Introduction

Pressure ulcer is tissue damage under prolonged mechanical loading. Persons with spinal cord injury confined to seats and other immobile patients confined to beds are likely to suffer from pressure ulcers.1,4,7 There are, generally speaking, two forms of pressure ulcers, superficial ulcers and deep tissue injury (DTI).1,39 DTI can develop into extensive ulceration fast and are more difficult to prevent and treat than superficial ulcers.3 Muscle tissues around skeletal prominences are highly susceptible to excessive internal stresses and strains caused by skeletal and epidermal loadings.43,54 Tissue compression beyond certain thresholds can directly cause tissue necrosis leading to DTI. Excessive compressive deformation can cause skeletal muscle cell necrosis.5,6,15,35 The duration that muscle cells can tolerate a given compression depends on the compressive stress level.65 High compressive stress can cause muscle cell damage in very short time and low compressive stress, if prolonged, can also cause cell damage. The lymphatic system removes the normally released biowastes and excess tissue fluid from the interstitial space to the circulation. Tissue compression can potentially compromise lymphatic transport and cause accumulation of metabolic biowastes and toxins released from the damaged tissues, which might contribute to further tissue damage.25,42,49

If the mechanical loading exceeds a certain threshold, the muscle cells may undergo apoptosis or necrosis,15,34,51,65 leading to tissue failure. Apoptosis, which is programmed cell death, has been shown as a result of mechanical stress in muscle cells.8,29 Intracellular caspases known as the effectors of apoptosis could be induced by mechanical force.22 When the intact cell membrane was compromised under compression, the caspases and other apoptotic agonists might be released from the damaged cell. Cytokines like tumor necrosis factors (TNF) and interleukins can be secreted by muscle cells in various situations.32,46,47 TNF-α possesses multiple biology functions in different cell types.61 Mechanical loading and injury can induce human skeletal muscle cells to release cytokines that can influence neutrophil responses.57 Stressed or injured muscle cells produce TNF-α acting as a local mediator.18,31 The increase of plasma membrane permeability under mechanical stress52,53 can allow a massive influx of Ca2+ that can increase mitochondrial generation of reactive oxygen species (ROS).21 The caspases, cytokines and ROS might be among the metabolic biowastes and toxins being accumulated in compressed tissues. Few literatures reported on the effects of the biowastes released from the mechanically damaged muscle cells on the normal cells. Such effects could be important to the propagation of DTI.

Cytokines like TNF-α can induce TNF receptors in skeletal muscle cells67 and suppress protein synthesis.14 Furthermore, TNF-α can also induce changes in the mechanical properties of cells24 and reorganization of actin cytoskeleton.62 Caspases could affect the mechanical properties of cells by cytoskeletal remodeling.48,55 ROS could also affect the cell mechanical responses.63,65 Accumulated biowastes secreted from damaged muscle cells might affect the mechanical properties of the surrounding muscle cells, causing more cells to be damaged under subsequent mechanical loadings.

Finite element (FE) modeling has been used in analyzing the internal conditions related to the etiology of DTI.38,44,60,64 Linder-Ganz et al.37 first established the human buttock FE model based on the morphological data from open MRI on specific seated human subjects. A semi-3D FE model representing the cross section of a human buttock seated on a cushion was developed in this study based on the work of Linder-Ganz and Gefen36 and Xiao et al.64 The above models were used to describe how the high stresses around the ischial tuberosity (IT) caused the muscle tissue damage propagation from the deep tissue to the skin. Multiphysics simulation was used in many biomechanically coupled problem such as the coupling between fluid flow and structural deformation on aortic valve functions,23 electrochemohydraulic transports in cortical bone,26 chemoelectromechanical activities in skeletal muscle,20 and the coupling of temperature and flow field in arteries.30 Multiphysics modeling was a good tool to study the diffusion of biowastes in the structurally deformed muscle tissue. Multiphysics models of cellular-scale transport in deformed muscles,50 oxygen diffusion in skeletal muscle cells under compressive deformation28 and intracellular oxygen level of muscle cells under stretching27 focused on the roles of cellular chemical diffusion in DTI. Relatively speaking, little attention has been given to modeling the coupled effects of tissue-scale mechanical loading and biowastes diffusion on muscle damage propagation in DTI.

