Center for Computational Visualization

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Lecture 8 Multiscale Bio-Modeling and
VisualizationTissue Models I Cardiac Muscle
Models
Chandrajit Bajaj http//www.cs.utexas.edu/bajaj
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Muscle Tissue Types

• Muscles can be divided into three main groups
  according to their structure
• Smooth muscle tissue.
• Skeletal muscle tissue.
• Cardiac (heart) muscle tissue

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Smooth Muscle

• Characteristics
• thin-elongated muscle cells, fibres. Fibres are
  pointed at their ends
• Each fibre has a single, large, oval nucleus.
• Each cell is filled with a specialised cytoplasm,
  the sarcoplasm and is surrounded by a thin cell
  membrane, the sarcolemma.
• Each cell has many myofibrils which lie parallel
  to one another in the direction of the long axis
  of the cell. They are not arranged in a definite
  striped (striated) pattern, as in skeletal
  muscles - hence the name smooth muscle .
• Interlace to form sheets or layers of muscle
  tissue rather than bundles.
• Smooth muscle is involuntary tissue. Forms the
  muscle layers in the walls of hollow organs such
  as the digestive tract (lower part of the
  oesophagus, stomach and intestines), the walls of
  the bladder, the uterus, various ducts of glands
  and the walls of blood vessels .

• Function
• Smooth muscle controls slow, involuntary
  movements such as the contraction of the smooth
  muscle tissue in the walls of the stomach and
  intestines
• The muscle of the arteries contracts and relaxes
  to regulate the blood pressure and the flow of
  blood.

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Skeletal (Striated) Muscle

• Characteristics
• Most abundant tissue in the vertebrate body.
  Muscles are attached to and bring about the
  movement of the various bones of the skeleton
• The entire muscle, such as the biceps, is
  enclosed in a sheath of connective tissue, the
  epimysium. This sheath folds inwards into the
  substance of the muscle to surround a large
  number of smaller bundles, the fasciculi.
• Fasciculi consist of still smaller bundles of
  elongated, cylindrical muscle cells, the fibres.
• Fibres is a syncytium, i.e. a cell that have many
  nuclei. The nuclei are oval in shaped and are
  found at the periphery of the cell, just beneath
  the thin, elastic membrane (sarcolemma).
• The sarcoplasm also has many alternating light
  and dark bands, giving the fibre a striped or
  striated appearance (hence the name striated
  muscle).
• Each muscle fibre is made up of many smaller
  units, the myofibrils.
• Each myofibril consists of small protein
  filaments, known as actin and myosin filaments.
• The myosin filaments are slightly thicker and
  make up the dark band (or A-band). The actin
  filaments make up the light bands (I-bands) which
  are situated on either side of the dark band.
• The actin filaments are attached to the Z-line.
  This arrangement of actin and myosin filaments is
  known as a sacromere.

• Function
• functions in pairs to bring about the coordinated
  movements of the limbs,jaws, eyeballs
• directly involved in the breathing process

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Cardiac Muscle Tissue

• Characteristics
• Unique tissue found only in the walls of the
  heart.
• combination characteristics of smooth muscle and
  some of skeletal muscle tissue. Fibres , like
  those of skeletal muscle, have cross-striations
  and contain numerous nuclei. Like smooth muscle
  tissue, it is involuntary.
• Differs from striated muscle in the following
  aspects they are shorter, the striations are not
  so obvious, the sarcolemma is thinner and not
  clearly discernible, there is only one nucleus
  present in the centre of each cardiac fibre and
  adjacent fibres branch but are linked to each
  other by muscle bridges. Spaces between different
  fibres are filled with areolar connective tissue
  which contains blood capillaries to supply the
  tissue with the oxygen and nutrients.

• Function
• contraction of the atria and ventricles of the
  heart.
• causes the rhythmical beating of the heart,
  circulating the blood and its contents throughout
  the body as a consequence

