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October 25, 2005 Start PresentationICSC 2005: Beijing
Object-oriented Modeling in the Service of MedicineFrançois E. Cellier, ETH Zürich
Àngela Nebot, Universitat Politècnica de Catalunya
October 25, 2005 Start PresentationICSC 2005: Beijing
System Complexity and theUnderstandability of Models
• As the systems that are being analyzed by mathematical models have grown in complexity over the years, they have become increasingly difficult to interpret and maintain.
• Modelers need to concern themselves with the understandability and maintainability of their models.
• Tools need to be developed that support them in this endeavor.
October 25, 2005 Start PresentationICSC 2005: Beijing
Object-oriented Modeling• The object-oriented modeling paradigm enables the modeler
to encapsulate knowledge in such a way that snippets of knowledge can be translated to a language familiar to the domain expert.
• The complexity of the models is locally contained by encapsulation and hierarchical composition of models.
• Models are being made more easily understandable by exploiting the two-dimensional nature of planar graphics.
October 25, 2005 Start PresentationICSC 2005: Beijing
Graphical Modeling• Models of subsystems can be encapsulated as
graphical objects, called icons.
• The icons can be topologically interconnected to form a two-dimensional network.
• Sub-networks of graphical objects can be grouped together to form new objects, for which icons can be designed. In this way, systems can be hierarchically composed from sub-systems forming a tree.
• The leaves of the tree must be described by equations.
October 25, 2005 Start PresentationICSC 2005: Beijing
Bond Graph Modeling• Bond graphs are one type of graphical object-
oriented models.
• They describe the power flow through a physical system.
• Since energy and power flow are common to all types of physical systems, bond graphs are domain independent.
• The equation-based leaf models of bond graphs can be pre-coded for all domains.
October 25, 2005 Start PresentationICSC 2005: Beijing
The Bond Model
• The modeling of physical systems by means of bond graphs operates on a graphical description of energy flows.
• The energy flows are represented as directed harpoons. The two adjugate variables, which are responsible for the energy flow, are annotated above (intensive: potential variable, “e”) and below (extensive: flow variable, “f”) the harpoon.
• The hook of the harpoon always points to the left, and the term “above” refers to the side with the hook.
ef
P = e · fe: Effortf: Flow
October 25, 2005 Start PresentationICSC 2005: Beijing
Sources in Bond Graph Representation
U 0
iva vb
U0
+U0
iSe
I 0I
va vb
u
0 Sf uI0
Voltage and current have opposite directions
Energy is being added to the system
October 25, 2005 Start PresentationICSC 2005: Beijing
Passive Electrical Elements in Bond Graph RepresentationRi
va vb
u
Civa vb
u
Liva vb
u
ui
R
ui
C
ui
I
Voltage and current have same directions
Energy is being taken out off to the system
October 25, 2005 Start PresentationICSC 2005: Beijing
Junctions
0e1
e2
e3f1
f2
f3
1e1
e2
e3f1
f2
f3
e1 = e2
e2 = e3
f1 – f2 – f3 = 0
f1 = f2
f2 = f3
e1 – e2 – e3 = 0
October 25, 2005 Start PresentationICSC 2005: Beijing
An Example I
October 25, 2005 Start PresentationICSC 2005: Beijing
An Example II
v0 = 0 P = v0 · i0 = 0
October 25, 2005 Start PresentationICSC 2005: Beijing
An Example III
October 25, 2005 Start PresentationICSC 2005: Beijing
Causal Bond Graphs
• Every bond defines two separate variables, the effort e and the flow f.
• Consequently, we need two equations to compute values for these two variables.
• It turns out that it is always possible to compute one of the two variables at each side of the bond.
• A vertical bar symbolizes the side where the flow is being computed.
ef
October 25, 2005 Start PresentationICSC 2005: Beijing
“Causalization” of the Sources
U0 = f(t)
I0 = f(t)
U0
iSe
Sf uI0
The source computes the effort.
The flow has to be computed on the right side.
The source computes the flow.
The causality of the sources is fixed.
October 25, 2005 Start PresentationICSC 2005: Beijing
“Causalization” of the Passive Elements
ui
R
u = R · i
ui
R
i = u / R
ui
Cdu/dt = i / C
ui
Idi/dt = u / I
The causality of resistors is free.
The causality of the storage elements is determined by the desire to use integrators instead of differentiators.
October 25, 2005 Start PresentationICSC 2005: Beijing
“Causalization” of the Junctions
0e1
e2
e3f1
f2
f3
e2 = e1
e3 = e1
f1 = f2 + f3
1e1
e2
e3f1
f2
f3
f2 = f1
f3 = f1
e1 = e2+ e3
Junctions of type 0 have only one flow equation, and therefore, they must have exactly one causality bar.
Junctions of type 1 have only one effort equation, and therefore, they must have exactly (n-1) causality bars.
