Microstructural analysis of deformation-induced hypoxic damage in skeletal muscle

Abstract

Deep pressure ulcers are caused by sustained mechanical loading and involve skeletal muscle tissue injury. The exact underlying mechanisms are unclear, and the prevalence is high. Our hypothesis is that the aetiology is dominated by cellular deformation (Bouten et al. in Ann Biomed Eng 29:153-163, 2001; Breuls et al. in Ann Biomed Eng 31:1357-1364, 2003; Stekelenburg et al. in J App Physiol 100(6):1946-1954, 2006) and deformation-induced ischaemia. The experimental observation that mechanical compression induced a pattern of interspersed healthy and dead cells in skeletal muscle (Stekelenburg et al. in J App Physiol 100(6):1946-1954, 2006) strongly suggests to take into account the muscle microstructure in studying damage development. The present paper describes a computational model for deformation-induced hypoxic damage in skeletal muscle tissue. Dead cells stop consuming oxygen and are assumed to decrease in stiffness due to loss of structure. The questions addressed are if these two consequences of cell death influence the development of cell injury in the remaining cells. The results show that weakening of dead cells indeed affects the damage accumulation in other cells. Further, the fact that cells stop consuming oxygen after they have died, delays cell death of other cells.

Fig. 1

Transverse cross-section of skeletal muscle after 2 h of mechanical loading, stained with Gomori’s trichrome: the damage pattern is a mixture of healthy (dark) and necrotic fibres (light, arrows) (Stekelenburg et al. 2006, with permission)

Fig. 2

Outline of finite element model: left Compression is applied to a mesh consisting of cells, ecm and capillaries, resulting in decreased capillary-cross-sections that determine the oxygen supply for the diffusion model. Healthy cells are oxygen sinks in the oxygen diffusion model, in which the partial oxygen pressures (pO₂) are calculated. When the resulting pO₂’s remain above a threshold, the tissue remains healthy, but if they fall below a threshold, damage starts to accumulate (see right). This leads to cell death for some cells, of which the properties change subsequently. This has consequences for both the deformation and diffusion, necessitating another loop of the model if not all cells have died yet. Right In the damage model, damage in each cell is updated according to the current extent of hypoxia. When the damage in all cells is still below the threshold for cell death, time is updated and damage accordingly until damage does exceed the death threshold in one or more cells

Fig. 3

Mesh and boundary conditions for deformation model: the mesh consists of cells (light grey), ecm (dark grey) and capillaries (holes, white). Movement in vertical direction is suppressed along the lower boundary of the mesh, and a downward displacement is prescribed on the upper boundary

Fig. 4

Compression versus time curves for hypoxic cell death in cases stopy (consumption stops in dead cells) and stopn (dead cells continue to consume oxygen): The graphs show from top to bottom the time it takes for respectively 3, 11 and all of the cells to die at compression levels up to 22%. In case stopy, cells die later than in case stopn. This effect is more pronounced after more cells have died and at lower compression levels

Fig. 5

Compression versus time curves for hypoxic cell death in cases propy (mechanical properties change in dead cells) and propn (mechanical properties do not change in dead cells): The graphs show from top to bottom the time it takes for respectively 1, 2, 3 and all of the cells to die at compression levels up to 19%. For high compression levels, cells eventually die later in case propy than in case propn