We hypothesized that biowastes released by mechanically damaged muscle cells could be toxic to other muscle cells in the neighborhood and would compromise the capability of the surrounding muscle cells to withstand compressive damage. We built multiphysics FE model to reveal the importance of biowastes toxification in the etiology of DTI.

Materials and Methods

Cell Culture

C2C12 mouse skeletal myoblasts (ATCC, Manassas, USA) were grown in tissue culture dishes (SPL Lifesciences, Korea) with growth medium consisting of high-glucose Dulbecco’s Modified Eagle Medium (Gibco, Life Technologies, USA), 10% fetal bovine serum (Gibco, Life Techologies, USA) and 1% Penicillin–Streptomycin (Gibco, Life Technologies, USA). The myoblasts were trypsinized by 0.25% Trypsin–EDTA (1×, Gibco, Life Technologies) for the cell passage process every three days to maintain the continuous passage. The myoblasts in this study were of passage 15–19. Myoblasts were seeded in low density (~2 × 104 cells cm−2) and cultured in monolayer in six-well plates and in 35 mm diameter tissue culture dishes (SPL Lifesciences, Korea) in a 37 °C, 5% CO2 humidified incubator for two days. The monolayers were about 80% confluent at the time of the experiments.

Collection of Biowastes

Two kinds of agarose gels were prepared by dissolving 0.5% (w/v) and 2% (w/v) agarose (Biosharp, Hefei, China) powder in Dulbecco’s phosphate-buffered saline (PBS, 1×, Gibco, Life Technologies) at 100 °C. The agarose solution was dispensed into the 35 mm petri dish and then cooled in room condition to form a 3 mm thick gel layer. A cylindrical gel of thickness 3 mm and diameter 14.8 mm was cut out and placed over a monolayer of myoblasts.

The compressive stress applied on the monolayer of myoblasts was provided by a Mach-1™ micromechanical system (Biomomentum Inc) at 37 °C and 5% CO2. A 30% uniaxial compression of the agarose gel was conducted in the Mach-1™ micromechanical testing system with a flat platen of diameter 25.4 mm. After the flat platen reached the top surface of the gel, 1 mL of culture medium was added into the tissue culture dish. About 150 Pa compressive stress was generated on the myoblasts under the 0.5% agarose gel for 15 min or 3 h with 30% gel compressive strain. About 3000 Pa compressive stress was generated on the myoblasts under the 2% agarose gel for 15 min or 3 h by 30% gel compressive strain. The details of this loading methodology was reported earlier.65

After compression with the specific intensity and duration, 1 mL of the culture medium containing the biowastes secreted by the damaged myoblasts was collected. Four groups of biowastes were collected—namely those from cells damaged under (i) prolonged low compressive stress (PLCS, i.e., 150 Pa for 3 h), (ii) prolonged high compressive stress (PHCS, i.e., 3000 Pa for 3 h), (iii) short-term high compressive stress (SHCS, i.e., 3000 Pa for 15 min) and (iv) short-term low compressive stress (SLCS, i.e., 150 Pa for 15 min).

Cell Toxicity Test

Myoblasts in six-well plates were cultured for 1, 3 and 5 h in the biowastes collected from the mechanically damaged myoblasts (SHCS and PLCS) as the treated groups. Myoblasts cultured in fresh culture medium were used as control. Propidium Iodide (PI) (Sigma, USA) at 10 μg mL−1 was used to stain the nuclei of the damaged cells with red fluorescence for cell damage assessment. Fluorescence microscopy was performed in an inverted microscope (ECLIPSE Ti, Nikon). A G-2B filter was used to capture the red fluorescence of PI. Images were taken at ×100 magnification with a CCD camera (DS-Fi1c-L3, Nikon Digital Sight). PI stained nuclei were counted using the ImageJ 1.46r (NIH). At the end of the experiment, the total number of the myoblasts in each well was counted after fixing the cells with 4% paraformaldehyde together with 0.1% Triton X-100 and PI staining. The toxicity of the biowastes was measured by calculating the percentage of PI-stained myoblasts in the mere presence of the biowastes to the total number of myoblasts in each well. One-way Analysis of variance (ANOVA) at 0.05 level of significance was used to test the significant difference in toxicity among the biowastes treatments.

