A Multiphase Flow in the Antroduodenal Portion of the Gastrointestinal Tract: A Mathematical Model

Abstract

A group of authors has developed a multilevel mathematical model that focuses on functional disorders in a human body associated with various chemical, physical, social, and other factors. At this point, the researchers have come up with structure, basic definitions and concepts of a mathematical model at the “macrolevel” that allow describing processes in a human body as a whole. Currently we are working at the “mesolevel” of organs and systems. Due to complexity of the tasks, this paper deals with only one meso-fragment of a digestive system model. It describes some aspects related to modeling multiphase flow in the antroduodenal portion of the gastrointestinal tract. Biochemical reactions, dissolution of food particles, and motor, secretory, and absorbing functions of the tract are taken into consideration. The paper outlines some results concerning influence of secretory function disorders on food dissolution rate and tract contents acidity. The effect which food density has on inflow of food masses from a stomach to a bowel is analyzed. We assume that the future development of the model will include digestive enzymes and related reactions of lipolysis, proteolysis, and carbohydrates breakdown.

A multiphase flow in the antroduodenum: some results of the mathematical modelling and computational simulation

“…For a more detailed description we presented a multiphase flow model in the 3D antroduodenum allowing for the mass sources/sinks due to particle dissolution, reactions between components, mixture components secretion and absorption, peristaltic movement, functional disorders of the tract [26]. The antroduodenum is a section of the gastrointestinal tract that includes the lower part of the stomach (antrum), the upper part of the small intestine (duodenum) and the pyloric outlet that divides antrum and duodenum.…”

Numerical Modeling of Acidity Distribution in Antroduodenum Aimed at Identifying Anomalous Zones at Consuming Drinks With Different Ph Level

“…В рамках описываемой в данной статье математической модели многофазного течения в антродуоденуме на предыдущих этапах ис-следования сформулированы концептуальная и математическая постановки задачи, разрабо-таны алгоритмы реконструкции трехмерной формы и моторики тракта по результатам УЗИ, получены некоторые результаты по скорости растворения пищи при нарушениях секретор-ной функции антродуоденума [26].…”

“…Таким образом, математическая постанов-ка задачи включает в себя запись уравнений сохранения массы и импульса для смеси жид-ких несжимаемых фаз, соотношений для векто-ра интенсивности потока массы за счет диффу-зионных процессов, соотношений для массовых источников за счет реакций, секреции и всасы-вания компонент, растворения пищи, начальных и граничных условий [26]. В первом приближе-нии все процессы полагаются изотермическими, поэтому в математическую постановку задачи не включаются температурные эффекты.…”

Numerical modeling of acidity distribution in antroduodenum aimed at identifying anomalous zones at consuming drinks with different pH level

“…We accomplished conceptual and mathematical tasking, worked out algorithms of 3D shape reconstruction and tract motility as per ultrasound results, obtained some results on food dissolution speed at disorders in antroduodenum secretory function at previous stages of the research within the frameworks of the mathematical model which is described in this paper and deals with multi-phase flow in antroduodenum [26].…”

“…So, mathematical tasking includes record of mass conservation and impulse conservation equations for a mixture of liquid incompressible phases, correlations for the intensity vector of mass flow at the expense of diffusion processes, correlations for mass sources at the expense of reactions, secretion, and components absorption, food dissolution, initial and boundary conditions [26]. At a first approximation all the processes are thought to be isothermal, so mathematical tasking doesn't include temperature effects.…”