Cardiac Electromechanics: The effect of contraction model on the mathematical problem and accuracy of the numerical scheme

Models of cardiac electromechanics usually contain a contraction model determining the active tension induced at the cellular level, and the equations of nonlinear elasticity to determine tissue deformation in response to this active tension. All contraction models are dependent on cardiac electro-physiology, but can also be dependent on\ud the stretch and stretch-rate in the fibre direction. This fundamentally affects the mathematical problem being solved, through classification of the governing PDEs, which affects numerical schemes that can be used to solve the governing equations. We categorise contraction models into three types, and for each consider questions such as classification and the most appropriate choice from two numerical methods (the explicit and implicit schemes). In terms of mathematical classification, we consider the question of strong ellipticity of the total strain energy (important for precluding ‘unnatural’ material behaviour) for stretch-rate-independent contraction models; whereas for stretch-rate-dependent contraction models we introduce a corresponding third-order problem and explain how certain choices of boundary condition could lead to constraints on allowable initial condition. In terms of suitable numerical methods, we show that an explicit approach (where the contraction model is integrated in the timestep prior to the bulk deformation being computed) is: (i) appropriate for stretch-independent contraction models; (ii) only conditionally-stable, with the stability criterion independent of timestep, for contractions models which just depend on stretch (but not stretch-rate), and (iii) inappropriate for stretch-rate-dependent models

Translocation of caveolin regulates stretch-induced ERK activity in vascular smooth muscle

Kawabe, J; Okumura, S; Lee, MC; Sadoshima, J; Ishikawa, Y, AMERICAN JOURNAL OF PHYSIOLOGY-HEART AND CIRCULATORY PHYSIOLOGY, 286(5), H1845-H1852, 2004. "Copyright 2004 by the American Physical Society." publisherMechanical stress contributes to vascular disease related to hypertension. Activation of ERK is key to mediating cellular proliferation and vascular remodeling in response to stretch stress. However, the mechanism by which stretch mediates ERK activation in the vascular tissue is still unclear. Caveolin, a major component of a flasklike invaginated caveolae, acts as an adaptor protein for an integrin-mediated signaling pathway. We found that cyclic stretch transiently induced translocation of caveolin from caveolae to noncaveolar membrane sites in vascular smooth muscle cells (VSMCs). This translocation of caveolin was determined by detergent solubility, sucrose gradient fractionation, and immunocytochemistry. Cyclic stretch induced ERK activation; the activity peaked at 5 min (the early phase), decreased gradually, but persisted up to 120 min (the late phase). Disruption of caveolae by methyl-β-cyclodextrin, decreasing the caveolar caveolin and accumulating the noncaveolar caveolin, enhanced ERK activation in both the early and late phases. When endogenous caveolins were downregulated, however, the late-phase ERK activation was subsided completely. Caveolin, which was translocated to noncaveolar sites in response to stretch, is associated with β_1-integrins as well as with Fyn and Shc, components required for ERK activation. Taken together, caveolin in caveolae may keep ERK inactive, but when caveolin is translocated to noncaveolar sites in response to stretch stress, caveolin mediates stretch-induced ERK activation through an association with β_1-integrins/Fyn/Shc. We suggest that stretch-induced translocation of caveolin to noncaveolar sites plays an important role in mediating stretch-induced ERK activation in VSMCs

Modulation of Stretch Reflexes of the Finger Flexors by Sensory Feedback from the Proximal Upper Limb Poststroke