Compressive Stress Damage Threshold

The method to determine the compressive stress damage threshold described in Yao et al.65 was used in this study. Briefly recapped, the myoblasts monolayer immerged in 1 mL of media with biowastes was covered under a 3 mm-thick agarose gel. The gel was loaded by a half-spherical indenter of 6.38 mm diameter in a Mach-1™ micromechanical testing system at 37 °C with 5% CO2 at a rate of 0.01 mm s−1 until the deformation at the center of the gel reached 50%. The radially varying compressive stress field generated by the indentation at the bottom surface of the gel was assumed effectively acting on the top surface the monolayer of myoblasts. Myoblasts treated by the SHCS biowastes were indented for 30, 70, 140, 160, 180 and 300 min and myoblasts treated by the PLCS biowastes were compressed for 15, 30, 50, 70, 100, 140 and 180 min. Myoblasts treated by the PHCS and SLCS biowastes were also compressed for 70 min for two-way ANOVA to determine the main experimental factor associated with the biowastes causing significant changes on the compressive damage threshold. The compressive stress profile applied on the myoblasts was adopted from the published data in Yao et al. simulating the same experimental configuration.65 PI was used to assess the spatial profiles of percentages of cells dead after indentation. The damage threshold of myoblasts was determined by the correlation between the cell damage percentage profile and the compressive stress profile acting on the myoblasts monolayer. With the criteria that the percentage cell damage within the damaged threshold circle was at least 3 times that in the peripheral region, the relation between the compressive damage threshold and the indentation duration was determined. Nonparametric ANOVA was performed using Kruskal–Wallis test with 0.05 level of significance to test the effects of the two kinds of biowastes treatments. The experimental data on the compressive stress threshold vs loading duration for each treatment of biowastes were fitted with a decreasing Boltzmann-type sigmoid function first developed by Linder-Ganz et al.:34

$$\sigma (t) = \frac{K}{{1 + e^{{a(t - t_{0} )}} }} + C$$
(1)

where K, \(t_{0}\), α and C are determined by least square curve-fitting; and \(\sigma (t)\) is the compressive stress threshold.

Multiphysics Finite Element Modeling

The biowastes generated by the mechanically damaged muscle cells could diffuse in the muscle tissue and lower the capability of the surrounding muscle cells to resist against compression damage by lowering the compressive damage threshold of the cells. Meanwhile, the biowastes released from the mechanically damaged cells may also depend on the loading scenarios. The coupling between the solid mechanics and the chemical diffusion of biowastes in the tissue level was modeled on the COMSOL Multiphysics platform. To simulate the damage propagation of DTI in the muscle tissues, a semi-3D FE cross-sectional model of a buttock seated on a cushion was developed based on the work of Linder-Ganz and Gefen36 and the subsequent work of Xiao et al.64 We also adopted the damage laws to determine the tissue damage by following the concepts in the original work of Linder-Ganz and Gefen.36 As shown in Fig. 1, the buttock FE model consisted of four parts: IT, muscle, fat and skin (as one part), and cushion. The slice thickness of all the parts was set as 4 mm. All the parts were meshed with tetrahedral elements totaling 21,621 in number. Unstructured quadratic tetrahedral elements were meshed in the Solid Mechanics module and unstructured linear tetrahedral elements were meshed in the Transport of Diluted Species module for the chemical diffusion of biowastes.

Figure 1
figure 1

Finite element model (COMSOL) of a human buttock (half) on an elastic cushion.

