Fig 1.
Flowchart depicting multiscale model.
(A) OpenSim model of rat hindlimb adapted from Johnson 2008 [16] simulates strains in the injured Achilles tendon. (B) Cell model predicts alignment based on the mechanical environment. (C) Fitted mean strain versus collagen I production curve (grey line) from four independent studies governs collagen production. (D) Agent-based model (ABM) of wound healing integrates migration, alignment, and collagen deposition by cells (blue) to predict scar collagen content and alignment (grey).
Fig 2.
Model predictions of collagen alignment and content match trends in tissue-level properties reported in the literature during healing of unrepaired tendons.
(A) Schematic of rat Achilles tendon transection injuries left to heal naturally. (B,C,E,F) We plotted data from studies (various colors) in which tendons healed unloaded (B,E) or loaded (C,F). We compared our predictions of collagen alignment (D) and content (G) to experimentally measured Young’s Moduli (B,C) and cross-sectional areas (E,F), see text for details.
Fig 3.
Effect of strain on cellular alignment and collagen synthesis.
(A) Estimated cellular strain profiles derived from tendon strain profiles predicted by modified rat hindlimb model. (B) Cellular alignment response curve generated by model of stress fiber dynamics in response to cyclic stretching at various magnitudes and a frequency of 1 Hz with a 1h on, 1h off repeating cycle during waking hours (gray line); open circles show the operating points on this curve for simulated unloading (light blue circle) and loading conditions (dark blue circle) in unrepaired tendons. (C) Response curve showing the effect of mean strain on fibroblast collagen synthesis rate (gray line), again overlaid with circles showing the operating points for the specific cases simulated in Fig 2.
Fig 4.
Model predictions of the effects of loading in unrepaired versus suture-repaired tendons also match experimentally observed tissue-level measures.
(A) Schematic of rat Achilles tendon transection injuries left unrepaired or repaired with sutures. (B,D) Studies [12,13,36] that tested both unloading (light color) and loading (dark color) conditions in either unrepaired (dashed blue lines) or repaired (solid red lines) tendons showed a lower Young’s modulus in the loaded, suture-repaired case and similar values in the other groups (B), the same trend predicted for collagen alignment by the model (C). Experimental data showed higher tendon cross-sectional area with loading regardless of repair status (D), matching model predictions of total collagen (E).
Fig 5.
Cellular strain profiles and corresponding responses for simulations shown in Fig 4.
(A) Estimated cellular strain profiles derived from tendon strain profiles predicted by hindlimb model in OpenSim. (B) Cellular alignment response curve generated by model of stress fiber dynamics (gray line, same as Fig 3) and operating points on that curve for unloading (light color) and loading (dark color) conditions in both unrepaired (blue) and suture-repaired (red) tendons. (C) Response curve showing the effect of mean strain on fibroblast collagen synthesis rate (gray line, same as Fig 3) and circles indicating the operating points for the different cases simulated.
Fig 6.
Angular histograms of cell stress fiber orientation from thermodynamic alignment model.
Loaded, suture-repaired tendons exhibited lower cell alignment compared to other conditions. Insets underneath legend labels show corresponding circular histograms of stress fiber (SF) orientation.
Fig 7.
Identical average stretch frequencies result in varying cell alignment predictions using cell model.
(A) Steady-state predicted alignment response curves for cells stretched in cycles of 6 hours at 1Hz followed by 6 hours of rest (0Hz) (purple), cycles of 1 hour at 1Hz followed by 1 hour of rest (orange), and continuous stretching at 0.5Hz (green). (B) Detailed time course of predicted alignment during 24 hours of intermittent stretch using two different duty cycles and a strain amplitude of 0.10. Each strain protocol was repeated until the difference in alignment at the end of two consecutive repetitions was less than 0.01.
Fig 8.
Rat hindlimb model implemented in OpenSim used joint angles, muscle activation, and passive tendon properties as inputs to determine tendon strains.
(A) Hip (brown) and knee (magenta) angle data from healthy rat gait measured by Garnier et al. [41] and ankle angle data measured by Liang et al. [42] in both unrepaired (blue) and suture-repaired (red) tendons. Black dashed line separates stance phase (first 75%) from swing phase (last 25%). (B) Depiction of model motion during the prescribed gait cycle. The color of the muscle fiber depicts the activation during that part of the gait cycle, ranging from maximum activation (1, red) to minimum activation (0, blue). Purple fibers (shown during the swing phase at 90%) depict the transition from maximum to minimum activation. (C) Final tendon strain output was calculated by taking the average (thick blue) of tendon strains in the lateral (purple) and medial (green) gastrocnemius and soleus (orange) musculo-tendon units.
Fig 9.
Flowchart adapted from Rouillard and Holmes [23] depicting the various decisions cells made in the agent-based model.
Red outlines indicate modifications introduced in the current study.
Fig 10.
Schematic of the agent-based model of wound healing in the injured rat Achilles tendon.
(A) Chemokine difference between the wound space and surrounding tissue drives cell migration into the wound. (B) Healthy Achilles tendon adjacent to the top and bottom of the wound space was comprised of fibroblasts (blue ovals) and highly aligned collagen (grey). The wound space was initially cell-free. (C) Cells migrated, proliferated, and synthesized and deposited collagen to create scar tissue within the wound area. (D) Magnification of the boxed area in (C) shows that the cells have different alignments and shapes determined by the cell alignment model and interact with 10μm x 10μm collagen patches (grey boxes). Each patch stored information on local collagen density (grayscale tone) and collagen alignment (lines). Cell sizes have been increased for visibility in this schematic.
Table 1.
Parameters used in ABM.