Mathematical modelling of the lower urinary tract

The lower urinary tract is one of the most complex biological systems of the human body as it involved hydrodynamic properties of urine and muscle. Moreover, its complexity is increased to be managed by voluntary and involuntary neural systems. In this paper, a mathematical model of the lower urinary tract it is proposed as a preliminary study to better understand its functioning. Furthermore, another goal of that mathematical model proposal is to provide a basis for developing artificial control systems. Lower urinary tract is comprised of two interacting systems: the mechanical system and the neural regulator. The latter has the function of controlling the mechanical system to perform the voiding process. The results of the tests reproduce experimental data with high degree of accuracy. Also, these results indicate that simulations not only with healthy patients but also of patients with dysfunctions with neurological etiology present urodynamic curves very similar to those obtained in clinical studies.

MINLP Model for the Synthesis of Heat Exchanger Networks with Handling Pressure of Process Streams

This paper introduces a new mathematical model for the simultaneous synthesis of heat exchanger networks (HENs), wherein the handling pressure of process streams is used to enhance the heat integration. The proposed approach combines generalized disjunctive programming (GDP) and mixed-integer nonlinear programming (MINLP) formulation, in order to minimize the total annualized cost composed by operational and capital expenses. A multi-stage superstructure is developed for the HEN synthesis, assuming constant heat capacity flow rates and isothermal mixing, and allowing for streams splits. In this model, the pressure and temperature of streams must be treated as optimization variables, increasing further the complexity and difficulty to solve the problem. In addition, the model allows for coupling of compressors and turbines to save energy. A case study is performed to verify the accuracy of the proposed model. In this example, the optimal integration between the heat and work decreases the need for thermal utilities in the HEN design. As a result, the total annualized cost is also reduced due to the decrease in the operational expenses related to the heating and cooling of the streams.

Chebanov law and Vakar formula in mathematical models of complex systems

Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.