基于混合模型的增生性瘢痕全过程数学建模及点阵激光治疗最优方案的理论研究

Although ablative fractional CO2 laser has demonstrated very obvious effect on the treatment of hypertrophic scars, the clinical application of this technology is still heavily dependent on personal experience rather than reliable evidences. As the applicants of this proposal, we have recently conducted some preliminary research by comparing the simulation results of some mathematic models with the clinical data of scars treated by fractional laser. It was found that the simulation results from the published mathematic models about the scar treated with fractional laser were comparable with the clinical manifestations, suggesting the validity of these models. Previously, we have also successfully established several agent-based models to simulate the colonisation of keratinocytes, the complex interactions between keratinocytes and fibroblasts in conventional monolayer cell culture, and the function of TGF beta1 during epidermal wound healing processes, which were all confirmed by corresponding biological experiments or researches from other groups. Therefore, it is reasonable to hypothesize that, the development of a hybrid model to simulate the whole process of a hypertrophic scar treated with fractional laser in combination of drugs will be extremely valuable to improve our mechanistic understanding of scar formation. Moreover, the computational model can be employed as a very useful platform to explore and optimize suitable fractional laser programs to treat scars more efficiently and cost effectively. Thus the aim of this proposed research is to establish a descrete-continuum hybrid model for the simulation of the whole process of scar formation. This novel modelling approach will be closely integrated with both experimental systems and clinical data to systematically investigate the internal mechanics of the scar development process and the macro-Vancouver scale index changes, which will inform the combined scar treatment programs based on both fractional laser and imported drugs. The success of this proposed study will provide a theoretical basis for the establishment of objective, optimal, personalized, fractional laser based scar treatment regimen.

剥脱性CO2点阵激光对增生性瘢痕的治疗效果明确，但是治疗方案制定严重依赖专家经验，缺乏可靠的证据支持。申请者关注于通过瘢痕数学模型进行点阵激光治疗方案的实验探索，我们团队前期已发表的研究对皮肤表皮细胞、成纤维细胞、TGF beta1生物学功能数学建模，很好的与生物学实验的结果相符合，并且我们对已发表的瘢痕部分过程的数学模型进行模拟点阵激光刺激后，发现刺激后瘢痕的生物学表现与临床过程也相符合。因此有理由假设：通过对瘢痕全过程数学建模，在此模型上进行点阵激光及合并药物的实验，能够较快速、低代价的探索点阵激光瘢痕治疗的最优方案。本项目联合生物学实验结论与计算机建模方法，重视瘢痕发展过程中的内部力学作用及宏观温哥华量表指标变化，建立基于混合模型的瘢痕全过程数学模型，在此基础上实验点阵激光及合并药物的最优组合方案。本研究将从方法学上为建立客观的、最优的、个体化的点阵激光瘢痕治疗方案提供理论基础。

剥脱性CO2点阵激光对增生性瘢痕的治疗效果明确，但是治疗方案制定严重依赖专家经验，缺乏可靠的证据支持。.本项目通过研究，对比并整合最新的瘢痕生长各个过程的数学模型，确定连续模型，离散模型以及连续离散混合模型的性质，优化并验证上述各类模型的稳定，快速以及准确的传统数值算法；明确微观模型与宏观临床变量的映射关系，包括力学，光学特性；模拟瘢痕在生长期以及稳定期的各类治疗方案，探索数值上的最佳临床方案。.最终，本研究确定了进行临床治疗模拟所需的瘢痕数学模型的最简形式；确定了瘢痕微观模型与宏观变量的映射对应关系；发现并验证了连续模型和混合模型比离散模型更适用于瘢痕系统的结论；验证了连续模型和混合模型在宏观上没有显著结果差异；得到了刚性网格有限元方法无法对瘢痕系统进行稳定数值求解的结论；确定了PINN网络能够对复杂非线性系统进行自适应求解；验证了PINN等深度神经网络能够利用GPU进行大规模分布式计算，从而能够在现有计算条件下取得快速收敛的结果。.这些结论说明，考虑数值运算的准确，稳定以及效率，瘢痕系统当前最适用的数学形式为连续模型，最合适的求解方法为PINN等深度神经网络数值求解。后续研究人员按照该研究路线最有可能快速，准确地模拟瘢痕系统。