Chapter 6, Problem 11RQ

Summary Introduction

Case summary: A 37-year-old woman met with an accident and is on a volume-cycled mechanical ventilator.

Characters in the case: A 37-year-old woman met with an accident.

Adequate information: The barometric pressure is 745 mm Hg. She was receiving ${\text{Fl}}_{{\text{O}}_{\text{2}}}$ of 0.50.

To determine: The total oxygen delivery, the arterial venous content difference, the intrapulmonary shunting, oxygen consumption, and the oxygen extraction ratio.

Explanation of Solution

Given information:

Cardiac output: 6 L/min

Hb: 11g/dL

${\text{Pa}}_{{\text{O}}_{\text{2}}}$: 60 mm Hg

${\text{P}\overline{\text{v}}}_{{\text{O}}_{\text{2}}}$: 35 mm Hg

${\text{Pa}}_{{\text{CO}}_2}$: 38 mm Hg

With this information,

$\begin{array}{cc}\hfill {\text{P}}_{{\text{A}}_{{\text{O}}_{\text{2}}}}& ={\text{(BP-PH}}_{\text{2}}{\text{O) Fl}}_{{\text{O}}_{\text{2}}}{\text{-Pa}}_{{\text{CO}}_{\text{2}}}\text{(1}\text{.25)}\hfill \\ \hfill & =\text{(745-47) 0}\text{.5 - 38(1}\text{.25)}\hfill \\ \hfill & =\text{(698)0}\text{.5 - 47}\text{.5}\hfill \\ \hfill & =\text{349 - 47}\text{.5}\hfill \\ \hfill & =\text{301}\text{.5}\hfill \end{array}$

$\begin{array}{cc}\hfill {\text{Cc}}_{{\text{O}}_{\text{2}}}& =\text{(Hb×1}\text{.34)}+{\text{(P}}_{\text{A}}{}_{{}_{{\text{O}}_{\text{2}}}}\text{×0}\text{.003)}\hfill \\ \hfill & =\text{(11×1}\text{.34)}+\text{(301}\text{.5×0}\text{.003)}\hfill \\ \hfill & =\text{14}\text{.74}+\text{0}\text{.90}\hfill \\ \hfill & =\text{15}\text{.64}\hfill \end{array}$

$\begin{array}{cc}\hfill {\text{Ca}}_{{\text{O}}_{\text{2}}}& =\text{(Hb×1}{\text{.34×Sa}}_{{\text{O}}_{\text{2}}}\text{)}+{\text{(Pa}}_{{\text{O}}_{\text{2}}}\text{×0}\text{.003)}\hfill \\ \hfill & =\text{(11×1}\text{.34×0}\text{.90)}+\text{(60×0}\text{.003)}\hfill \\ \hfill & =\text{13}\text{.266+0}\text{.18}\hfill \\ \hfill \text{=13}\text{.44}\end{array}$

$\begin{array}{cc}\hfill {\text{C}}_{\overline{\text{v}}}& =\text{(Hb×1}{.34}_{\times }\text{)}+{\text{(P}}_{\overline{\text{v}}}\text{×0}\text{.003)}\hfill \\ & =\text{(11×1}\text{.34×0}\text{.65)}+\text{(35×0}\text{.003)}\hfill \\ & =\text{9}\text{.581}+\text{0}\text{.105}\hfill \\ & =\text{9}\text{.686}\hfill \end{array}$

A)

$\begin{array}{cc}\hfill \text{Total}\text{oxygen delivery}& ={\text{Q}}_{\text{T}}\times {\text{Ca}}_{{\text{O}}_{\text{2}}}\times \text{10}\hfill \\ \hfill & =\text{6}\times \text{13446}\times \text{10}\hfill \\ \hfill & =\text{806}{\text{.76 ml O}}_{\text{2}}\text{/min}.\hfill \end{array}$

B)

$\begin{array}{cc}\hfill \text{Arterial-venous oxygen content difference C(a}-{\text{v)}}_{O_2}& ={\text{Ca}}_{O_2}-{\text{C}}_{\overline{\text{v}}}\hfill \\ \hfill & =13.44-9.68\hfill \\ \hfill & =3.760{\text{mL/dL O}}_2\hfill \end{array}$

C)

$\begin{array}{cc}\hfill \text{Intrapulmonary shunting (}\frac{\text{QS}}{\text{QT}}\text{)}& =\frac{{\text{Cc}}_{{\text{O}}_{\text{2}}}{\text{-Ca}}_{{\text{O}}_{\text{2}}}}{{\text{Cc}}_{{\text{O}}_{\text{2}}}{\text{-Cv}}_{{\text{O}}_{\text{2}}}}\hfill \\ \hfill & =\frac{\text{15}\text{.64}-\text{13}\text{.44}}{\text{15}\text{.64}-\text{9}\text{.68}}\hfill \\ \hfill & =\frac{\text{2}\text{.198}}{\text{5}\text{.958}}\hfill \\ \hfill & =\text{0}\text{.37 \%}\hfill \end{array}$

D)

$\begin{array}{cc}\hfill {\text{Oxygen consumption }}_{\dot{\text{V}}}& ={\dot{\text{Q}}}_{\text{T}}{\text{[C(a-}}_{\overline{\text{v}}}\times \text{10]}\hfill \\ \hfill & =\text{6}\times \text{3}\text{.760}\times \text{10}\hfill \\ \hfill & =\text{225}\text{.6}\text{mL}{\text{O}}_2\text{/min}\hfill \end{array}$

E)

$\begin{array}{cc}\hfill \text{Oxygen extraction ratio}& =\frac{{\text{Ca}}_{O_2}-{\text{C}\overline{\text{v}}}_{O_2}}{{\text{Ca}}_{O_2}}\hfill \\ \hfill & =\frac{13.44-9.68}{13.44}\hfill \\ \hfill & =\frac{3.760}{13.446}\hfill \\ \hfill & =0.279\hfill \end{array}$

Conclusion

Therefore it can be concluded that $806.76\text{mL}\text{O2/min}$ is the total oxygen delivery, $225.6\text{mL}\text{O2/min}$ is the oxygen consumption, the intrapulmonary shunting is 36.8%, $3.7\text{mL/dL}$ is the arterial-venous oxygen content difference, and 0.279 is the oxygen extraction ratio.