Computational Modeling of the Cardiovascular and Neuronal System
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1 BIOEN 6900 Computational Modeling of the Cardiovascular and Neuronal System Overview Introduction to Anatomy Overview Overview History Rationale Topics Literature Introduction to Anatomy Macroscopic Cellular Molecular Modeling Summary Computational Modeling of the Cardiovascular and Neuronal System - Page 2
2 Anatomical Models of the Heart Leonardo da Vinci ( ), Anatomical Handbooks Computational Modeling of the Cardiovascular and Neuronal System - Page 3 Functional Cardiac Model Leonardo da Vinci, Codex Arundel Computational Modeling of the Cardiovascular and Neuronal System - Page 4
3 Anatomical Models of Brain Leonardo da Vinci, The Early Drawings, 1490 Andreas Vesalius, De Fabricia, 1543 Computational Modeling of the Cardiovascular and Neuronal System - Page 5 Classification of Lesson Computational Biology Genom Proteom Cell Tissue Organ Lesson covers Electrophysiology Mechanics Metabolism Body Computational Modeling of the Cardiovascular and Neuronal System - Page 6
4 Rationale Medical question Pharmaceutical question Technical question Experimental study with human Experiment with physical model Computer simulation Solution Numerical methods Mathematical modeling Computational Modeling of the Cardiovascular and Neuronal System - Page 7 Introduction to Anatomy Macroscopic Cellular Molecular Membrane Ion channels Sarcomere proteins Modeling Analytical Imaging and image processing based Computational Modeling of the Cardiovascular and Neuronal System - Page 8
5 Electrophysiological Modeling of Membranes and Ion Channels Membrane models Experimental studies Molecular structure Equivalent circuits Ion channel models Experimental studies Classification Molecular structure Hodgkin-type models Markovian models Solving of ordinary differential equations I Computational Modeling of the Cardiovascular and Neuronal System - Page 9 Electrophysiological Modeling of Cells Experimental studies Hodgkin-Huxley membrane model Modeling of neurons! i Modeling of cardiac myocytes I m I C I Na I K Solving of ordinary differential equations II C m R Na R K V Na V k +! e Computational Modeling of the Cardiovascular and Neuronal System - Page 10
6 Modeling of Electrical Conduction in Cardiac and Neuronal Tissue Experimental studies Nodes of Ranvier Synapses Gap Junctions Modeling Approaches Cellular automata Reaction diffusion equations Numerical Methods Finite Element methods I Finite Difference methods I Computational Modeling of the Cardiovascular and Neuronal System - Page 11 Modeling of Force in Myocytes Experimental studies approaches Modeling and numerical A M ATP A M M ATP M A M ADP M ADP P i M ADP A M ADP A M ADP P i A M ADP P i Computational Modeling of the Cardiovascular and Neuronal System - Page 12
![Mechanical Modeling of Tissue Experimental studies Definitions and physical laws Stress [N/m 2 ] Strain and stress tensors Constitutive relationships Numerical Methods Finite element methods II](/docs-images/87/97054079/images/7-0.jpg "Finite difference methods II Strain [m/m] Computational Modeling of the Cardiovascular and Neuronal System - Page 13 Modeling of Blood Flow in Tissue and Organs Experimental studies Definitions and")
7 Mechanical Modeling of Tissue Experimental studies Definitions and physical laws Stress [N/m 2 ] Strain and stress tensors Constitutive relationships Numerical Methods Finite element methods II Finite difference methods II Strain [m/m] Computational Modeling of the Cardiovascular and Neuronal System - Page 13 Modeling of Blood Flow in Tissue and Organs Experimental studies Definitions and physical laws Lung Velocity and stress tensors Constitutive relationships Numerical solution Lumped parameter models Finite element methods III Finite difference methods III Body Computational Modeling of the Cardiovascular and Neuronal System - Page 14
