MLE example Let us consider a mock loop simulator of the - - PDF document

Lesson 14 Another example of MLE: mock loop circuits for in vitro studies

• f the cardiovascular system.

Ettore Lanzarone April 20, 2020

MEDICAL SUPPORT SYSTEMS FOR CHRONIC DISEASES

Engineering and Management for Health University of Bergamo

LESSON 14

MLE example

Let us consider a mock loop simulator of the cardiovascular system, i.e., a circuit that mimics the physiological or pathological conditions of the human circulation.

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Lesson 14

MLE example

To have a reliable description of the circulation, it is fundamental that the parameters of the afterload circuit fit those of the physiological or pathological condition to study. Such afterload circuit is modeled via a lumped parameter model:

MLE example

Parameters Rc, C and Rp can be dimensioned while designing the compnents of the circuit. However, the itertance L does not correspond to any component of the circuit, and inertial effects are always present; importance of estimating it to have a value similar to that in the vascular system to study. This parameter also affects the apparent value of the

• ther parameters; thus, all of them have to be estimated

from the physical circuit to assess its effectiveness.

Lesson 14

MLE example

They can be estimated via an MLE approach. Equations of the afterload circuit: They give a first order ODE for P(t)

MLE example

Discretization of the ODE:

Lesson 14

MLE example

Dataset:

• Text file attached
• Time discretization step is 0.005 seconds

MLE example

Tasks:

• Assume errors to write a fair conditioned density for each Pi
• Write the likelihood function (or better the log likelihood function)
• Estimate the parameters of the circuit
• Compare with those of the attached scientific papers and with those of Sharp and

Dharmalingam (see previous lesson on lumped parameter models of circulation)

Lesson 14

MLE example