By Roustem N. Miftahof, Hong Gil Nam
Mathematical modelling of physiological platforms offers to develop our realizing of complicated organic phenomena and pathophysiology of illnesses. during this e-book, the authors undertake a mathematical method of symbolize and clarify the functioning of the gastrointestinal method. utilizing the mathematical foundations of skinny shell concept, the authors patiently and comprehensively consultant the reader during the primary theoretical options, through step by step derivations and mathematical routines, from uncomplicated concept to advanced physiological types. functions to nonlinear difficulties with regards to the biomechanics of belly viscera and the theoretical barriers are mentioned. specified recognition is given to questions of advanced geometry of organs, results of boundary stipulations on pellet propulsion, in addition to to scientific stipulations, e.g. useful dyspepsia, intestinal dysrhythmias and the impact of gear to regard motility issues. With finish of bankruptcy difficulties, this ebook is perfect for bioengineers and utilized mathematicians.
Read or Download Mathematical Foundations and Biomechanics of the Digestive System PDF
Similar physiology books
The Biology and Anatomy & body structure is helping sequence is designed to supply a evaluation of the goals and vocabulary coated by means of many teachers. This sequence is in note-like structure to complement any scholar examine consultant and gives a self try out on the finish of every textual content to aid with fabric overview of the subject lined.
Certain carbohydrates are a major and engaging subject in biochemical and melanoma study. in accordance with a sequence of invited lectures, this publication makes a speciality of the targeted position that certain carbohydrates play in nature and replicate the author's amazing profession in biochemical learn. another themes coated are the houses of membrane glycoproteins, fascinated about the resistance of cells to medications, and the metabolism of sugars and sialic acids, either one of which shape a pivotal position within the author's experiences.
Now in its 6th version, colour Atlas of body structure covers the whole topic of human body structure and brilliantly reports every thing scientific scholars want to know to move their pre-clinical body structure assessments. Sections contain the nerves and muscle mass, blood, respiratory, the cardiovascular procedure, digestion, and copy.
Respiratory is likely one of the most simple motor actions an important for survival of the person. it truly is lower than overall keep watch over of the relevant worried method, which adjusts breathing intensity and frequency reckoning on the situations the person reveals itself. hence this quantity not just studies the fundamental keep an eye on platforms of respiratory, positioned within the caudal brainstem, but additionally the better mind areas, that adjust intensity and frequency of respiratory.
- Lipoxygenases in Inflammation
- Proteinuria: Basic Mechanisms, Pathophysiology and Clinical Relevance
- Human Anatomy
- Physiological pharmaceutics : barriers to drug absorption
- Human Physiology: An Integrated Approach (6th Edition)
- Molecular Basis of Thyroid Hormone Action
Additional resources for Mathematical Foundations and Biomechanics of the Digestive System
Setting Fi ðα1 ; α2 Þ ¼ 0 from Eq. 9) for the displacement vector, we have ∗ m m = mz ∗ S ρ2′ r2 Mz ∗ M Sz ∗ α2 ρ1′ α∗ 2 α∗ 1 r1 Hz m r2 α2 M(αi) r1 α1 S Fig. 2 Fictitious deformation of the surface. 34 Shells of complex geometry νðα1 ; α2 Þ ¼ Hðα1 ; α2 Þm: (2:29) Ã from the surface S to S . Evidently, the measured along m Here Hðαi Þ is the distance Ã vector equation of S can be written as Ã r ¼ rðα1 ; α2 Þ þ Hðα1 ; α2 Þm: Let (2:30) Ã Hðα1 ; α2 Þ ¼ Hz þ Hðα1 ; α2 Þ: (2:31) Then, on substituting Eq.
By substituting Eqs. 28) are used to calculate the Christoffel symbols Ãk Ã ðzÞk Gij on S . Gij are calculated from Eqs. 27) by replacing Azi and their derivatives for Ai and @Ai =@α1;2 , respectively. Ã in Fig. 3. Let a For example, consider a shell of complex geometry S as shown Ã cylinder ofÃ constant radius R0 be the reference surface for S. 30). Introduce polar coordinates α1 and α2 on S, such that α1 is the axial and α2 is the polar angular coordinate. They are related to the global Cartesian coordinates by 40 Shells of complex geometry À Á rðαi Þ ¼ xi þ yj þ z k ¼ R0 i sin α2 þ k cos α2 þ α1 j: (2:59) The Lamé parameters Ai and curvatures kij are given by A1 ¼ 1; k11 ¼ 1=R1 ¼ 0; A2 ¼ R0 ; k12 ¼ 0; k22 ¼ 1=R2 ¼ 1=R0 : (2:60) For the coefﬁcients θi ¼ 1 þ Hðαi Þ=Ri we have θ1 ¼ 1; θ2 ¼ 1 þ Hðαi Þ=R0 : (2:61) Hence, from Eq.
3 The extrinsic geometry of the surface and a local base fn; nb ; τ g associated with a curve Γ. τ ¼ dr dα1 dα2 þ r2 : ¼ r1 ds ds ds (1:13) By applying the Frenet–Serret formula for the derivative of τ with respect to s we get n dτ ¼ ; ds Rc (1:14) n is the vector normal to Γ. By substituting Eq. 8) we obtain n¼ 2 X 2 X i¼1 k¼1 rik dαi dαk dα2 dα2 þ r1 1 þ r2 2 ; ds ds ds ds (1:15) where rik ¼ @2r @2r ¼ ; @αi @αk @αk @αi rik ¼ rki : and n such that m n ¼ cos j. Then the Let φ be the angle between the vectors m yields scalar product of Eq.
Mathematical Foundations and Biomechanics of the Digestive System by Roustem N. Miftahof, Hong Gil Nam