Determining Changes in Blood Volume in the Thorax

To relate blood volume changes to impedance changes, we use the simplified model of the thorax, described in Figure 25.5. We designate the cross sections of blood and tissue and their longitudinal impedances by A _b, A _t, Z _b, and Z _t, respectively. The total longitudinal impedance of the model is

(25.6)

where	Z	= longitudinal impedance of the model
	Z b	= impedance of the blood volume
	Z t	= impedance of the tissue volume

The relationship between the impedance change of the thorax and the impedance change of the blood volume is found by differentiating Equation 25.6 with respect to Z _b:

(25.7)

The impedance of the blood volume with blood resistivity r_b based on the cylindrical geometry of Figure 25.5, is:

(25.8)

where	rb	= blood resistivity
	A b	= cross-section of the blood area
	l	= length of the thorax model

The relationship between changes in blood volume v _b and the blood volume impedance is found by solving for the blood volume in Equation 25.8 and differentiating:

(25.9)

where

v b

= blood volume

We finally derive the dependence of the change in blood volume on the change in thoracic impedance by solving for dZ _b in Equation 25.7 and substituting it into Equation 25.9:

(25.10)

	Лекция 11. ИМПЕДАНСНЫЙ МЕТОД РЕГИСТРАЦИИ ЧАСТОТЫ ДЫХАНИЯ в мониторах

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