Effect of biomaterial stiffness on cardiac mechanics in a biventricular infarcted rat heart model with microstructural representation of in situ intramyocardial injectate

Intramyocardial delivery of biomaterials is a promising concept for treating myocardial infarction. The delivered biomaterial provides mechanical support and attenuates wall thinning and elevated wall stress in the infarct region. This study aimed at developing a biventricular finite element model of an infarcted rat heart with a microstructural representation of an in situ biomaterial injectate, and a parametric investigation of the effect of the injectate stiffness on the cardiac mechanics. A three-dimensional subject-specific biventricular finite element model of a rat heart with left ventricular infarct and microstructurally dispersed biomaterial delivered one week after infarct induction was developed from ex vivo microcomputed tomography data. The volumetric mesh density varied between 303 mm-3 in the myocardium and 3,852 mm-3 in the injectate region due to the microstructural intramyocardial dispersion. Parametric simulations were conducted with the injectate’s elastic modulus varying from 4.1 to 405,900 kPa, and myocardial and injectate strains were recorded. With increasing injectate stiffness, the end-diastolic median myocardial fibre and cross-fibre strain decreased in magnitude from 3.6% to 1.1% and from −6.0% to −2.9%, respectively. At end-systole, the myocardial fibre and cross-fibre strain decreased in magnitude from −20.4% to −11.8% and from 6.5% to 4.6%, respectively. In the injectate, the maximum and minimum principal strains decreased in magnitude from 5.4% to 0.001% and from −5.4% to −0.001%, respectively, at end-diastole and from 38.5% to 0.06% and from −39.0% to −0.06%, respectively, at end-systole. With the microstructural injectate geometry, the developed subject-specific cardiac finite element model offers potential for extension to cellular injectates and in silico studies of mechanotransduction and therapeutic signalling in the infarcted heart with an infarct animal model extensively used in preclinical research. ### Competing Interest Statement The authors have declared no competing interest. * Symbol : Description a : Material parameter, dimension of stress afs : Material parameter defining coupling from in the fibre and sheet directions, with a dimension of stress ai : Material parameter, defined for i = f and s in the fibre and sheet directions, respectively, with stress dimension ā, āi, āfs : Govern the isotropic response of the infarcted myocardium B : Governs the shape of peak isometric tension-sarcomere length relation B : Dimensionless material parameter in Holzapfel model bfs : Material parameter defining coupling from in the fibre and sheet directions, dimensionless bi : Material parameter, defined for i = f and s in the fibre and sheet directions, respectively, dimensionless C10 : Coefficient used in Abaqus to describe the material stiffness in a Neo-Hookean strain energy density function Ca : Peak intracellular calcium concentration D : Parameter for elastic materials defining the compressibility of the material E : Elastic modulus ECa50 : Length-dependent calcium sensitivity H : Parameter to define the pathological degree of the tissue I4f : Transversely isotropic invariant in the fibre direction I4s : Transversely isotropic invariant in the sheet direction I8fs : Orthotropic invariant from coupling in fibre and sheet direction Ii : Isotropic invariants in principal directions J : Third deformation gradient invariant as measures of the volume change of compressible materials P : Parameter scaling the isotropic response of the diseased tissue T : Stress tensor T(a) : Active stress tensor T(p) : Passive stress tensor uc : Unit vector in the circumferential direction ul : Unit vector in the longitudinal direction W : Strain energy density function αh : Helix angle αt : Transverse angle εEL : Element strain; mean value of strains at integration points in an element εIP,i : Strain at integration point i in an element with i = 1 to 4 K : Bulk modulus N : Poisson’s ratio Σ : Stress