心脏作功的动力学过程──考虑动功率的最小功原理

DYNAMIC PROCESS OF HEARd WORKING -A PRINCIPLE OF LEAST CARDIAC WORK WITH CARDIAC KINETIC ITEM

心脏最小功原理是描述心脏做功动力学过程的一种有效模型，在文献［１］中，作者在忽略心脏动功率前提下，给出了心脏做功动力学过程的解析解．但由于动功率在心脏整个做功过程中，特别是在某些病理状态下，占有相当比例，因此，在分析心脏动态做功过程时，应该考虑心脏的总体对外做功．当计入动功率后，方程由原来的线性变成非线性，问题复杂许多，已无法应用原来的解析方法．本文在牛顿法的基础上，得到一种考虑动功率项求解非线性方程组的方法．实例计算表明该方法收敛速度快，所得结果与动物实验相符合．从而使得最小功原理的计算得到完善，为进一步研究心脏做功的动力学过程奠定理论基础．

The principle of least cardiac work is a valid model which describes the dynamic process when the heart is working. In the previous study[1],analytic solutions of the cardiac process were abtained, but during heart working,specially on some pathological conditions,the kinetic power takes certain percent of the total power.So,when we analyse the cardiac dynamic process,we should analyse the total cardiac work.When the kinetic power was calculated,the equations are changed from the initial linear equations to the non-linear ones.The questions are more complex,and it can not be solved by the former analytic method. In the present study,on the foundation of the Newton Method,we get a new method that the non-linear equations with the kinetic item can be solved.The example calculation shows that this method convergents fast and the results are accord with the experiment results.Thus,the method perfects the calculation of the principle of least cardiac work,and it makes a theoretical foundation to research the cardiac dynamic process.