Fig 1.
Work flow and schematic of the PUABM.
(A) Work Flow utilized in constructing the PUABM. The ABM was built iteratively, incorporating domain knowledge and data from the literature, then validated with clinical data. Initially, pressure directly injured tissue, thereby inciting inflammation. Ischemia/reperfusion injury was next added as a cause of injury, and the complexity of the inflammatory response was increased. Clinical data were next used to calibrate parameters in the model, and the model was subjected to sensitivity analysis and in silico trials. (B) A schematic illustrates how model components interact to simulate two mechanisms of injury: ischemia/reperfusion injury and damage due to inflammation. A tissue cell (muscle, fat, or skin) is situated over a bony prominence. When pressure is applied, oxygen supply is reduced and the cell becomes ischemic, leading to tissue damage. Simultaneously, the enzyme xanthine dehydrogenase is converted into xanthine oxidase. Thus, reactive oxygen species (ROS) are produced when pressure is released and oxygen flows back to the cell, causing further damage. Tissue damage causes the cell to release DAMPs, which, along with local concentrations of pro-inflammatory cytokines activate both neutrophils (N) and macrophages (M1, M2) when these mediators are present above a given threshold parameter. For example, a sufficiently high local concentration of DAMPs activates neutrophils to secrete TNF-α, which can activate macrophages to a pro- inflammatory M1 phenotype. Tissue damage is ameliorated by anti-inflammatory mediators [TGF-β1].
Table 1.
Summary of agents, data layers, and their interactions encoded in the ABM.
Fig 2.
Model Verification: Mechanisms Lead to Expected Behaviors in Baseline Conditions.
(A) Negative controls verify that the model behaves as expected in various situations. Green: undisturbed, tissue health is stable for >5000 hours (data past 1000 h not shown). Yellow: an initial period of 12 h of ischemia causes damage to the tissue, but after release no further damage was incurred. Red: a characteristic damage curve for an ulcer caused by acute inflammation after 40% initial injury (similar to 2C). Blue: a characteristic damage curve for a pressure ulcer resulting from the default parameters for the model. (B) The ischemia/reperfusion injury mechanism was validated by varying the period of pressure (on/off) cycles. Increasing the length of a pressure cycle allowed us to decrease the number of reperfusion events over the same length of ischemia. Pressure switched from on to off (or vice versa) once every 2, 6, or 12 h. y-axis is total damage, x-axis is time (h). Pressure cycle length did not seem to affect the total amount of damage until just after t = 400 h. At that time point, the simulations with the shortest cycles (black) show a sudden increase in damage, which visually corresponds to the formation of an ulcer (see inset). Eventually, ischemic injury in simulations with the longest cycle length (green) causes these simulations to incur more overall damage. (C) A 35% initial injury without pressure is sufficient to induce self-perpetuating, damaging inflammation, leading to an ulcer. The relative dynamics of the response are as expected from the literature: an initial influx and activation of neutrophils, followed by M1 macrophages, and then followed by M2 macrophages. (D) In 10–20% of simulations with the same parameters and starting conditions, though the inflammatory response was incited, it did not become self-sustaining and consequently no ulcer formed. The trajectories of inflammatory cells are characteristic of each of these outcomes. Data were normalized per cell type, and so quantities are not relative.
Fig 3.
Simulations of the PUABM match key features of clinical images.
(A) Simulations achieved visual appearances with characteristics similar to each stage of PU development. The first row of clinical images come from the National Pressure Ulcer Advisory Panel (images from npuap.org, used with permission) and are of different subjects. Images in the second row are from people with SCI enrolled in a prospective study of PU at each stage. Irregular shapes and increasing nearby damage are observed in both sets of clinical data. (B) Numbers indicate days post-injury. Simulated ulcers evolve with visual characteristics that match PU progression observed in people with SCI. Two simulation time courses are matched against one patient from our study. We match key features: irregular shapes, nearby satellite ulcers (open arrows), jagged edges (solid arrows), and decreasing tissue health across the field.
Fig 4.
Bimodal outcomes are determined by 125 ticks (5 simulated days) prior to the appearance of post-SCI ulcers.
Panel (A) shows two simulations that were initiated with the same set of parameter values but evolved different levels of damage over time. In panel (B) these levels are characterized by a bimodal distribution of tissue damage at tick t = 1000 (day 42). The upper panel is a histogram of these values and the lower panel shows the bimodal distribution estimated from 1000 simulations with the same parameters and initial conditions. (C) Some individual features display very different trajectories between resolved and ulcerated simulation outcomes. Means and standard deviations of 1000 simulations are plotted. Upper 3 panels are the features plotted over the first 200 ticks (8.3 days); lower panels show the full time course of 1000 ticks. (D) 1-Nearest Neighbor performance versus length of sequences in training set was determined for various numbers of included features. (E) Percent of simulations resulting in ulceration after restarting from saved states at indicated restart tick. The saved states were derived from simulations that originally resulted in either ulceration or resolving inflammation.
Fig 5.
Sensitivity analysis reveals a unique contribution for all damage mechanisms, but simulated tissue is most sensitive to oxygen.
(A) We partitioned parameter values according to which damage mechanism they affected. Panel (B) shows a global sensitivity analysis comparing the effects of the three mechanisms of damage on tissue health outcomes. Each mechanisms is simulated at two levels: with maximal or negligible effects. In panels C-E, sensitivity analysis was performed on parameters within each mechanistic module. All sensitivity analyses are shown with model snapshots at time t = 400 h (approximately 2.5 weeks). Default parameters are marked with asterisks. (C) Tissue sensitivity to oxygen parameters. The parameter governing oxygen production varies in each row. Each column represents a value of the parameter controlling how sensitive the tissue is to local oxygen concentrations. When oxygen production is plentiful, the simulated tissue becomes insensitive to other oxygen parameters (bottom row). Panel (D) illustrates tissue sensitivity to pressure intensity and period. Pressure intensity varies in each row. Each column represents a value of pressure cycle length. As the cycle length increases, the number of reperfusion events decreases for the same period of ischemia. Increased pressure leads to more damage, while fewer reperfusion events lead to lower damage at t = 400 h. Panel (E) illustrates tissue sensitivity to inflammatory mediators. Each column represents a value of the parameter controlling how sensitive the tissue is to local TNF-α concentrations. The parameter controlling tissue sensitivity to TGF-β1 varies in each row. Increasing sensitivity to TNF-α leads to earlier ulceration and more damage, while increased sensitivity to TGF-β1 leads to decreased tissue damage.
Fig 6.
In silico clinical trials suggest little efficacy for corticosteroids or DAMP inhibitors.
Simulations are shown at t = 700 h. We varied both the dose and timing of corticosteroid administration, simulated as an injection into the bloodstream, under (A) alternating pressure and (B) 40% initial injury conditions. When inflammatory cells were neutralized early enough but pressure continued, overall damage decreased, but ulceration was not prevented. Without continuous pressure cycles, the earliest dose of steroids was successful in stemming ulcer formation, but later applications did not. We then varied both the dose and timing of administration of a neutralizing antibody to HMGB1, simulated as a topical cream applied to the entire field. This targeted approach had (C) no apparent effect during simulations with alternating pressure, but (D) was able to slow ulcer formation after a 40% initial injury without pressure.