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Length-tension relationships in skeletal and
cardiac muscle represents tension developed
during isometric contraction. The physiological
range is the sarcomere length within which the
muscle normally functions.
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Cardiac muscle tissue structure function ?
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The two- and three-dimensional organization of a
sarcomere
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Titin and nebulin Titan spans the distance from
one Z disk to the next M line.
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Changes in a sarcomere during contraction
During contraction the thick and thin filaments
do not change length but slide past each other.
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Excitation-contraction coupling
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Excitation-contraction coupling and relaxation in
cardiac muscle
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Molecular Basis of Contraction
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Regulatory role of tropomyosin and troponin
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Towards Finite Element Models of Sarcomeres
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Quadrilateral Meshing of Circles in 2D
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Algorithm Pipeline for Particle Meshing
Voronoi diagram
Quad Tessellation
Recursive Quad Subdivision
Multi-Linear Centroid Smoothing
Adaptive Quadrilateral Mesh
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Voronoi Computation and Simplification
Cf Imai, Iri, et. al. 1985, Sugihara, Iri et.
al. 1992,
Short Edge Removal and Boxing
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Quad Tesselation of Each Voronoi Cell
Radial and Angular Quad Subdivision
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Adaptive Quad Decomposition via Radial and
Angular Subdivision
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Adaptive Recursive Subdivision MLCS
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Recursive Subdivision (cf Chaitin,
Catmull-Clark)
Limit Curves, and Surface are C2
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Recursive Subdivision with Multi-Linear Centroid
Smoothing (MLCS)
Univariate case the subdivision rule for cubic
B-splines can be expressed as linear subdivision
followed by smoothing with the mask (
). Geometric interpretation of mask reposition
a vertex as the midpoint of the midpoints of the
two segments that contain the vertex. Bivariate
case Bi-cubic subdivision is equivalent to
Bi-linear subdivision followed by smoothing with
the tensor product of the univariate mask with
itself, i.e.

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Multivariate Subdivision I

• Generalization to MLCS
• Multi linear Interpolation Centroid smoothing

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MLCS Subdivision II

• MLCS Subdivision of a cube

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MLCS Subdivision III

• Hexahedron
• The hexahedron is a polyhedron with 6 planar
  faces.
• A hexahedral mesh consists of only the hexahedra

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MLCS Subdivision IV

• Hexahedral mesh with MLCS

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MLCS Subdivision V

• MLCS with Creases

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Adaptive Hexahedral Meshing of Particles in 3D
D
C
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A
G
F
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H
J
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Extra Slides

• Cardiac musclephysiology

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Human cardiac muscle cells physiology
http//www.bmb.leeds.ac.uk/illingworth/muscle/car
diac
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Control cardiac muscle contraction I

• The Na/K ATPase or sodium pump (1) works
  continuously, using the energy from ATP to
  maintain a high K concentration inside the cells
  and a high Na concentration in the extracellular
  fluid (ECF). The cell membrane (sarcolemma) is
  usually more permeable to potassium ions than to
  sodium ions, and this gives rise to a membrane
  potential of about 80mV (inside negative) in
  relaxed muscle. Calcium ions are also removed
  from the cytosol into the ECF by an ATP-driven
  calcium pump (2) in all tissues. Cardiac muscle
  possesses an additional sodium/calcium exchange
  protein (3). This export system is driven by the
  pre-existing sodium ion gradient. The calcium
  concentration inside resting cells is low, but
  rises sharply during contractions.
• The sarcolemma is very thin (about 6 nm) so the
  80mV membrane potential equates to a voltage
  gradient of about 13,000,000 volts per metre! All
  membrane components are subject to intense
  electric fields, and protein conformations are
  greatly influenced by the membrane potential.
  "Voltage gated" ion channels will only conduct
  over a narrow range of membrane potentials,
  whereas "ligand gated" ion channels (such as the
  acetylcholine receptor in voluntary muscle)
  require specific chemical activators.

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Control cardiac muscle contraction II

• Contraction in cardiac muscle is triggered by a
  wave of membrane depolarisation which spreads
  from neighbouring cells. The change in electric
  field activates voltage gated sodium channels (4)
  in the sarcolemma, each of which allows a few
  hundred positively charged sodium ions to enter
  the negatively charged cytosol, further reducing
  the cardiac membrane potential until the whole
  sarcolemma is depolarised.
• The sodium channel undergoes a second
  conformational change, as a result of which these
  channels close spontaneously after a few
  milliseconds in all excitable tissues. In cardiac
  muscle, but NOT skeletal muscle, slower
  voltage-gated calcium channels, probably
  identical with dihydropyridine receptors (5) take
  over and maintain a positive inward current for
  several hundred milliseconds (in human ventricle)
  during the plateau phase of the cardiac action
  potential. As in nerves and skeletal muscle, the
  membrane potential in cardiac muscle is
  eventually restored to its resting value by a
  delayed efflux of positive potassium ions from
  the cells.

