object-oriented modeling in the service of medicine

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

http://www.ethz.ch/


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.

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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.

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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.

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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.

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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 · f e: Effortf: Flow

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Sources in Bond Graph Representation

U 0iva vb

U0

+U0

iSe

I 0Iva vb

u

0 Sf uI0

Voltage and current have opposite directions

Energy is being added to the system

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Passive Electrical Elements in Bond Graph RepresentationRiva vb

u

Civa vb

u

Liva vbu

ui

R

ui

C

ui

I

Voltage and current have same directions

Energy is being taken out off to the system

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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

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An Example I

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An Example II

v0 = 0 P = v0 · i0 = 0

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An Example III

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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

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“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.

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“Causalization” of the Passive Elements

ui

Ru = R · i

ui

Ri = 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.

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“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.

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“Causalization” of the Bond Graph

U0.eU0.f

L1.

fL

1.e

R1.

eR

1.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

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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

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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.

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Effort Flow Generalized Momentum

Generalized Position

e f p q

Electrical Circuits

Voltageu (V)

Currenti (A)

Magnetic Flux (V·sec)

Chargeq (A·sec)

Translational Systems

ForceF (N)

Velocityv (m / sec)

MomentumM (N·sec)

Positionx (m)

Rotational Systems

TorqueT (N·m)

Angular Velocity (rad / sec)

TorsionT (N·m·sec)

Angle (rad)

Hydraulic Systems

Pressurep (N / m2)

Volume Flowq (m3 / sec)

Pressure MomentumΓ (N·sec / m2)

VolumeV (m3)

Chemical Systems Chem. Potential (J / mol)

Molar Flow (mol/sec)

- Number of Molesn (mol)

Thermodynamic Systems

TemperatureT (K)

Entropy FlowS’ (W / K)

- EntropyS (J / K )

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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.

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Transporter Model I

Diagram Window

Icon Window

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Transporter Model II

Equation window

Documentation window

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Container Model

Diagram Window

Icon Window

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Valve Model (Transporter)

Diagram Window

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Heart Chamber (Container)

Diagram Window

Icon Window

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Left Ventricle (Heart Chamber)

Diagram Window

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The Heart

Diagram Window

Icon Window

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The Thorax

Diagram Window

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The Cardiovascular System

Icon Window

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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.

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Simulation Results (Valsalva Maneuver)

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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.

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object-oriented modeling in the service of medicine

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