Mathematical Modeling for Slide Tracheoplasty.

IF 1.7 3区 医学 Q2 SURGERY
Journal of Surgical Research Pub Date : 2025-10-01 Epub Date: 2025-08-06 DOI:10.1016/j.jss.2025.07.005
Deniz Piyadeoglu, Pelin Ayşe Gökgöz, Namik Ciblak, Cemal A Kutlu
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引用次数: 0

Abstract

Introduction: The objective of this study is to create a mathematical model and calculate precise cut lengths for slide tracheoplasty (ST) to achieve better postoperative results. This study also is a pioneer in a novel field where mathematics and medicine intersect and is aimed to be used for achieving precise preoperative planning for many risky medical procedures.In ST, the trachea is divided into two segments with two longitudinal cuts and one oblique cut. These segments are then slid onto each other to widen the lumen of the stenotic segment. The postoperative stenotic segment diameter is directly determined by the longitudinal incisions and the subsequent oblique incision. We propose a mathematical model to estimate tracheal cut lengths preoperatively to achieve the desired tracheal lumen diameter.

Methods: The oblique cut creates an ellipse. After sliding, the suture line becomes the perimeter of another ellipse, equal to the sum of the initial ellipse perimeter and twice the longitudinal cut length. Longitudinal cuts determine the angle of the oblique cut and lengthen the perimeter of the final ellipse, the horizontal projection of which is a circle with the desired tracheal diameter. This mathematical model uses a novel perimeter equation, two geometric constraints, and a novel tissue area constraint. Exact solutions are found. Using this model, the longitudinal cut length to achieve the target diameter is determined preoperatively.

Results: The mathematical model provides a closed-form solution to calculate the necessary longitudinal cut lengths to achieve a desired postoperative tracheal diameter. It integrates geometric and tissue area constraints to accurately predict the final lumen size. A practical implementation of the model was developed in Microsoft Excel, allowing for user-friendly, real-time calculation of cut lengths with adjustable inputs for preoperative tracheal dimensions and target diameters.

Conclusions: We present a novel mathematical model for preoperative planning in ST. By precisely linking incision geometry to final tracheal diameter, this tool supports more accurate and individualized surgical planning. The model offers a promising example of how mathematical approaches can enhance precision in complex surgical procedures and improve clinical outcomes.

气管滑梯成形术的数学建模。
前言:本研究的目的是建立数学模型并计算出滑片气管成形术(ST)的精确切口长度,以达到更好的术后效果。这项研究也是数学和医学交叉的新领域的先驱,旨在为许多有风险的医疗程序实现精确的术前计划。在ST中,气管分为两段,纵切两段,斜切一段。然后这些节段彼此滑动以扩大狭窄节段的管腔。术后狭窄节段直径直接由纵向切口和随后的斜切口决定。我们提出了一个数学模型,以估计气管切割长度术前达到理想的气管管腔直径。方法:斜切形成一个椭圆。滑动后,缝合线成为另一个椭圆的周长,等于初始椭圆周长和纵向切割长度的两倍。纵向切口决定了斜切口的角度,并延长了最终椭圆的周长,其水平投影是一个具有所需气管直径的圆。该数学模型采用了一个新的周长方程、两个几何约束和一个新的组织面积约束。得到了精确解。利用该模型,术前确定达到目标直径的纵向切割长度。结果:数学模型提供了一个封闭形式的解决方案来计算必要的纵向切割长度,以达到理想的术后气管直径。它集成了几何和组织面积约束,以准确预测最终的流明大小。在Microsoft Excel中开发了该模型的实际实现,允许用户友好,实时计算切口长度,并可调节术前气管尺寸和目标直径的输入。结论:我们提出了一种新的st术前计划数学模型,通过精确地将切口几何形状与最终气管直径联系起来,该工具支持更准确和个性化的手术计划。该模型提供了一个有希望的例子,说明数学方法如何提高复杂外科手术的精度和改善临床结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
3.90
自引率
4.50%
发文量
627
审稿时长
138 days
期刊介绍: The Journal of Surgical Research: Clinical and Laboratory Investigation publishes original articles concerned with clinical and laboratory investigations relevant to surgical practice and teaching. The journal emphasizes reports of clinical investigations or fundamental research bearing directly on surgical management that will be of general interest to a broad range of surgeons and surgical researchers. The articles presented need not have been the products of surgeons or of surgical laboratories. The Journal of Surgical Research also features review articles and special articles relating to educational, research, or social issues of interest to the academic surgical community.
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