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Control cardiac muscle contraction III

• Dihydropyridine drugs (e.g. verapamil
  nifedipine) inhibit calcium entry into heart and
  reduce blood pressure. About 10 of the calcium
  needed to activate cardiac contraction enters
  during each beat from the ECF. This is often
  described as "trigger calcium". The remainder is
  released from the sarcoplasmic reticulum through
  a channel known as the ryanodine receptor (6).
  Ryanodine receptors are widely distributed in the
  body, and are present in non-muscle tissues such
  as the brain. The genes coding for this enormous
  protein (5037 amino acids) have been sequenced.
  Different tissues have their own specific
  isoenzymes. The operation of the ryanodine
  receptor depends in a mysterious way on the flow
  of calcium ions through the dihydropyridine
  receptors in cardiac muscle, but not in other
  muscle types.
• Calcium ions from both sources bind to the
  regulatory protein troponin-C located in the thin
  filaments (7), leading to a change in filament
  shape. This allows flexible head groups from the
  protein myosin in the thick filaments (8) to
  interact with the protein actin in the thin
  filaments. A change in myosin conformation causes
  the thick and thin filaments to slide against
  each other and hydrolyse ATP, which provides the
  energy for contraction. Movement and ATP
  hydrolysis continue until the calcium ions are
  removed from the cytosol at the end of each
  contraction. Most of the calcium ions are
  returned to the sarcoplasmic reticulum by a
  calcium pump (9) but about 10 leave the cell via
  proteins (2) and (3) described above. Calcium
  ions are stored within the sarcoplasmic reticulum
  loosely bound to a protein, calsequestrin (10).

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Control cardiac muscle contraction IV

• In cardiac muscle circulating hormones like
  catecholamines and glucagon bind to specific
  receptors (11) on the outer surface of the
  sarcolemma, changing their shape. This change is
  communicated via G-proteins (12) within the
  sarcolemma to adenyl cyclase (13) bound to the
  internal face of the sarcolemma. Several
  G-proteins are known, some activatory, others
  inhibitory. They all slowly hydrolyse GTP while
  working, although it is not clear what advantage
  this confers on the cell. Adenyl cyclase
  manufactures 3'5' cyclic AMP, which is
  continuously destroyed by a phosphodiesterase
  enzyme. The steady-state concentration of cyclic
  AMP depends on the balance between synthesis and
  degradation. Cyclic AMP in turn controls the
  activity of cyclic AMP-dependent protein kinase.
  This enzyme phosphorylates several of the
  proteins involved in the contraction process, and
  temporarily alters their properties until a
  protein phosphatase restores the status quo ante
  by removing the phosphate group.
• The sodium pump (1) is activated by
  phosphorylation, which allows it to handle the
  increased ion traffic across the sarcolemma when
  cardiac work output rises.
• The dihydropyridine receptor (5) is activated by
  phosphorylation, increasing calcium entry into
  the cells. The ryanodine receptor (6) is also
  activated, increasing the rate of calcium release
  from the sarcoplasmic reticulum. The troponin-I
  component in the thin filaments (7) is
  phosphorylated and this reduces calcium binding
  to the neighbouring troponin-C. (This may be a
  defence mechanism preventing tetany in cardiac
  muscle, which would be rapidly fatal.)

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Control cardiac muscle contraction V

• A small protein called phospholamban associated
  with the sarcoplasmic reticulum calcium pump (9)
  is phosphorylated, and this accelerates calcium
  uptake by the S.R. pump. (A fast heart rate
  requires quick relaxation as well as rapid
  contraction.)
• The enzymes triglyceride lipase (14) and glycogen
  phosphorylase (15) are activated by
  phosphorylation. These enzymes catalyse the first
  steps in the mobilisation of food reserves. They
  eventually increase the supply of ATP and provide
  the energy for the anticipated extra work.
• These changes take place in a coordinated
  sequence over many seconds, so that the initial
  response to adrenalin may be a pounding heart,
  but both the rate and the force of contraction
  tend to return to normal when the stimulation is
  prolonged.

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Modulation of cardiac contraction by
catecholamines
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Action potential of a cardiac contractile cell
The phase numbers are a convention.
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Refractory periods and summation in skeletal and
cardiac muscle
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Action potentials in cardiac autorhythmic cells
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