Stress Relaxation of Porcine Gluteus Muscle Subjected to Sudden Transverse Deformation as Related to Pressure Sore Modeling

Computational studies of deep pressure sores (DPS) in skeletal muscles require information on viscoelastic constitutive behavior of muscles, particularly when muscles are loaded transversally as during bone-muscle interaction in sitting and lying immobilized patients. In this study, we measured transient shear moduli $G(t)$ of fresh porcine muscles in vitro using the indentation method. We employed a custom-made pneumatic device that allowed rapid $(2000mm∕s)$$4mm$ indentations. We tested 8 gluteus muscles, harvested from 5 adult pigs. Each muscle was indented transversally (perpendicularly to the direction of fibers) at 3 different sites, 7 times per site, to obtain nonpreconditioned (NPC) and preconditioned (PC) $G(t)$ data. Short-term $(GS)$ and long-term $(GL)$ shear moduli were obtained directly from experiments. We further fitted measured $G(t)$ data to a biexponential equation $G(t)=G1∙exp(−t∕τ1)+G2∙exp(−t∕τ2)+G∞$⁠, which provided good fit, visually and in terms of the correlation coefficients. Typically, plateau of the stress relaxation curves (defined as 10% difference from final $GL$⁠) was evident $∼20s$ after indentation. Short-term shear moduli $GS$ (mean NPC: $8509Pa$⁠, PC: $5711Pa$⁠) were greater than long-term moduli $GL$ (NPC: $609Pa$⁠, PC: $807Pa$⁠) by about an order of magnitude. Statistical analysis of parameters showed that only $G2$ was affected by preconditioning, while $GL$⁠, $GS$⁠, $G∞$⁠, $τ1$⁠, $τ2$⁠, and $G1$ properties were unaffected. Since DPS develop over time scales of minutes to hours, but most stress relaxation occurs within $∼20s$⁠, the most relevant property for computational modeling is $GL$ (mean $∼700Pa$⁠), which is, conveniently, unaffected by preconditioning.