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The elastic moduli of IT and cushion was set as 7 GPa12 and 1 MPa64 respectively, with Poisson’s ratio ν = 0.3. Muscle and fat-skin layers were assumed to be hyperelastic. The Poisson’s ratios of muscle and fat-skin were assumed to be 0.49, as nearly incompressible. The Neo–Hookean strain energy potential for hyperelasticity was in the following form:

$$U_{\text{neo}} = \frac{1}{2}G\left( {\bar{I}_{1} - 3} \right) + \frac{1}{2}K\left( {J_{\text{el}} - 1} \right)^{2}$$
(2)

where U is the strain energy per unit reference volume; \(J_{\text{el}}\) is the elastic volume ratio; \(\bar{I}_{1}\) is the first deviatoric strain invariant defined as:

$$\bar{I}_{1} = \bar{\lambda }_{1}^{2} + \bar{\lambda }_{2}^{2} + \bar{\lambda }_{3}^{2}$$
(3)

\(\bar{\lambda }_{i}\) are the deviatoric principal stretches \(\bar{\lambda }_{i} = J^{{ - \frac{1}{3}}} \lambda_{i}\); \(\lambda_{i}\) are the principal stretches; J is the total volume ratio; G is the long-term shear modulus as we only consider the equilibrium minimum principal stress and K is the bulk modulus calculated given the shear modulus and Poisson’s ratio using the following equation:

$$\upsilon = \frac{3(K/G) - 2}{6(K/G) + 2}$$
(4)

The long-term shear modulus G was taken to be 600 Pa for the muscle layer45 and 143 Pa for the fat-skin layer.9,10,17,56,64 The bulk modulus K was calculated to be 29.80 kPa for the muscle layer and 7.10 kPa for the fat-skin layer. The nodes at the bottom of the cushion were fixed in all directions. The penalty method was used for the contact pressure at all the interfaces between different parts of the model. The contact pressure penalty factor was taken to be 2 MPa m−1 between cushion and fat-skin, 6 MPa m−1 between fat-skin and IT, 19 MPa m−1 between muscle and IT as well as between muscle and fat-skin. Displacement boundary condition being free in-plane and fixed out-of-plane was applied at both the anterior and posterior surfaces of all the parts. A displacement of 9 mm was applied on the superior surface of IT.33,37,41

The transport of biowastes generated by the damaged muscle cells through the undeformed skeletal muscle tissue was modeled in COMSOL by the following chemical diffusion equation:

$$\frac{\partial C}{\partial t} + \nabla \cdot ( - D\nabla C) = R_{C}$$
(5)

where C is the concentration of the biowastes, R C is the release rate of biowastes from damaged muscle cells, and D is the diffusion coefficient of the biowastes in muscle tissue. Temperature was assumed constant and uniform. For parametric analysis, D was allowed to range from 10−10 to 10−7 m2 s−1 with 10−9 m2 s−1 as the reference setting.2,11,19,58,59 Muscle cells remain intact when the compressive stress and the loading duration were below the compressive damage stress-duration threshold curve, i.e. within the safe region. The region above the compressive damage stress-duration threshold curve is referred as the damage region, where muscle cells will be mechanically damaged. When the muscle cells are in the safe region, R C = 0, which means there are no biowastes released from the cells. When the muscle cells are in the damage region, R C becomes non-zero, ranging from 10−7 to 100 mol m−3 s−1 for parametric analysis with 10−6 mol m−3 s−1 as the reference setting. We assumed the damaged cells could continuously release biowastes at a certain rate only after loading duration t0 as timeline of releasing biowastes which ranging from 30 to 180 min with 120 min as the reference setting. The release rate of biowastes from the damaged muscle cells was governed by the following equation:

$$R_{\rm C} = \left\{ {\begin{array}{*{20}c} R & {{\text{when}}\;\sigma _{{33}} > \sigma _{t} \;{\text{and}}\;t{\text{ > }}\;{{t}}_{0} } \\ 0 & {{\text{Otherwise}}} \\ \end{array} } \right.$$
(6)

where \(\sigma_{33}\) is the minimum principal stress in the muscle tissue; \(\sigma_{t}\) is the compressive stress damage threshold of muscle cells; and t is the loading duration in the unit of minute. The compressive damage stress-duration threshold curve determined the damage of muscle cells. For normal myoblasts, the threshold curve was reported to take the following form:65

$$\sigma_{N} = \frac{340}{{1 + e^{0.118(t - 160.3)} }} + 8.95$$
(7)

