Table 1.
State variables with descriptions.
Fig 1.
Schematic diagram of locally irradiated superficial thermal burn, the state variables, and their relationships.
The model consists of the thermal burn compartment where cell populations experience damage from thermal fluence and the surrounding tissue compartment where resident immune cell populations experience damage from a prompt radiation dose. The variables model the inflammatory and early proliferation phases of wound healing. State variables are represented using circles and squares. The solid black lines indicate transitions between different cellular states. Solid lines that feedback into the state variable indicate proliferation. Initiated cellular interactions are captured by dotted lines and remain locally concentrated. Blue and white colors are used to distinguish between upregulation (i.e., increasing in response to the cells themselves) and destruction/inhibition, respectively. The toxic triangles indicate cell transitions and interactions affected by ionizing radiation that have been incorporated into the model.
Fig 2.
M1 macrophage ratio to total macrophages and damage variable with varying prompt radiation doses.
The M1 ratio (panel A) denotes the total expression of M1 macrophages as a ratio of the total activated macrophage response such that 1 corresponds with 100% M1 activated macrophages and 0 corresponds with 0% M1 activated macrophages (100% M2 activated macrophages). Panel B shows the corresponding damage variable indicating damage resolution over time. Prolonged pro-inflammatory behavior has been widely evidenced to delay the wound healing process [48].
Table 2.
Initial conditions for the variables in the surrounding tissue compartment.
Table 3.
Parameters selected to be estimated or fixed using the sensitivity analysis results and the parameter selection algorithm.
Fig 3.
Plots of damage () and debris (
) for a superficial thermal burn with varying levels of radiation. Panel A shows
and panel B shows
. Superficial thermal burns alone should heal fully within 4 to 5 days. The introduction of ionizing radiation delays the immune response and results in prolonged healing times.
Fig 4.
Plots of undamaged cells in the surrounding tissue supplied by the bloodstream.
Panel A represents neutrophils, panel B represents macrophages, panel C represents lymphocytes, and panel D represents fibroblasts. Populations in the surrounding tissue are affected by both the initial cellular injury from ionizing radiation as well as reduced influx due to microvasculature damage in the surrounding tissue.
Fig 5.
Plots of immune cells in the injury compartment.
Panel A represents neutrophils, panel B represents M1 macrophages, panel C represents L1 lymphocytes, panel D represents M2 macrophages, and panel E represents L2 lymphocytes. Immune cell response in the injury is delayed due to ionizing radiation exposure.
Fig 6.
Plots of fibroblasts (Ftb) and damage (Damtb) in the thermal injury.
Ionizing radiation exposure alters fibroblast function resulting in reduced proliferative abilities and irregular collagen deposition, delaying damage resolution.
Fig 7.
Plots of pathogen (Ptb) and damage (Dam_tb) at the thermal injury site.
Since ionizing radiation is associated with risk of bacterial infiltration leading to infection, the model includes the capability to capture prolonged bacterial presence and delayed healing which could result in a non-healing wound and chronic inflammation.