Wound healing consists of a sequence of biological processes often grouped into different stages. Interventions applied to accelerate normal wound healing must take into consideration timing with respect to wound healing stages in order to maximize treatment effectiveness. Macrophage polarization from M1 to M2 represents a transition from the inflammatory to the proliferative stage of wound healing. Accelerating this transition may be an effective way to accelerate wound healing; however, it must be induced at the appropriate time. We search for an optimal spatio-temporal regime to apply wound healing treatment in a mathematical model of wound healing. In this work we show that to maximize effectiveness, treatment must not be applied too early or too late with respect to peak inflammation. We also show that the effective spatial distribution of treatment depends on the heterogeneity of the wound surface. In conclusion, this research provides a possible optimal regime of therapy that focuses on macrophage activity and a hypothesis of treatment outcome to be tested in future experiments. Finding optimal regimes for treatment application is a first step toward the development of intelligent algorithms for wound treatment that minimize healing time.
The bidomain model is considered to be the gold standard for numerical simulation of the electrophysiology of cardiac tissue. The model provides important insights into the conduction properties of the electrochemical wave traversing the cardiac muscle in every heartbeat. However, in normal resolution, the model represents the average over a large number of cardiomyocytes, and more accurate models based on representations of all individual cells have therefore been introduced in order to gain insight into the conduction properties close to the myocytes. The more accurate model considered here is referred to as the EMI model since both the extracellular space (E), the cell membrane (M) and the intracellular space (I) are explicitly represented in the model. Here, we show that the bidomain model can be derived from the cell-based EMI model and we thus reveal the close relation between the two models, and obtain an indication of the error introduced in the approximation. Also, we present numerical simulations comparing the results of the two models and thereby highlight both similarities and differences between the models. We observe that the deviations between the solutions of the models become larger for larger cell sizes. Furthermore, we observe that the bidomain model provides solutions that are very similar to the EMI model when conductive properties of the tissue are in the normal range, but large deviations are present when the resistance between cardiomyocytes is increased.
Frontiers in Physics
Golden Fractal Jubilee: 50 Years of Bridging Art and Science