Witten M
Mech Ageing Dev. 1985 Nov;32(2-3):141-77. doi: 10.1016/0047-6374(85)90077-6.
In this paper, I continue my investigation into the modeling of senescence in biological hierarchies. Making use of my previous discussion on non-reestablishable biological components, I derive a mathematical model which has Gompertzian-like dynamics. I show how this model may be approximated, in certain instances, by a Gompertzian equation. I then demonstrate how our approach yields a biological interpretation for the parameters in the Gompertzian equation. I then demonstrate how changes in the parameter values may be interpreted in light of the biology. Subsequently, I review the literature on the allometry of aging, and I demonstrate how my reliability model may be used to obtain--in a qualitative manner--some of the lifespan curves found in the literature. I close my discussion by constructing a more complex reliability model which incorporates the deterministic failure of biological components with stochastic aspects of senescence.
在本文中，我继续对生物层级体系中的衰老建模进行研究。利用我之前关于不可重建生物成分的讨论，我推导出一个具有类冈珀茨动力学的数学模型。我展示了在某些情况下，该模型如何能用冈珀茨方程来近似。然后我说明了我们的方法如何为冈珀茨方程中的参数给出生物学解释。接着我展示了如何根据生物学来解释参数值的变化。随后，我回顾了关于衰老异速生长的文献，并展示了我的可靠性模型如何能定性地得出文献中发现的一些寿命曲线。我通过构建一个更复杂的可靠性模型来结束我的讨论，该模型将生物成分的确定性失效与衰老的随机方面结合了起来。
