How Do Differential Equations Model Electric Circuits in Medical Devices?

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SUMMARY

This discussion focuses on modeling electric circuits in medical devices, specifically using differential equations to analyze the behavior of a pacemaker circuit. The circuit consists of an electric battery, a capacitor, and the heart acting as a resistor. The key equation involves determining the electric tension E(t) applied to the heart, with E(t1) set to E0. The resistance and capacitance are constant, leading to the conclusion that this scenario can be modeled using a first-order linear differential equation.

PREREQUISITES
  • Understanding of differential equations, specifically first-order linear equations.
  • Basic knowledge of electric circuits, including components like capacitors and resistors.
  • Familiarity with the concept of electric tension and its application in medical devices.
  • Ability to interpret and translate mathematical problems from Spanish to English.
NEXT STEPS
  • Study the principles of first-order linear differential equations in detail.
  • Research the role of capacitors in electric circuits, particularly in medical applications.
  • Learn about the mathematical modeling of electric circuits using differential equations.
  • Explore the specific applications of differential equations in biomedical engineering.
USEFUL FOR

Students and professionals in biomedical engineering, electrical engineering, and anyone interested in the mathematical modeling of medical devices, particularly pacemakers.

itzela
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Hi Guys... I'm trying to learn diff.eq on my own and I'm stuck on a problem and I don't even know where or how to begin:

the problem is: the pacemaker shown in the figure (first attatchment) is made up of an electric battery, a small capacitor, and the heart which functions like a resistance in the circuit. When the commuter S connects to P the capacitor charges, when S is connected to Q the capacitor discharges sending an electric shock to the heart. During this time the electric tension E applied to the heart is given by: (second attatchment).

The resistance and the capacitance are both constant...
what is:
E(t)= ? E(t1) = Eo

Would it be a first order linear equation?
Is it homogenous?
What would be the value of the initial voltage?

- i translated it directly from spanish so if further clarifying of the problem is needed please let me know.
 

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any advice on how to start?
 

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