\(\sigma_{N}\) is the compressive stress damage threshold in the unit of pascal. We assumed the compressive damage stress-duration threshold of muscle tissues was similar to that of the myoblasts. From the in vitro experimental results reported later, we could represent the compressive damage stress-duration threshold of the myoblasts after the treatment of biowastes as \(\sigma_{\text{B}}\) for all concentration of biowastes. The compressive stress damage threshold for the muscle tissues was defined as:

$$\sigma_{t} = \left\{ {\begin{array}{*{20}c} {\sigma_{N} \quad {\text{ when }}C < C_{t} } \\ {\sigma_{\text{B}} \quad {\text{ when }}C \ge C_{t} } \\ \end{array} } \right.$$
(8)

where C t is the chemical damage threshold of muscle cells for biowastes effect. For parametric analysis, C t was allowed to range from 0 to 10−3 mol m−3 with 0 mol m−3 as reference setting. The biowastes can affect normal muscle cells when its concentration gets above a certain threshold C t. The distribution of minimum principal stress in the muscle layer and the diffusion of biowastes could be simulated as coupled processes of mechanical deformation and chemical diffusion. The solid mechanics module and biowastes diffusion module are one-way coupled in COMSOL. The diffusion equation was solved in the undeformed geometry with linear tetrahedral elements and the generation of the chemicals was based on the compressive stress results in the solid mechanics module. The diffusion coefficient of the biowastes was independent on the deformation results in the solid mechanics module. The propagation of muscle damage was presented by the percentage of damaged muscle tissue volume calculated based on the compressive stress damage threshold \(\sigma_{t}\) at each time point. The release rate of biowastes from damaged cells, the chemical damage threshold for biowastes, the diffusion coefficient of biowastes in muscle tissue and timeline of releasing biowastes were parametrically analyzed to show how these factors may influence the propagation of muscle damage.

Results

Biowastes Toxicity

Normal myoblasts were treated for 1, 3, and 5 h with the PLCS biowastes. Comparing the percentages of cells damaged, two-way ANOVA showed significant difference between the PLCS group and the non-treated control group (p < 0.05) (Fig. 2a). This showed that the biowastes released by muscle cells damaged under chronic mechanical loading showed significant toxicity to other normal muscle cells. The biowastes treatment duration did not exhibit statistically significant effects among the three treatment durations.

Figure 2
figure 2

(a) Percentages of myoblasts dead after treatments with PLCS biowastes for 1, 3, and 5 h showed significant increases compared to those in the control, indicating the toxicity of the PLCS biowastes. (*p < 0.05). (b) Percentages of myoblasts dead after treatments with SHCS biowastes for 1, 3, and 5 h showed no significant differences compared to those in the control, indicating the non-toxicity of the SHCS biowastes.

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Normal myoblasts were treated for 1, 3, and 5 h with the SHCS biowastes. Comparing the percentages of cell damaged in the SHCS group with those in the non-treated group, two-way ANOVA showed no significant difference between the two groups (p > 0.05) (Fig. 2b). The statistical power of 0.8 was satisfied with a sample size of 3 with type I error less than 0.05 for two-tailed test for the three biowastes treatment durations. This showed that there was no significant lethal effect of the biowastes released by cells acutely damaged under brief exposure to very high stress.

Damage Stress Threshold

The typical spatial profiles of the percentage cell damage in the PLCS and SHCS groups were shown in Fig. 3a. The extent of cells damaged expanded with increasing indentation duration. Around the center of the indented area, longer loading duration led to higher percentages of cells damaged in both groups. (Table 1).

