Journal of Higher Education Research

Prior experiments with physarum polycephalum, a plasmodial slime mold, have shown its inherent biological ability to adapt to the surroundings. When placed in an environment with food surrounding it, it builds a network of biological pipelines to the food that reinforces heavily used pipelines and withdraws those rarely used. Interestingly, the human body displays a similar ability. The development of our circulatory system is in the absence of our brain or nervous system, which suggests humans mimic low level organisms in the regard that our biological transportation systems are self-regulating and self-constructing. Like slime molds, this adaptive quality suggests that our biological networks follow a method of lowest energy consumption: energy is allocated to maintaining and constructing only the most efficient paths. Thus, the purpose of our model is to explain the biological mechanism of how organisms construct a pipeline network through a mathematical model. The model is developed using 2 main assumptions: (1) The network exists in a hexagonal grid system and (2) there only exists nodes that are sinks, sources, or neither. Borrowing Kirchhoff’s Law and other electric circuit principles, we determine an energy function for the construction and maintenance of a biological pipeline network in our model dependent on the current, conductivity, and pressure within the pipelines. The method we develop in this paper is called the negative gradient flow method. Given any initial values for the pipeline, the negative gradient flow method is an algorithm for unconstrained nonlinear optimization that finds at each instant the next set of values to most minimize the function until eventually reaching the minimizer values. Accomplishing the main goal of this paper, the negative gradient flow improves upon existing models at replicating natural phenomena since it is based on the evolutionary advantage of lowest energy consumption.