Nonlinear Dynamics in Physiology and Medicine by Anne Beuter, Leon Glass, Michael C. Mackey, Michele S.

By Anne Beuter, Leon Glass, Michael C. Mackey, Michele S. Titcombe

This booklet offers with the applying of arithmetic in modeling and knowing physiological structures, specially these regarding rhythms. it's divided approximately into sections. within the first a part of the publication, the authors introduce principles and methods from nonlinear dynamics which are appropriate to the research of organic rhythms. the second one half comprises 5 in-depth case stories during which the authors use the theoretical instruments built prior to enquire a few physiological methods: the dynamics of excitable nerve and cardiac tissue, resetting and entrainment of organic oscillators, the consequences of noise and time hold up at the scholar mild reflex, pathologies linked to blood mobilephone replication, and Parkinsonian tremor. One novel characteristic of the ebook is the inclusion of classroom-tested machine workouts all through, designed to shape a bridge among the mathematical thought and physiological experiments.

This e-book might be of curiosity to scholars and researchers within the common and actual sciences desirous to find out about the complexities and subtleties of physiological structures from a mathematical perspective.

The authors are participants of the Centre for Nonlinear Dynamics in body structure and medication. the fabric during this e-book used to be built to be used in classes and used to be offered in 3 summer time colleges run by means of the authors in Montreal.

Show description

Read Online or Download Nonlinear Dynamics in Physiology and Medicine PDF

Similar basic science books

Neurophysiology in Neurosurgery: A Modern Intraoperative Approach

This ebook is now five years outdated, however it is still the easiest, so much complex and so much finished booklet on intraoperative neurophysiology tracking. it isn't a rookies' e-book, at lest no longer for rookies who should not have an intensive historical past in neurophysiology, yet it really is an indispensible reference. every person with a major curiosity in IONM must have a duplicate.

Gene Therapy of the Central Nervous System: From Bench to Bedside

Few parts of biomedical learn supply higher possibilities for extensively new treatments for devastating illnesses that experience kept away from remedy to this point than gene treatment. this is often rather precise for the mind and worried approach, the place gene move has develop into a key expertise for easy examine and has lately been translated to human remedy in different landmark medical trials.

Biomechanics: Principles and Applications, Second Edition

Frequently, functions of biomechanics will version system-level points of the human physique. hence, nearly all of technological growth up to now looks in system-level equipment improvement. extra lately, biomechanical projects are investigating organic sub-systems resembling tissues, cells, and molecules.

Thiol Redox Transitions in Cell Signaling, Part A: Chemistry and Biochemistry of Low Molecular Weight and Protein Thiols

This quantity, besides its better half (volume 475), offers tools and protocols facing thiol oxidation-reduction reactions and their implications as they relate to cell signaling. This first installment of Cadenas and Packer's two-volume remedy in particular bargains with glutathionylation and dethiolation, and peroxide elimination by way of peroxiredoxins/thioredoxins and glutathione peroxidases.

Additional info for Nonlinear Dynamics in Physiology and Medicine

Sample text

13. 21). The initial conditions are g(O) =O and g'(O) >O. neighborhood of a fixed point, in which case the associated linear system will have a Jacobian matrix as matrix of coefficients. The classification of the type and stability of fixed points is not as clean and elegant as in the case of two-dimensional systems, and, of course, phase spaces of high dimension are difficult to represent graphically! The matrix approach is necessary in these cases to carry out a systematic investigation. 24) = h(x,y,z), there will be three eigenvalues to characterize the stability of a fixed point, corresponding to three roots of a cubic polynomial, which is given as the determinant of a matrix.

17) is well known in linear algebra as the eigenvalue problem. 18) where det denotes the determinant of the matrix. The determinant of a matrix with 2 rows and 2 columns is defined by det 1 ~ ~ 1= ad - bc. 18) is called the characteristic equation. 18) yields >. 2 - (A+ D)>. 19) which is equivalent to equation (2. 18). 1 = --2- + J(A-D)2+4BC 2 ' >. 2 = A+D _ J(A-D)2+4BC_ 2 2 The roots of the characteristic equation are called the characteristic roots, or eigenvalues. 15) are given by + K 2 e>-.

9) This equation states that the rate of change of the concentration c as a function of time is the difference between the intake i/V and the removal kc. 9) satisfies c* = i/kV. 9) has a derivative (with respect to c) that is the negative constant -k. 9). 10. For an arbitrary nonlinear function f(x), it might be difficult or impossible to determine a solution analytically. 10. Drug distribution evolution in the one-compartment model. namics. For example, any point for which f(x) =O is a fixed point.

Download PDF sample

Rated 4.40 of 5 – based on 21 votes