Figure 3
figure 3

(a) Percentages of myoblasts damaged under indentation after PLCS and SHCS biowastes treatments. Results were derived from the PI fluorescent images taken after different indentation durations. (b) The relationships between the compressive stress thresholds and the tolerance durations of myoblasts with PLCS and SHCS biowastes treatments, as compared to myoblasts without pre-treatment with PLCS/SHCS biowastes.64 Curve-fitted parameters are listed in Table 2.

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Table 1 The peak percentages of myoblasts damaged in the PLCS and the SHCS biowastes treated groups as compared to the non-treated myoblasts64 for various indentation durations.
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The relationship between the compressive stress threshold and the tolerance duration of PLCS and SHCS biowastes treated cells were shown in Fig. 3b. For the indentation durations of 30, 70, and 140 min, the compressive stress thresholds of the PLCS group were significantly (p < 0.05) lower than those at the corresponding time points for the SHCS group (Fig. 3b). Furthermore, the SHCS biowastes treated cells showed no significant difference when compared to the data on normal cells reported by Yao et al.65 The biowastes released from the myoblasts damaged under PLCS could significantly weaken the capability of the otherwise normal myoblasts to resist compressive damage, while the biowastes secreted from myoblasts damaged under SHCS did not show such effect significantly. The parameters from curve-fitting the experimental damage thresholds of compressive stress versus tolerance duration were shown in Table 2 for the PLCS and SHCS groups. The compressive damage stress-duration threshold of muscle cells after biowastes treatments could be described as below:

$$\sigma_{B} = \frac{347}{{1 + e^{0.0527(t - 54.7)} }} + 10.83$$
(9)
Table 2 The model parameters obtained from curve-fitting the experimental results of the PLCS and the SHCS biowastes treated groups using the sigmoid function represented by Eq. (1), as compared to the non-treated myoblasts.64
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The compressive damage thresholds at loading duration 70 min of myoblasts treated by biowastes collected from damaged myoblasts in SHCS, PHCS, SLCS and PLCS groups were shown in Fig. 4. Two-way ANOVA with Tukey’s post hoc test showed that loading duration was the main factor that influenced the effect of biowastes secreted from the damaged muscle cells. Cell damage caused by short loading duration could not generate biowastes as toxic as those from prolonged loading duration. Cell damage caused by prolonged loading could generate biowastes that could lower the compressive damage stress-duration threshold of normal myoblasts. We assumed a loading duration of 2 h was enough to cause the loaded muscle cells to release significantly toxic biowastes to its immediate vicinity, as the compressive damage stress-duration threshold curve of normal myoblasts started to drop sharply at around 2 h.65

Figure 4
figure 4

Two-way ANOVA showed that loading duration apparently had a significant effect on the toxicity of the biowastes generated from the damaged myoblasts, which in turn led to a significant change in the compressive damage threshold of the myoblasts. (*p < 0.05).

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COMSOL Multiphysics Simulation

The distributions of minimum principal stress in the buttock-cushion system and in the muscle layer were shown in Fig. 5. The compressive stress was highest at the site in the muscle layer beneath the IT bone, which was most vulnerable to damage. The release of toxic biowastes was determined by the compressive damage stress-duration threshold of muscle cells could in-turn change the compressive damage threshold of the muscle cells in the neighborhood. The patterns of propagation of muscle damage with and without the biowastes effect were simulated using the reference parameters (D = 10−9 m2 s−1; R C = 10−6 mol m−3 s−1; t 0 = 120 min; C t = 0 mol m−3) and the results were shown in Fig. 6. The number of damaged elements (red area) in the muscle layer with the biowastes effect was larger than that without the biowastes effect in the time span of 2–3 h. The biowastes could worsen the tissue damage faster if they were not cleared from the tissues.

Figure 5
figure 5

Distribution of minimum principal stress in the buttock-cushion system (upper figure) and in the muscle tissue (lower figure).

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Figure 6
figure 6

Evolution of damage (red area) in the muscle tissue under prolonged skeletal loading with and without the effect of biowastes, using reference parameters, D = 10−9 m2 s−1; R C = 10−6 mol m−3 s−1; t 0 = 120 min; C t = 0 mol m−3.