Neural coupling of proximal and distal upper limb segments may have functional implications in the recovery of hemiparesis after stroke. The goal of the present study was to investigate whether the stretch reflex response magnitude of spastic finger flexor muscles poststroke is influenced by sensory input from the shoulder and the elbow and whether reflex coupling of muscles throughout the upper limb is altered in spastic stroke survivors. Through imposed extension of the metacarpophalangeal (MCP) joints, stretch of the relaxed finger flexors of the four fingers was imposed in 10 relaxed stroke subjects under different conditions of proximal sensory input, namely static arm posture (3 different shoulder/elbow postures) and electrical stimulation (surface stimulation of biceps brachii or triceps brachii, or none). Fast (300°/s) imposed stretch elicited stretch reflex flexion torque at the MCP joints and reflex electromyographic (EMG) activity in flexor digitorum superficialis. Both measures were greatest in an arm posture of 90° of elbow flexion and neutral shoulder position. Biceps stimulation resulted in greater MCP stretch reflex flexion torque. Fast imposed stretch also elicited reflex EMG activity in nonstretched heteronymous upper limb muscles, both proximal and distal. These results suggest that in the spastic hemiparetic upper limb poststroke, sensorimotor coupling of proximal and distal upper limb segments is involved in both the increased stretch reflex response of the finger flexors and an increased reflex coupling of heteronymous muscles. Both phenomena may be mediated through changes poststroke in the spinal reflex circuits and/or in the descending influence of supraspinal pathways

Cerebellar Learning in an Opponent Motor Controller for Adaptive Load Compensation and Synergy Formation

This paper shows how a minimal neural network model of the cerebellum may be embedded within a sensory-neuro-muscular control system that mimics known anatomy and physiology. With this embedding, cerebellar learning promotes load compensation while also allowing both coactivation and reciprocal inhibition of sets of antagonist muscles. In particular, we show how synaptic long term depression guided by feedback from muscle stretch receptors can lead to trans-cerebellar gain changes that are load-compensating. It is argued that the same processes help to adaptively discover multi-joint synergies. Simulations of rapid single joint rotations under load illustrates design feasibility and stability.National Science Foundation (IRI-90-24877, IRI-87-16960); Office of Naval Research (N00014-92-J-1309); Consejo Nacional de Ciencia y Technología (63462); Air Force Office of Scientific Research (F49620-92-J-0499); Defense Advanced Research Projects Agency (AFOSR 90-0083, ONR N00014-92-J-4015

Peripheral Mediators of Colorectal Nociception and Sensitization

Several ion channels are thought to facilitate colorectal afferent neuron sensitization, which contributes to abdominal pain in irritable bowel syndrome (IBS). In the present work, I hypothesized that two such channels – TRPV1 and P2X3 – cooperate to mediate colorectal pain and hypersensitivity. To test this, I employed TRPV1-P2X3 double knockout (TPDKO) mice and pharmacological antagonists and evaluated combined channel contributions to whole- organism responses to colorectal distension (CRD) and afferent fiber responses to colorectal stretch. Baseline responses to CRD were unexpectedly greater in TPDKO compared with control mice, but zymosan-produced CRD hypersensitivity was absent in TPDKO mice. Relative to control mice, proportions of afferent mechano-sensitive and -insensitive classes were not different in TPDKO mice. Whereas responses of mucosal and serosal class afferents to mechanical probing were unaffected, responses of muscular (but not muscular/mucosal) afferents to stretch were significantly attenuated in TPDKO mice as was sensitization by inflammatory soup of both muscular and muscular/mucosal afferents. In pharmacological studies, the TRPV1 antagonist A889425 and P2X3 antagonist TNP-ATP, alone and in combination, applied onto stretch-sensitive afferent endings attenuated afferent responses to stretch; combined antagonism produced greater attenuation. In the aggregate, these observations suggest that: (1) genetic manipulation of TRPV1 and P2X3 leads to reduction in colorectal mechanosensation peripherally and compensatory changes and/or disinhibition of other channels centrally and (2) combined pharmacological antagonism produces more robust attenuation of mechanosensation peripherally than single antagonism. The relative importance of these channels appears to be enhanced in hypersensitivity, highlighting the potential utility of multi-target pharmacotherapy in IBS

How Spinal Neural Networks Reduce Discrepancies between Motor Intention and Motor Realization