8 Modeling of Cellular Metabolism Experimental studies Mitochondria Metabolites and Enzymes ATP Hydrolysis Computational Modeling Computational Modeling of the Cardiovascular and Neuronal System - Page 15 Forward Problems in Bioelectromagnetism I-III Instructor: Jeroen Stinstra Source Modeling Modeling of conductivity Boundary element method Computational Modeling of the Cardiovascular and Neuronal System - Page 16
9 Integration and Coupling of Models Experimental studies Modules Interfaces Metabolism Force development Anatomy Electrophysiology Structure mechanics Computational Modeling of the Cardiovascular and Neuronal System - Page 17 Computational Models as Tools for Research and Development Electro-mechanical modeling tools Channels Cells Cell clusters Heart Brain SCIRun Virtual Cell JSim MeetMan Tools Applications Clinical therapy and diagnosis Drug development and testing Development of biomedical instrumentation Research in biology, bioengineering and medicine Computational Modeling of the Cardiovascular and Neuronal System - Page 18
10 Material Literature Hille: Sachse: Malmivuo, Plonsey: Bathe: Buchanan: Ion Channels of Excitable Membranes Sinauer Associates Computational Cardiology LNCS 2966, Springer Press Bioelectromagnetism Oxford University Press Finite Element Procedures Prentice Hall Schaum s outlines: Finite Element Analysis Slides Computational Modeling of the Cardiovascular and Neuronal System - Page 19 Cardiovascular System Lung Mammalian heart central component of cardiovascular system mostly composed of muscle connected to blood vessels transports blood to/from body and lung autonomous function, but modulated by nervous system divided in two subsystems, left and right, each consisting of atrium and ventricle Body Computational Modeling of the Cardiovascular and Neuronal System - Page 20
11 Heart in Thorax Right lobe of lung Left lobe of lung Blood vessels Blood vessels Computational Modeling of the Cardiovascular and Neuronal System - Page 21 Horizontal Cut Through Thorax Computational Modeling of the Cardiovascular and Neuronal System - Page 22
12 Heart From Right Side Aorta Vena cava superior Coronary arteries Auricula dexter Vena cava inferior Computational Modeling of the Cardiovascular and Neuronal System - Page 23 Heart from Dorsal Left atrium Vena cava inferior Sinus coronarius Right atrium Right ventricle Left ventricle Computational Modeling of the Cardiovascular and Neuronal System - Page 24
13 Left and Right Ventricle Atrioventricular valves Chordae tendineae Chordae tendinae Right ventricle Left ventricle Papillary muscles Papillary muscles Septum Computational Modeling of the Cardiovascular and Neuronal System - Page 25 Opened Right Ventricle with Valve and Papillary Muscles Computational Modeling of the Cardiovascular and Neuronal System - Page 26
14 Opened Left Ventricle Semilunar valve Mitral valve Chordae tendineae Papillary muscle Computational Modeling of the Cardiovascular and Neuronal System - Page 27 Semilunar Valve Computational Modeling of the Cardiovascular and Neuronal System - Page 28
15 Opened Right Atrium and Ventricle Vena cava superior Fossa ovalis (Foramen ovale) Vena cava inferior Sinus coronarius Musculi pectinati Computational Modeling of the Cardiovascular and Neuronal System - Page 29 Conduction System in Cow Heart (Lewis 1925) Computational Modeling of the Cardiovascular and Neuronal System - Page 30
16 Microscopic Anatomy of Cardiac Tissue Myocytes are connected at intercalated discs intracellular space via gap junctions mechanical coupling (Saffitz et al. 99) Computational Modeling of the Cardiovascular and Neuronal System - Page 31 Microscopic Cellular Anatomy Myocyte of ventricular myocardium cylinder-shaped length: !m diameter: ca. 8-15!m (Hoyt et al. 89) Myocyte (M) and capillary (C) mechanically coupled by fibers of connective tissue (collagen and elastin) (Caulfield et al. 79) Computational Modeling of the Cardiovascular and Neuronal System - Page 32