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Figure 7a showed the comparison of the effects of different diffusion coefficients of the biowastes in the muscle layer with the release rate of the biowastes R; the chemical damage threshold C t and timeline of releasing biowastes t 0 kept at the reference values. Larger diffusion coefficient of the biowastes could allow the biowastes diffuse faster to the whole muscle layer causing faster expansion of damage in the muscle tissue. When the diffusion coefficient reached 10−7 m2 s−1, the damage progression was not much affected by further increase in the diffusion coefficient. When there were toxic biowastes generated, even a small diffusion coefficient could cause more damage than the situation without biowastes.

Figure 7
figure 7

(a) Larger diffusion coefficient of biowastes in the muscle tissue, (b) higher release rate of biowastes from damaged muscle cells, (c) lower chemical damage threshold of muscle cells against biowastes, and (d) earlier timeline of releasing biowastes of muscle cells leads to earlier expansion of muscle damage under prolonged skeletal loading.

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The comparison of the effects of different release rates of biowastes was shown in Fig. 7b with the diffusion coefficient D; the chemical damage threshold C t and timeline of releasing biowastes t 0 kept at the reference values. A higher release rate of biowastes could cause a faster expansion of muscle damage. When the release rate reached 10−5 mol m−3 s−1, the damaged tissue volume was not much increased by further increase in the release rate.

The comparison of the effects of different chemical damage threshold of muscle cells against the toxic biowastes was shown in Fig. 7c with the diffusion coefficient D; the release rate R and timeline of releasing biowastes t 0 kept at the reference values. A higher chemical damage threshold against the toxic biowastes could slow down the effects of biowastes on the damage expansion.

With an earlier time point when the damaged cells could release their biowastes, the effects of the biowastes on the damage expansion will be advanced (Fig. 7d), with the diffusion coefficient D; the release rate R and the chemical damage threshold C t kept at the reference values.

Discussion

From the results in Figs. 2a and 2b, the PLCS biowastes were different from the SHCS biowastes. The PLCS biowastes were clearly toxic to normal myoblasts while the SHCS biowastes appeared not so. The biowastes released from myoblasts under prolonged low compressive loading might contain cytokines, caspases and ROS which are known to be toxic to cells and can affect the mechanical properties of cells. Cells under PLCS apparently responded by producing toxic biowastes. Such toxic biowastes could be released and diffused to the surrounding, compromising other cells in the neighborhood. On the other hand, high compressive stress could rupture cells causing cell deaths immediately before a significant amount of toxic biowastes could be generated. The compressive damage stress-duration threshold of normal myoblasts65 showed that a compressive stress of 3000 Pa could cause cell death immediately. Such loading for 15 min might not give enough time for cells to respond via signaling pathways to produce harmful biowastes with apoptotic agonists, toxic cytokines, and ROS.

Increased cell damage with the increase of indentation duration was observed in both PLCS and SHCS biowastes treated samples (Table 1). PLCS biowastes compromised cell viability under compressive stress. The tolerance of myoblasts against compressive damage after PLCS biowastes treatments appeared to be significantly decreased after around 50 min of loading (Table 2), which was much faster than those of the SHCS biowastes treated myoblasts (Fig. 3b) and the normal myoblasts.65 PLCS biowastes could cause earlier breakdown of cell membranes under compressive stress than SHCS biowastes and normal culture media. The mechanical strength of cells decreased with loading duration and could be further compromised by the accumulated biowastes released from other neighboring cells that had succumbed earlier to the prolonged mechanical challenge. In contrast, myoblasts undergoing acute cell death might not as much affect the neighboring cells via the biowastes released upon their abrupt ruptures.

The results implied that the accumulated biowastes released from the muscle cells damaged under PLCS can compromise the capability of the remaining cells to withstand the subsequent mechanical damages. The accumulation of biowastes in vivo could also be caused by blocked lymphatic drainages due to tissue deformation under mechanical loading. The inability of the compromised lymphatics to drain the toxic biowastes could further harm the remaining intact cells.

