Introduction

Pharmacologic approaches for promoting angiogenesis have been utilized to accelerate healing of chronic wounds in diabetic patients with varying degrees of success. We hypothesize that the distribution of proangiogenic drugs in the wound area critically impacts the rate of closure of diabetic wounds. To evaluate this hypothesis, we developed a mathematical model that predicts how spatial distribution of VEGF-A produced by delivery of a modified mRNA (AZD8601) accelerates diabetic wound healing.

Methods

We modified a previously published model of cutaneous wound healing based on coupled partial differential equations that describe the density of sprouting capillary tips, chemoattractant concentration, and density of blood vessels in a circular wound. Key model parameters identified by a sensitivity analysis were fit to data obtained from an in vivo wound healing study performed in the dorsum of diabetic mice, and a pharmacokinetic model was used to simulate mRNA and VEGF-A distribution following injections with AZD8601. Due to the limited availability of data regarding the spatial distribution of AZD8601 in the wound bed, we performed simulations with perturbations to the location of injections and diffusion coefficient of mRNA to understand the impact of these spatial parameters on wound healing.

Results

When simulating injections delivered at the wound border, the model predicted that injections delivered on day 0 were more effective in accelerating wound healing than injections delivered at later time points. When the location of the injection was varied throughout the wound space, the model predicted that healing could be accelerated by delivering injections a distance of 1–2 mm inside the wound bed when compared to injections delivered on the same day at the wound border. Perturbations to the diffusivity of mRNA predicted that restricting diffusion of mRNA delayed wound healing by creating an accumulation of VEGF-A at the wound border. Alternatively, a high mRNA diffusivity had no effect on wound healing compared to a simulation with vehicle injection due to the rapid loss of mRNA at the wound border to surrounding tissue.

Conclusions

These findings highlight the critical need to consider the location of drug delivery and diffusivity of the drug, parameters not typically explored in pre-clinical experiments, when designing and testing drugs for treating diabetic wounds.

中文翻译：

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数学模型预测糖尿病伤口愈合的加速取决于 VEGF-A mRNA (AZD8601) 的空间分布

介绍

促进血管生成的药理学方法已被用于加速糖尿病患者慢性伤口的愈合，并取得了不同程度的成功。我们假设促血管生成药物在伤口区域的分布严重影响糖尿病伤口的闭合率。为了评估这一假设，我们开发了一个数学模型，该模型预测通过递送修饰的 mRNA (AZD8601) 产生的 VEGF-A 的空间分布如何加速糖尿病伤口的愈合。

方法

我们修改了基于耦合偏微分方程的先前发表的皮肤伤口愈合模型，该方程描述了圆形伤口中发芽毛细血管尖端的密度、趋化剂浓度和血管密度。通过敏感性分析确定的关键模型参数与在糖尿病小鼠背部进行的体内伤口愈合研究中获得的数据相吻合，并且使用药代动力学模型来模拟注射 AZD8601 后的 mRNA 和 VEGF-A 分布。由于关于 AZD8601 在伤口床中空间分布的数据的可用性有限，我们对注射位置和 mRNA 扩散系数进行了扰动模拟，以了解这些空间参数对伤口愈合的影响。

结果

当模拟在伤口边缘进行的注射时，该模型预测在第 0 天进行的注射在加速伤口愈合方面比在以后的时间点进行的注射更有效。当整个伤口空间的注射位置不同时，该模型预测，与同一天在伤口边缘进行的注射相比，通过在伤口床内 1-2 毫米的距离进行注射可以加速愈合。对 mRNA 扩散性的扰动预测，限制 mRNA 的扩散会通过在伤口边缘产生 VEGF-A 的积累来延缓伤口愈合。或者，与使用载体注射的模拟相比，高 mRNA 扩散率对伤口愈合没有影响，因为伤口边界处的 mRNA 快速丢失到周围组织。

结论

这些发现强调了在设计和测试用于治疗糖尿病伤口的药物时，考虑药物递送位置和药物扩散性的关键需要，这些参数通常在临床前实验中未探索。