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Inflammatory Cascade

The initial phase involving platelet aggregation and leukocyte recruitment. Key mediators include histamine and cytokines, initiating the debridement and signaling necessary for subsequent repair.
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The statement of the theorem

Let Ci(t,x)C_i(t, \textbf{x}) be the concentration of cytokine ii at time tt and position x\textbf{x}. The spatio-temporal evolution of the cytokine concentration is governed by the reaction-diffusion equation:\n∂Ci∂t=Di∇2Ci+Ri(C)−kiCi+Si(C,Platelets)\frac{\partial C_i}{\partial t} = D_i \nabla^2 C_i + R_i(\mathbf{C}) - k_i C_i + S_i(\mathbf{C}, \text{Platelets})\nwhere DiD_i is the diffusion coefficient, Ri(C)R_i(\mathbf{C}) represents the source/sink terms from cellular activity (e.g., macrophage release), kik_i is the degradation rate, and SiS_i models the signaling dependence on platelet activation and leukocyte presence.