Prognostic medication: prediction by a macroscopic equation model for actual medical histories of illness with various recovery speeds

Abstract

A network theory model based on a nonlinear differential equation (Naitoh in Jpn J Ind Appl Math 28:15-26, 2011a; Proceedings of JSST 2011 international conference on modeling and simulation technology, pp 322–327, b, Naitoh and Inoue in J Artif Life Robot 18:127–132, 2013) macroscopically showed a possibility for explaining interaction mechanism of six groups of molecules on information and function in human beings. In this paper, we show that time-dependent computational results of the number of vigorous cells agreed well with individual medical histories of illness for actual patients. Computational results showed illness with three types of recovery speeds: illness with fast recovery speed having recovery period of several months, with medium speed like leukemia or small cell carcinoma having one or two-year-recovery period, and with low speed having recovery period about five years like the symptom of illness named “anti-N-methyl-d-aspartate (anti-NMDA) receptor encephalitis”. It is stressed that both of the period under unresponsive state in early stage and total years needed to recover cognitive function completely in anti-NMDA receptor encephalitis can be simulated. These results may indicate that the model macroscopically and essentially describes time-dependent activation level of human beings.

Appendix: Influence of random noise on lifespan [12]

In this report, a small amount of numerical errors was used instead of stochastic disturbance entering from the outside of the human being, which results in good agreements between computations and actual data of medical history of illness.

To go further, stochastic differential equations including random noise, which are shown in our previous reports [17, 18], can be discretized in time by numerical methods having higher-order of accuracy. Then, terms of random noise in the equations can be calculated using random number generators in computers. Magnitude of the random noises should be evaluated basically by actual noise data, which should be measured from actual patients and obtained many times per year, over a certain period of time. Other theoretical evaluation may also be included, which comes from statistical vagueness (statistical indeterminacy) related to relatively smaller number of molecules in molecular group than that for continuum mechanics (deterministic model) [19,20,21]

Accidental cases like a traffic accident can be considered here. Although it is difficult to predict death or physical problem due to accidental cases with the model, these cases are only 0.05% of the population according to Fig. 14 [22]. Therefore, we can say that the model has a possibility for predicting life patterns for most cases except for 0.05% of accidental cases.

Fig. 14

Changes in mortality rate for each case of death [22]