This paper attempts a rational, step-by-step reconstruction of many aspects of the mammalian neural circuitry known to be involved in the spinal cord's regulation of opposing muscles acting on skeletal segments. Mathematical analyses and local circuit simulations based on neural membrane equations are used to clarify the behavioral function of five fundamental cell types, their complex connectivities, and their physiological actions. These cell types are: α-MNs, γ-MNs, IaINs, IbINs, and Renshaw cells. It is shown that many of the complexities of spinal circuitry are necessary to ensure near invariant realization of motor intentions when descending signals of two basic types independently vary over large ranges of magnitude and rate of change. Because these two types of signal afford independent control, or Factorization, of muscle LEngth and muscle TEnsion, our construction was named the FLETE model (Bullock and Grossberg, 1988b, 1989). The present paper significantly extends the range of experimental data encompassed by this evolving model.National Science Foundation (IRI-87-16960, IRI-90-24877); Instituto Tecnológico y de Estudios Superiores de Monterre

Modelling the evolution of cerebral aneurysms: biomechanics, mechanobiology and multiscale modelling

Intracranial aneurysms (IAs) are abnormal dilatations of the cerebral vasculature. Computational modelling may shed light on the aetiology of the disease and lead to improved criteria to assist diagnostic decisions. We briefly review models of aneurysm evolution to date and present a novel fluid-solid-growth (FSG) framework for patient-specific modelling of IA evolution. We illustrate its application to 4 clinical cases depicting an IA. The section of arterial geometry containing the IA is removed and replaced with a cylindrical section: this represents an idealised section of healthy artery upon which IA evolution is simulated. The utilisation of patient-specific geometries enables G&R to be explicitly linked to physiologically realistic spatial distributions and magnitudes of haemodynamic stimuli. In this study, we investigate the hypothesis that elastin degradation is driven by locally low wall shear stress (WSS). In 3 out of 4 cases, the evolved model IA geometry is qualitatively similar to the corresponding in vivo IA geometry. This suggests some tentative support for the hypothesis that low WSS plays a role in the mechanobiology of IA evolution

Microstructural analysis of skeletal muscle force generation during aging.

Human aging results in a progressive decline in the active force generation capability of skeletal muscle. While many factors related to the changes of morphological and structural properties in muscle fibers and the extracellular matrix (ECM) have been considered as possible reasons for causing age-related force reduction, it is still not fully understood why the decrease in force generation under eccentric contraction (lengthening) is much less than that under concentric contraction (shortening). Biomechanically, it was observed that connective tissues (endomysium) stiffen as ages, and the volume ratio of connective tissues exhibits an age-related increase. However, limited skeletal muscle models take into account the microstructural characteristics as well as the volume fraction of tissue material. This study aims to provide a numerical investigation in which the muscle fibers and the ECM are explicitly represented to allow quantitative assessment of the age-related force reduction mechanism. To this end, a fiber-level honeycomb-like microstructure is constructed and modeled by a pixel-based Reproducing Kernel Particle Method (RKPM), which allows modeling of smooth transition in biomaterial properties across material interfaces. The numerical investigation reveals that the increased stiffness of the passive materials of muscle tissue reduces the force generation capability under concentric contraction while maintains the force generation capability under eccentric contraction. The proposed RKPM microscopic model provides effective means for the cellular-scale numerical investigation of skeletal muscle physiology. NOVELTY STATEMENT: A cellular-scale honeycomb-like microstructural muscle model constructed from a histological cross-sectional image of muscle is employed to study the causal relations between age-associated microstructural changes and age-related force loss using Reproducing Kernel Particle Method (RKPM). The employed RKPM offers an effective means for modeling biological materials based on pixel points in the medical images and allow modeling of smooth transition in the material properties across interfaces. The proposed microstructure-informed muscle model enables quantitative evaluation on how cellular-scale compositions contribute to muscle functionality and explain differences in age-related force changes during concentric, isometric and eccentric contractions