A simple model of cardiac muscle for multiscale simulation: Passive mechanics, crossbridge kinetics and calcium regulation

Syomin, F. A.; Tsaturyan, Andrey K.

doi:10.1016/j.jtbi.2017.02.021

Cited by 14 publications

(34 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Starling's law for a whole heart is usually characterized by the slope of the curve connecting the end‐systolic points on the pressure‐volume loops obtained at different preload (end‐diastolic volume or pressure). The implementation of the Starling's law by our multiscale model is provided by the cell‐level model of LV myocardium that reproduces so‐called length‐dependent activation, which means an increased Ca 2+ sensitivity of regulatory proteins at higher sarcomere length . Although we did not try to match parameters of our cell model to obtain the best fit to a particular data set, the model reproduced typical characteristics of a normal heartbeat including changes in LV shape and the ventricular pressure (Figures ).…”

Section: Discussionmentioning

confidence: 99%

“…The ventricular wall was treated as an incompressible transversely isotropic continuous medium. The constitutive equation for myocardium was as follows:

boldT = T_{is} - p boldE + ((), \frac{F_{italicact} + F_{italictit}}{l_{s} / l_{s 0}}) boldB,

where T is is an isotropic part of stress tensor T , which was specified by a strain‐energy exponential function depending on the first and the second invariants of the right Cauchy‐Green strain tensor, p is pressure caused by myocardium incompressibility, E is a unit tensor, and the last term is an anisotropic stress caused by forces applied along muscle fibres to the area perpendicular to the fibre direction. The tensor B is a dyadic product of the strained unit vectors aligned with muscle fibres, and scalars F act and F tit are an active tension generated by muscle and a passive tension of titin, a sarcomere protein connecting myosin filaments to Z‐discs.…”

Section: Methodsmentioning

confidence: 99%

“…The active tension F act produced by the actin‐myosin interaction was specified as follows:

F_{act} = N \cdot W ((), l_{s}) \cdot e \cdot n \cdot ((), δ + θ ((), δ)),

where n and δ are the fraction of actin‐bound myosin heads in the overlap zone of the thin (actin) and thick (myosin) filaments in sarcomeres and the ensemble‐average strain of the heads, respectively; N and e are the number of myosin heads per unstrained cross‐sectional area in a half‐sarcomere thick layer of cardiac muscle and stiffness of an actin‐bound myosin head; θ is a fraction of the strongly bound force‐generating myosin heads among all actin‐bound heads; and W is the normalized length of the overlap zone. The kinetics of the actin‐myosin interaction and its Ca 2+ regulation was described earlier . Variables n and δ are described by kinetic ODEs assuming that attachment and detachment of myosin heads to/from actin depended only on δ .…”

Section: Methodsmentioning

confidence: 99%

“…Intracellular calcium concentration C Ca was determined by the following processes: calcium influx, which was set by a given time‐function I Ca ( t ), calcium uptake, calcium binding to Tn, and other Ca 2+ buffers . Here, we had modified the kinetic equation for C Ca slightly compared with Syomin and Tsaturyan where the first‐order kinetics of Ca 2+ uptake was assumed. Here, it had a form

((), 1 + \frac{k_{B} B_{Ca}}{{((), C_{Ca} + k_{B})}^{2}}) \frac{\partial C_{Ca}}{\partial t} = I_{Ca} ((), t) - \frac{Y_{1 Ca} ((), C_{Ca}^{2} - C_{0}^{2})}{C_{Ca}^{2} + Y_{2 Ca}^{2}} - C_{Tn} \frac{\partial ((), A_{1} W ((), l_{S}) + A_{2} ((), 1 - W ((), l_{S})))}{\partial t},

where k B and B Ca are the half‐saturating Ca 2+ concentration and the total concentration of Ca 2+ buffer in the cytosol, C Tn is the total concentration of Tn, Y 1Ca is the uptake rate, and Y 2Ca and C 0 are constant parameters.…”

Section: Methodsmentioning

confidence: 99%

“…Because of the left ventricle is the major blood pump in the heart, one can use a complex multiscale model to simulate only the LV contraction, while other heart chambers can be treated as reservoirs with time‐dependent elasticity within a lumped parameter model. Previously, we developed a new simple model of myocardium based on a kinetic model of muscle contraction and its activation . The model described all major properties revealed in mechanical experiments with skeletal and cardiac muscles: steady‐state force and stiffness dependence on shortening or lengthening velocity, mechanical responses to sudden changes in muscle length, or load.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Multiscale simulation of the effects of atrioventricular block and valve diseases on heart performance

