is not a reasonable representation of a material\u27s relaxation spectrum. The DQLV model is robust, simple, and unbiased. It is able to identify ranges of time constants over which the Fung QLV model\u27s typical box spectrum provides an accurate representation of a particular material\u27s temporal relaxation spectrum, and is effective at providing a fit to this model. The DQLV spectrum also reveals when other forms or discrete time constants are more suitable than a box spectrum. After validating the approach against idealized and noisy data, we applied the methods to analyze medial collateral ligament stress-relaxation and sinusoidal excitation data and identify the strengths and weaknesses of an optimal Fung QLV fit. Taken together, the tools in this dissertation form a comprehensive approach to characterizing the mechanics of viscoelastic biological tissues, and to dissecting the micromechanical mechanisms that underlie a tissue\u27s viscoelastic responses

Cardiac electrophysiology and mechanoelectric feedback : modeling and simulation

Cardiac arrhythmia such as atrial and ventricular fibrillation are characterized by rapid and irregular electrical activity, which may lead to asynchronous contraction and a reduced pump function. Besides experimental and clinical studies, computer simulations are frequently applied to obtain insight in the onset and perpetuation of cardiac arrhythmia. In existing models, the excitable tissue is often modeled as a continuous two-phase medium, representing the intracellular and interstitial domains, respectively. A possible drawback of continuous models is the lack of flexibility when modeling discontinuities in the cardiac tissue. We introduce a discrete bidomain model in which the cardiac tissue is subdivided in segments, each representing a small number of cardiac cells. Active membrane behavior as well as intracellular coupling and interstitial currents are described by this model. Compared with the well-known continuous bidomain equations, our Cellular Bidomain Model is better aimed at modeling the structure of cardiac tissue, in particular anisotropy, myofibers, fibrosis, and gap junction remodeling. An important aspect of our model is the strong coupling between cardiac electrophysiology and cardiomechanics. Mechanical behavior of a single segment is modeled by a contractile element, a series elastic element, and a parallel elastic element. Active force generated by the sarcomeres is represented by the contractile element together with the series elastic element. The parallel elastic element describes mechanical behavior when the segment is not electrically stimulated. Contractile force is related to the intracellular calcium concentration, the sarcomere length, and the velocity of sarcomere shortening. By incorporating the influence of mechanical deformation on electrophysiology, mechanoelectric feedback can be studied. In our model, we consider the immediate influence of stretch on the action potential by modeling a stretch-activated current. Furthermore, we consider the adap- tation of ionic membrane currents triggered by changes in mechanical load. The strong coupling between cardiac electrophysiology and cardiac mechanics is a unique property of our model, which is reflected by its application to obtain more insight in the cause and consequences of mechanical feedback on cardiac electrophysiology. In this thesis, we apply the Cellular Bidomain Model in five different simulation studies to cardiac electrophysiology and mechanoelectric feedback. In the first study, the effect of field stimulation on virtual electrode polarization is studied in uniform, decoupled, and nonuniform cardiac tissue. Field stimulation applied on nonuniform tissue results in more virtual electrodes compared with uniform tissue. Spiral waves can be terminated in decoupled tissue, but not in uniform, homogeneous tissue. By gradually increasing local differences in intracellular conductivities, the amount and spread of virtual electrodes increases and spiral waves can be terminated. We conclude that the clinical success of defibrillation may be explained by intracellular decoupling and spatial heterogeneity present in normal and in pathological cardiac tissue. In the second study, the role of the hyperpolarization-activated inward current If is investigated on impulse propagation in normal and in pathological tissue. The effect of diffuse fibrosis and gap junction remodeling is simulated by reducing cellular coupling nonuniformly. As expected, the conduction velocity decreases when cellular coupling is reduced. In the presence of If, the conduction velocity increases both in normal and in pathological tissue. In our simulations, ectopic activity is present in regions with high expression of If and is facilitated by cellular uncoupling. We also found that an increased If may facilitate propagation of the action potential. Hence, If may prevent conduction slowing and block. Overexpression of If may lead to ectopic activity, especially when cellular coupling is reduced under pathological conditions. In the third study, the influence of the stretch-activated current Isac is investigated on impulse propagation in cardiac fibers composed of segments that are electrically and mechanically coupled. Simulations of homogeneous and inhomogeneous cardiac fibers have been performed to quantify the relation between conduction velocity and Isac under stretch. Conduction slowing and block are related to the amount of stretch and are enhanced by contraction of early-activated segments. Our observations are in agreement with experimental results and explain the large differences in intra-atrial conduction, as well as the increased inducibility of atrial fibrillation in acutely dilated atria. In the fourth study, we investigate the hypothesis that electrical remodeling is triggered by changes in mechanical work. Stroke work is determined for each segment by simulating the cardiac cycle. Electrical remodeling is simulated by adapting the L-type Ca2+ current ICa,L such that a homogeneous distribution of stroke work is obtained. With electrical remodeling, a more homogeneous shortening of the fiber is obtained, while heterogeneity in APD increases and the repolarization wave reverses. These results are in agreement with experimentally observed distributions of strain and APD and indicate that electrical remodeling leads to more homogeneous shortening during ejection. In the fifth study, we investigate the effect of stretch on the vulnerability to AF. The human atria are represented by a triangular mesh obtained from MRI data. To model acute dilatation, overall stretch is applied to the atria. In the presence of Isac, the membrane potential depolarizes, which causes inactivation of the sodium channels and results in conduction slowing or block. Inducibility of AF increases under stretch, which is explained by an increased dispersion in refractory period, conduction slowing, and local conduction block. Our observations explain the large differences in intra-atrial conduction measured in experiments and provide insight in the vulnerability to AF in dilated atria. In conclusion, our model is well-suited to describe cardiac electrophysiology and mechanoelectric feedback. For future applications, the model may be improved by taking into account new insights from cellular physiology, a more accurate geometry, and hemodynamics