17 Intracellular Structures of Myocytes: Sarcomeres Sarcoplasmic reticulum Terminal cisternae Mitochondrion Transversal tubuli Z-disc Sarcoplasmic reticulum Dyad Computational Modeling of the Cardiovascular and Neuronal System - Page 33 Major Subdivisions of the Cerebral Cortex (figure from Computational Modeling of the Cardiovascular and Neuronal System - Page 34
18 Median Sagittal Cut Through Human Brain (figure from Computational Modeling of the Cardiovascular and Neuronal System - Page 35 Horizontal Cut Through Visible Man Head Computational Modeling of the Cardiovascular and Neuronal System - Page 36
19 Major Components of Neurons (Malmivuo and Plonsey, Bioelectromagnetism, 1993) Computational Modeling of the Cardiovascular and Neuronal System - Page 37 Connected Neurons (Slice of Life project: Neurons in the hippocampus located inside the temporal lobe) Computational Modeling of the Cardiovascular and Neuronal System - Page 38
20 Molecular Structure of Cell Membrane hydrophobic Phospholipid hydrophilic Nitrogen Oxygen Phosphor Carbon (Hydrogen not represented) ~ 6 nm (Structure data from Heller, Schaefer and Schulten, J. Phys. Chem., 1993) Computational Modeling of the Cardiovascular and Neuronal System - Page 39 Molecular Structure of Transmembrane Proteins Transmembrane proteins: connexons, ion channels, pumps, and -exchangers Example: Molecular structure of potassium channel Kcsa of bacterium streptomyces lividans, color-coded amino acids Structure data from Molecular Modeling Database, NIH, USA side from top ~ 6 nm Computational Modeling of the Cardiovascular and Neuronal System - Page 40
21 Molecular Structure of Proteins in Sarcomere 2 µm Actin Myosin Actin Z Disc Molecular Structure of Tropomyosin Structure data for species gallus gallus from Molecular Modeling Database, NIH, USA (Gordon, Regnier, and Homsher, News Physiol. Sci., 2001, modified) Computational Modeling of the Cardiovascular and Neuronal System - Page 41 Anatomical Modeling Optical measurements Microscopic Macroscopic Imaging Computed Tomography Magnetic Resonance Tomography Ultrasonic Tomography Analytical description Image processing Anatomical model Computational Modeling of the Cardiovascular and Neuronal System - Page 42
22 Anatomical Model: Confocal, Truncated Ellipsoids b 1 b2 base a 1 a 2 equato r apex a 1, a 2 : Major axis b 1, b 2 : Minor axis Focus length: f = a 2 " b 2 n x n x m cubic elements Computational Modeling of the Cardiovascular and Neuronal System - Page 43 MR-Imaging of Canine Heart Right Ventricle Left Ventricle Right Ventricle Left Ventricle Apex Apex frontal lateral (Sachse, Henriquez, Seemann, Riedel, Werner, Penland, Davis and Hsu, CinC, 2001) Computational Modeling of the Cardiovascular and Neuronal System - Page 44
23 Anatomical Model View into left ventricle View into right ventricle Computational Modeling of the Cardiovascular and Neuronal System - Page 45 Anatomical Model: Visible Man Data Set Tissue Fiber orientation Conduction system Computational Modeling of the Cardiovascular and Neuronal System - Page 46
24 Model of Macroscopic Anatomy with Fiber Orientation Auricula dexter Auricula sinister Left atrium Right ventricle Left ventricle Apex cordis Computational Modeling of the Cardiovascular and Neuronal System - Page 47 Anatomical Model of Brain via Image Processing Skin Gray matter White matter CSF Skull (Wolters, Anwander, Tricoche, Lew, and Johnson, Proc. Int. Conf. Bioelectromagn., 2005) Computational Modeling of the Cardiovascular and Neuronal System - Page 48
25 Anatomical Model of Brain via Image Processing (F. B. Sachse, Ph.D. thesis, 1997) Computational Modeling of the Cardiovascular and Neuronal System - Page 49 Summary Overview History Rationale Topics Literature Introduction to Anatomy Macroscopic Cellular Molecular Modeling Computational Modeling of the Cardiovascular and Neuronal System - Page 50
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