On parameter interpretability of phenomenological-based semiphysical models in biology

Estimation of glucose rate of appearance in portal vein circulation using a phenomenological-based model

The joint work of the stomach and the small intestine plays a fundamental role in human digestion. In the stomach, food is turned into a semi-fluid mixture that is slowly released into the small intestine, where most enzymatic reactions occur, and nutrients are absorbed as they become available. This whole process is closely related to glucose homeostasis, mainly because of the appearance of glucose in the portal system and the energetic expenditure of the process itself. The current phenomenological-based model describes such effects of the digestive process on blood glucose concentration. It considers enzymatic and mechanical transformations, energetic expenditure, and the impact of macro-nutrients, fiber, and water on overall digestion and glucose absorption. The model estimates the rate of glucose appearance in the portal vein and is intended to be further integrated into existing models for other human organs and used in model-based systems such as an artificial pancreas with automated insulin delivery.

ASAS-NANP symposium: Mathematical Modeling in Animal Nutrition: The power of identifiability analysis for dynamic modeling in animal science:a practitioner approach

Constructing dynamic mathematical models of biological systems requires estimating unknown parameters from available experimental data, usually using a statistical fitting procedure. This procedure is usually called parameter identification, parameter estimation, model fitting, or model calibration. In animal science, parameter identification is often performed without analytic considerations on the possibility of determining unique values of the model parameters. These analytical studies are related to the mathematical property of structural identifiability, which refers to the theoretical ability to recover unique values of the model parameters from the measures defined in an experimental setup and use the model structure as the sole basis. The structural identifiability analysis is a powerful tool for model construction because it informs whether the parameter identification problem is well-posed (i.e., the problem has a unique solution). Structural identifiability analysis is helpful to determine which actions (e.g., model reparameterization, choice of new data measurements, and change of the model structure) are needed to render the model parameters identifiable (when possible). The mathematical technicalities associated with structural identifiability analysis are very sophisticated. However, the development of dedicated, freely available software tools enables the application of identifiability analysis without needing to be an expert in mathematics and computer programming. We refer to such a non-expert user as a practitioner for hands-on purposes. However, a practitioner should be familiar with the model construction and software implementation process. In this paper, we propose to adopt a practitioner approach that takes advantage of available software tools to integrate identifiability analysis in the modeling practice in the animal science field. The application of structural identifiability implies switching our regard of the parameter identification problem as a downstream process (after data collection) to an upstream process (before data collection) where experiment design is applied to guarantee identifiability. This upstream approach will substantially improve the workflow of model construction toward robust and valuable models in animal science. Illustrative examples with different levels of complexity support our work. The source codes of the examples were provided for learning purposes and to promote open science practices.

A phenomenological-based model of the endometrial growth and shedding during the menstrual cycle

The human endometrium presents a remarkable growth dynamic with an outstanding regenerative capacity. This work aims to develop a phenomenological-based dynamic model to predict the volume changes in the functional layer of the endometrium in each phase of the menstrual cycle. This model considers changes in the endometrial tissue, the blood flow through the spiral arteries, the shedding of the endometrial cells, and the menstrual blood flow. The input variables are estrogen and progesterone; these hormone dynamics are taken from a pre-existing and validated model. Key parameters are modified in order to know their effect on the state variables. The model response was quantitatively assessed using the experimental data of the endometrial cycle reported in the literature. The proposed model provides a better insight into the interactions between ovarian hormones and the endometrial cycle by coupling both physiological processes.

Collaborative Control Applied to BSM1 for Wastewater Treatment Plants

This paper describes a design procedure for a collaborative control structure in Plant Wide Control (PWC), taking into account the existing controllable parameters as a novelty in the procedure. The collaborative control structure includes two layers, supervisory and regulatory, which are determined according to the dynamics hierarchy obtained by means of the Hankel matrix. The supervisory layer is determined by the main dynamics of the process and the regulatory layer comprises the secondary dynamics and controllable parameters. The methodology proposed is applied to a wastewater treatment plant, particularly to the Benchmark Simulation Model No 1 (BSM1) for the activated sludge process, comparing the results with the use of a Model Predictive Controller in the supervisory layer. For determining controllable parameters in the BSM1 control, a new specific oxygen mass transfer model in the biological reactor has been developed, separating the kLa volumetric mass transfer coefficient into two controllable parameters, kL and a.

A phenomenological-based semi-physical model of the kidneys and its role in glucose metabolism

The kidneys play an important role in glucose homeostasis in three ways: Via endogenous glucose production from non-carbohydrate precursors (e.g. glutamine, lactate, alanine, glycerol) during both postprandial and post-absorptive states; via glucose filtration and reabsorption by the glomerulus and proximal tubule, respectively; and via glucose utilization and the elimination of its excess in the urine when glucose levels exceed 180mg/dl. The renal release of glucose into the circulation occurs mainly in the renal cortex and results from the glucose phosphorylating capacity of those renal cells, meaning that, cells in the renal cortex can form glucose-6-phosphate. Considering glucose filtration and reabsorption, the kidneys filtrate and reabsorb all circulating glucose, rendering the urine virtually glucose-free in a healthy person. Finally, the kidneys take up glucose from the circulation for energetic self-supply. Besides their role in glucose metabolism, the kidneys are the major site of insulin clearance from the systemic circulation, removing approximately 50% of peripheral insulin. In this regard, insulin clearance by kidneys occurs by degradation in the proximal tubule after being filtered in the glomerulus. All the aforementioned mechanisms affect the glucose concentration levels in the blood, preventing the parametrization of a mathematical model for patients with diabetes mellitus, in the implementation of an artificial pancreas. Aiming for a complete physiological model of the glucose homeostasis, a physiological submodel of the kidneys is presented in a way not described in the literature so far. This submodel is a phenomenological-based semi-physical model with a basic structure rooted in the conservation law and for which the parameters are interpretable. The model's results coincide well with the available clinical data reported for kidney functions associated with glucose and insulin.