A major assumption in the in silico study is that the model was established as a 3D thin slice rather than a full-3D model. The anterior and posterior surface of the geometry were assumed be free in-plane and fixed out-of-plane, which might exaggerate the compressive stress value. The highest internal compressive stress in the muscle was found, as expected, below the IT bone. Tissue damage initiated around the bony prominence. Both were similar to those reported in previous studies.36,64 Direct comparisons in terms of absolute values were not further pursued, due to differences in the details of the models. We recommend that the predictions of the present in silico model be interpreted as trends of the biowastes effects, and not necessarily in terms of their absolute values, since the damage laws were based only on our in vitro data. A full 3D model would still be required if the effects of out-of-plane need to be further elucidated.

Results from the multiphysics FE modeling illustrated the effect of the biowastes generated by damaged muscle tissue on the propagation of tissue damage. This implication is relevant to the development of clinical pressure ulcers from DTI. The biowastes could cause faster tissue damage if the biowastes cannot be timely removed. The estimated diffusion coefficient of biowastes in the uncompressed muscle tissue ranged from 0.83 to 1.22 × 10−9 m2 s−1.2,11,19,58,59 In human lower limb, the mean diffusion coefficient in skeletal muscle were reportedly in the range of 1.31–1.41 × 10−9 m2 s−1.66 Parametric analysis of the diffusion coefficient indicated that with an increase of diffusion coefficient, the propagation of muscle damage became faster. The imbalance between capillary filtration and lymph drainage could cause tissue edema which might be developed in DTI.40 The tissue edema could increase the diffusion coefficient.13 During the development of DTI, the edema could make the tissue damage more severe through faster diffusion of biowastes. In vitro study revealed that free diffusion of large molecules (10–150 kDa) decreased during deformation.16 In vivo study showed the diffusion of small molecules was not influenced by deformation of muscle tissue, but the observed decrease in diffusion coefficient was associated with a decrease of muscle temperature.59 The diffusion coefficient during the development of DTI might vary but the damage propagation changed little when the diffusion coefficient was less than 10−9 m2 s−1. Damage propagation was sensitive to the diffusion coefficient larger than 10−9 m2 s−1. Real-time measurement of diffusion coefficient during the development of DTI could support the multiphysics simulation with more accurate parameters. Figure 7b indicated faster release of biowastes from the cells to the surrounding could cause more severe tissue damage. Blockage of lymphatic system might significantly inhibit the removal of biowastes in the tissue and thus increase the accumulation of biowastes leading to faster damage. The muscle tissue might be tolerant to biowastes up to certain biowastes concentration, above which, the muscle tissue would find it difficult to cope with. Figure 7c indicated that a higher chemical damage threshold of the muscle tissue against the biowastes could help slow down the effects of biowastes on the propagation of damage. Figure 7d indicated the timeline of releasing biowastes from muscle cells were important to the beginning of the damage propagation which might be guide for the clinical need of repositioning frequency of vulnerable patients to prevent DTI. In silico model indicated the biowastes could lead to faster or earlier propagation of damage in the muscle tissue, and thus biowastes accumulation and in vivo tissue diffusion coefficient could be important factors related to pressure ulcer development from DTI.

The in vitro experiments revealed the importance of biowastes which could be cytotoxic and could compromise the capability of intact normal cells to resist compressive damage. Although the multi-physics simulation in this study is a big step from the cellular level to tissue level, it does suggest the potential relevance of the timing and rate of release and the subsequent diffusion of these biowastes to the clinical development of DTI.

There were few literature reports on the exact compositions of the biowastes released by muscle cells damaged under mild but prolonged mechanical insults, nor on the general biochemical environment in the tissues at risk of DTI in vivo. We have raised the issue of biowastes accumulation under prolonged mild mechanical loading as a potentially important factor in the etiology of DTI. Strategies that could lead to a decrease in the production of toxic biowastes, timely removal of the toxic biowastes through in situ neutralization, or blunting the cell receptors of the toxic proteins in the biowastes could be explored as potential interventions to prevent the clinical development of DTI. The identification and quantification of the major toxins in the biowastes released from muscle cells under prolonged mild loading would be essential to the development of these strategies.