Syomin

Zberia

Tsaturyan

2019

Numer Methods Biomed Eng

Self Cite

View full text Add to dashboard Cite

A new mathematical model of the cardiovascular system is proposed. The left ventricle is described by an axisymmetric multiscale model where myocardium is treated as an incompressible transversely isotropic medium with a realistic distribution of fibre orientation. Active tension and its regulation by Ca2+ ions are described by our recent kinetic model. A lumped parameter model is used for the simulation of blood circulation, in which the left and right atria and the right ventricle are described by a system of ordinary differential equations for active pressure‐volume relationships. The stress and strain of the left ventricle myocardium were calculated by the finite element method implemented by the authors. The changes in the haemodynamics upon changes in preload of a healthy heart, upon physical exercise, and in case of atrioventricular block with different types of arrhythmias were simulated. To simulate the effect of stenosis or regurgitation of the aortic or mitral valves, the hydraulic and inertial flow resistances of the heart valves were set as functions of their orifice areas. The model reproduced a number of phenomena observed in clinical practice, including the classification of the severity of valve disease.

show abstract

Section: Discussionmentioning

confidence: 99%

“…The ventricular wall was treated as an incompressible transversely isotropic continuous medium. The constitutive equation for myocardium was as follows:

boldT = T_{is} - p boldE + ((), \frac{F_{italicact} + F_{italictit}}{l_{s} / l_{s 0}}) boldB,

Section: Methodsmentioning

confidence: 99%

“…The active tension F act produced by the actin‐myosin interaction was specified as follows:

F_{act} = N \cdot W ((), l_{s}) \cdot e \cdot n \cdot ((), δ + θ ((), δ)),

Section: Methodsmentioning

confidence: 99%

((), 1 + \frac{k_{B} B_{Ca}}{{((), C_{Ca} + k_{B})}^{2}}) \frac{\partial C_{Ca}}{\partial t} = I_{Ca} ((), t) - \frac{Y_{1 Ca} ((), C_{Ca}^{2} - C_{0}^{2})}{C_{Ca}^{2} + Y_{2 Ca}^{2}} - C_{Tn} \frac{\partial ((), A_{1} W ((), l_{S}) + A_{2} ((), 1 - W ((), l_{S})))}{\partial t},

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multiscale simulation of the effects of atrioventricular block and valve diseases on heart performance

Syomin

Zberia

Tsaturyan

2019

Numer Methods Biomed Eng

Self Cite

View full text Add to dashboard Cite

show abstract

Effect of strain‐dependent conduction slowing on the re‐entry formation and maintenance in cardiac muscle: 2D computer simulation

Syomin

Galushka

Tsaturyan

2023

Numer Methods Biomed Eng

Self Cite

View full text Add to dashboard Cite

The effect of mechano‐electrical feedback on re‐entry formation and maintenance was studied using a model of myocardial electromechanics that accounts for two components of myocardial conductivity and delayed strain‐dependent changes in membrane capacitance that causes a conduction slowing. Two scenarios were simulated in 2D numerical experiments: (i) propagation of an excitation–contraction wave beyond the edge of a nonconductive nonexcitable obstacle; (ii) circulation of a re‐entry wave around a nonconductive nonexcitable obstacle. The simulations demonstrated that the delayed strain‐dependent deceleration of the conduction waves promotes the detachment of the excitation‐contraction waves from the sharp edge of an elongated obstacle and modulates the re‐entry waves rotating around a compact obstacle. The data show that the mechano‐electrical feedback, together with an increase in the stimulation frequency and an increase in the excitation threshold, is an arrhythmogenic factor that must be taken into account when analyzing the possibility of the re‐entry formation.

show abstract

Multiscale modeling of ventricular–vascular dysfunction in pulmonary arterial hypertension

Vélez-Rendón

Valdez‐Jasso

2019

Current Opinion in Biomedical Engineering

View full text Add to dashboard Cite

A simple model of cardiac muscle for multiscale simulation: Passive mechanics, crossbridge kinetics and calcium regulation

Cited by 14 publications

References 57 publications

Multiscale simulation of the effects of atrioventricular block and valve diseases on heart performance

Multiscale simulation of the effects of atrioventricular block and valve diseases on heart performance

Effect of strain‐dependent conduction slowing on the re‐entry formation and maintenance in cardiac muscle: 2D computer simulation

Multiscale modeling of ventricular–vascular dysfunction in pulmonary arterial hypertension

Contact Info

Product

Resources

About