An integrated formulation of anisotropic force–calcium relations driving spatio-temporal contractions of cardiac myocytes

Abstract

Isolated cardiac myocytes exhibit spontaneous patterns of rhythmic contraction, driven by intracellular calcium waves. In order to study the coupling between spatio-temporal calcium dynamics and cell contraction in large deformation regimes, a new strainenergy function, describing the influence of sarcomere length on the calcium-dependent generation of active intracellular stresses, is proposed. This strain-energy function includes anisotropic passive and active contributions that were first validated separately from experimental stress-strain curves and stress-sarcomere length curves, respectively. An extended validation of this formulation was then conducted by considering this strainenergy function as the core of an integrated mechano-chemical three-dimensional model of cardiac myocyte contraction, where autocatalytic intracellular calcium dynamics were described by a representative two-variable model able to generate realistic intracellular calcium waves similar to those observed experimentally. Finite-element simulations of the three-dimensional cell model, conducted for different intracellular locations of triggering calcium sparks, explained very satisfactorily, both qualitatively and quantitatively, the contraction patterns of cardiac myocytes observed by time-lapse videomicroscopy. This integrative approach of the mechano-chemical couplings driving cardiac myocyte contraction provides a comprehensive framework for analysing active stress regulation and associated mechano-transduction processes that contribute to the efficiency of cardiac cell contractility in both physiological and pathological contexts.

Mathematical modelling of active contraction in isolated cardiomyocytes

“…15). As in Example 1, we observe a bending behaviour, also in accordance with simulations in Tracqui & Ohayon (2009), and in general expected for an fibre-dependent activation (see Rossi et al, 2012). …”

“…If we regard a compound of cells instead, we may assume that the myocytes are aligned along the direction of the collagen fibres (Stålhand et al, 2011). We specify Algorithm 1 Semi-discrete mechano-chemical coupling Table 3 that agree with the tests in Tracqui & Ohayon (2009).…”

“…As in Tracqui et al (2008) and Tracqui & Ohayon (2009), these are incorporated through an instantaneous increase in the parameter ν 1 (we use ν 1,0 = 2.45ν 1 ) on the desired location. These correspond to the smallest values that are able to onset the calcium wave propagation.…”

“…The term ν 1 represents an inflow flux plus intracellular calcium pulses originated from the asynchrony of calcium pools receptors (Goldbeter et al, 1990), ν 2 and ν 3 account for low and high levels of free cytosolic calcium flux pumped from the sarcoplasmic reticulum, and ν 4 models an efflux of calcium out of the cell following a chemical exchange process (Tracqui & Ohayon, 2009). In Fig.…”

From biological and clinical experiments to mathematical models

“…Article 12 is 'An integrated formulation of anisotropic force-calcium relations driving spatio-temporal contractions of cardiac myocytes' by Tracqui & Ohayon (2009). This article focuses on the dynamics of calcium waves and applies a PDE model to experiments on cardiomyocytes.…”