The Mitral Laboratory, Yale School of Medicine, New Haven, Connecticut; Section of Cardiac Surgery, Department of Surgery, Yale School of Medicine, New Haven, Connecticut.
Section of Cardiac Surgery, Department of Surgery, Yale School of Medicine, New Haven, Connecticut.
Semin Thorac Cardiovasc Surg. 2019 Autumn;31(3):399-411. doi: 10.1053/j.semtcvs.2019.01.008. Epub 2019 Jan 8.
Mathematical modeling tries to simplify understanding and proposes a fundamental mechanism that governs the motion and function of a complex biological system such as a mitral valve (MV) motion which represents a dynamic interplay between papillary muscle (PM) position in the context of left ventricular (LV) shape dynamics. Current therapeutic strategies to intervene on the MV may not have exploited these relationships due to lack of understanding of the interactions. We present a MV 3D mathematical model characterized by LV shape dynamics to understand fundamental working principles of ventriculo-papillary-mitral complex. A complex 3D functional unit of MV apparatus was mathematically modeled based on a principle of dynamics. The model comprises of primary components including the annulus, anterior leaflet, posterior leaflet, chordae tendineae, anterior and posterior PM, and LV wall based on normal anatomical reference values from published series. Simulations based on Carpentier's classification of MV disease were created as well as based on LV shape dynamics and presented graphically. Autodesk Inventor (Autodesk Inc., San Rafael, CA) and Matlab (Mathworks, Natick, MA) were used for modeling and analysis. A stepwise analysis and mathematical models of the annulus, leaflets, chords, PMs, and LV were obtained by combining finite element analysis and computerized model creations. The model was then applied to Carpentier's functional classification. PM positions extrapolated based on different LV deformation in normal and mitral regurgitation (MR) model resulted in a different degree of MV leaflet coaptation with regurgitation (presented numerically and graphically). Abnormal MV coaptation was amended by manipulating PM positions independent with LV size or shape deformation, demonstrating that PM positioning maneuver may improve leaflet coaptation. LV dilation combined with increased interpapillary muscle distance turned out to intensify the level of leaflet prolapse, creating even greater regurgitation volume. Our mathematical model may provide a clue to complex interactions in play within a mitral, papillary, and LV complex. The model offers a possibility of manipulating various variables to obtain the desired outcome.
数学建模试图简化理解，并提出一个基本机制，该机制控制着二尖瓣（MV）运动等复杂生物系统的运动和功能，二尖瓣运动代表了左心室（LV）形状动力学背景下乳头肌（PM）位置的动态相互作用。目前干预 MV 的治疗策略可能由于缺乏对相互作用的理解而没有利用这些关系。我们提出了一个 MV 3D 数学模型，该模型以 LV 形状动力学为特征，以了解心室-乳头肌-二尖瓣复合体的基本工作原理。基于动力学原理，对 MV 装置的复杂 3D 功能单元进行了数学建模。该模型包括基于已发表系列中正常解剖参考值的瓣环、前瓣、后瓣、腱索、前乳头肌和后乳头肌以及 LV 壁等主要组件。根据 MV 疾病的 Carpentier 分类以及基于 LV 形状动力学创建了模拟，并以图形方式呈现。Autodesk Inventor（Autodesk Inc.，San Rafael，CA）和 Matlab（Mathworks，Natick，MA）用于建模和分析。通过组合有限元分析和计算机模型创建，获得了瓣环、瓣叶、腱索、PM 和 LV 的逐步分析和数学模型。然后将模型应用于 Carpentier 的功能分类。根据正常和二尖瓣反流（MR）模型中不同的 LV 变形推断出 PM 位置，导致 MV 瓣叶不同程度的反流闭合（以数字和图形方式呈现）。通过独立于 LV 大小或形状变形来操纵 PM 位置来纠正异常 MV 闭合，证明 PM 定位操作可能改善瓣叶闭合。LV 扩张加上乳头肌之间距离的增加导致瓣叶脱垂程度加剧，从而产生更大的反流量。我们的数学模型可能为二尖瓣、乳头肌和 LV 复合体中存在的复杂相互作用提供线索。该模型提供了操纵各种变量以获得所需结果的可能性。
