Chapter 6, Problem 11RCC

a.

To determine

To define: The cardiac output of the heart.

Answer to Problem 11RCC

The cardiac output of the heart is the volume of blood pumped by the heart per unit time, that is, the rate of flow into the aorta.

Explanation of Solution

Given information :

Cardiac Output of the heart.

The cardiac output of the heart is the volume of blood pumped by the heart per unit time, that is, the rate of flow into the aorta.

b.

To determine

To explain: How the cardiac output can be measure by the dye dilution method.

Answer to Problem 11RCC

  $F=\frac{A}{{\displaystyle {\int }_0^{T}c\left(t\right)dt}}$

where the amount of dye $A$ is known and the integral can be approximated from the concentration readings.

Explanation of Solution

Given information :

Dye dilution method.

Concept used :

The dye dilution method is used to measure the cardiac output. Dye is injected into the

Right atrium and flows through the heart into the aorta. A probe inserted into the aorta

measures the concentration of the dye leaving the heart at equally spaced times over a time

interval until the dye has cleared.

The dye dilution method is used to measure the cardiac output. Dye is injected into the

Right atrium and flows through the heart into the aorta. A probe inserted into the aorta

measures the concentration of the dye leaving the heart at equally spaced times over a time

interval $\left[0,T\right]$ until the dye has cleared.

Let $c\left(t\right)$ be the concentration of the dye at time $t$ .

If we divide $\left[0,T\right]$ into subintervals of equal length $\Delta t$ , then the amount of dye that flows

past the measuring point during the subinterval from $t=t_{i-1}\text{ to }t=t_i$ is approximately.

  $\left(\text{Concentration}\right)\left(\text{Volume}\right)=c\left(t_i\right)\left(F\Delta t\right)$

Where $F$ is the rate of flow that we are trying to determine. Thus the total amount of dye

is approximately

  ${\displaystyle \sum _{i=1}^{n}c\left(t_i\right)\left(F\Delta t\right)}=F{\displaystyle \sum _{i=1}^{n}c\left(t_i\right)\Delta t}$

and, letting $n\to \infty$ , we find that the amount of dye is

  $A=F{\displaystyle {\int }_0^{T}c\left(t\right)dt}$

Thus the cardiac output is given by

  $F=\frac{A}{{\displaystyle {\int }_0^{T}c\left(t\right)dt}}$

where the amount of dye $A$ is known and the integral can be approximated from the concentration readings.