October 25, 2005 Start PresentationICSC 2005: Beijing
“Causalization” of the Bond Graph
U0.eU0.f
L1.
f
L1.
e
R1.
e
R1.
f
R2.fR2.e
C1.f
C1.e
C1.e C1.eU0.e
U0.
e
R1.f R1.f
U0 .e = f(t)U0 .f = L1 .f + R1 .f dL1 .f /dt = U0 .e / L1
dC1 .e /dt = C1 .f / C1
C1 .f = R1 .f – R2 .fR2 .f = C1 .e / R2
R1 .e = U0 .e – C1 .eR1 .f = R1 .e / R1
e
October 25, 2005 Start PresentationICSC 2005: Beijing
The Four Base Variables of the Bond Graph Methodology
• Beside from the two adjugate variables e and f, there are two additional physical quantities that play an important role in the bond graph methodology:
p = e · dt
Generalized Momentum:
Generalized Position: q = f · dt
October 25, 2005 Start PresentationICSC 2005: Beijing
Relations Between the Base Variables
e f
qp
R
CI
Resistor:
Capacity:
Inductivity:
e = R( f )
q = C( e )
p = I( f )
Arbitrarily non-linear functions in 1st and 3rd quadrants
There cannot exist other storage elements besides C and I.
October 25, 2005 Start PresentationICSC 2005: Beijing
Effort Flow Generalized Momentum
Generalized Position
e f p q
Electrical Circuits
Voltage
u (V)
Current
i (A)
Magnetic Flux
(V·sec)
Charge
q (A·sec)
Translational Systems
Force
F (N)
Velocity
v (m / sec)
Momentum
M (N·sec)
Position
x (m)
Rotational Systems
Torque
T (N·m)
Angular Velocity
(rad / sec)
Torsion
T (N·m·sec)
Angle
(rad)
Hydraulic Systems
Pressure
p (N / m2)
Volume Flow
q (m3 / sec)
Pressure Momentum
Γ (N·sec / m2)
Volume
V (m3)
Chemical Systems Chem. Potential
(J / mol)
Molar Flow
(mol/sec)
- Number of Moles
n (mol)
Thermodynamic Systems
TemperatureT (K)
Entropy FlowS’ (W / K)
- EntropyS (J / K )
October 25, 2005 Start PresentationICSC 2005: Beijing
Hemodynamics• The hemodynamics describe the flow of blood
through the heart and the blood vessels, i.e., the flow of blood through the cardiovascular system.
• The hemodynamics of the human body can be interpreted as a hydromechanical system. Blood is similar to water, blood vessels can be inerpreted as pipes, and the heart chambers act as hydraulic pumps.
• Some of the chambers and vessels contain valves that act like check valves, preventing a backflow.
October 25, 2005 Start PresentationICSC 2005: Beijing
Transporter Model I
Diagram Window
Icon Window
October 25, 2005 Start PresentationICSC 2005: Beijing
Transporter Model II
Equation window
Documentation window
October 25, 2005 Start PresentationICSC 2005: Beijing
Container Model
Diagram Window
Icon Window
October 25, 2005 Start PresentationICSC 2005: Beijing
Valve Model (Transporter)
Diagram Window
October 25, 2005 Start PresentationICSC 2005: Beijing
Heart Chamber (Container)
Diagram Window
Icon Window
October 25, 2005 Start PresentationICSC 2005: Beijing
Left Ventricle (Heart Chamber)
Diagram Window
October 25, 2005 Start PresentationICSC 2005: Beijing
The Heart
Diagram Window
Icon Window
October 25, 2005 Start PresentationICSC 2005: Beijing
The Thorax
Diagram Window
October 25, 2005 Start PresentationICSC 2005: Beijing
The Cardiovascular System
Icon Window
October 25, 2005 Start PresentationICSC 2005: Beijing
The Cardiovascular System
Heart Rate Controller
Myocardiac Contractility Controller
Peripheric Resistance Controller
Venous Tone Controller
Coronary Resistance Controller
Central Nervous System Control (Qualitative Model)
Regenerate
Regenerate
Regenerate
Regenerate
Regenerate
Heart
Circulatory Flow Dynamics
Carotid Sinus Blood Pressure
Recode
Hemodynamical System (Quantitative Model)
TH
B2
Q4
D2
Q6
PAC Pressure of the arteries in the brain.
October 25, 2005 Start PresentationICSC 2005: Beijing
Simulation Results (Valsalva Maneuver)
October 25, 2005 Start PresentationICSC 2005: Beijing
Summary• Object-oriented graphical modeling has helped us translate a
hydro-mechanical model of the cardiovascular system into a representation that medical personnel can interpret and deal with.
• The knowledge at each layer was suitably encapsulated for limiting the local complexity to a level that can be represented on a single screen.
• No manual translation from the high-level representation to executable simulation code is needed. The graphical model at each level contains all of the model equations at that level and underneath it. Hence the model can be compiled in a fully automated fashion and simulated thereafter.