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Formula
1.What is the Bohr equation for calculating dead space (V_D /V_T)?
2.Define dead space, and identify the two components of total dead space.
3.What is the normal value of V_D/V_T?
4.Derive the Bohr equation.
公式系列：
1.何为计算死腔量（V_D/V_T）的波尔方程？
2.请叙述死腔量的定义，并叙述总死腔量两个不同部分的区别。
3.V_D/V_T的正常值？
4.试推导波尔方程。

参考答案：
1.何为计算死腔量（V_D /V_T ）的波尔方程？
假设为理想的肺，肺泡进行气体交换。每次呼吸从肺呼出的气体量（V_E ）包括来自于肺气体交换（肺泡气）、V_A 以及来自于通气道的不参与气体交换的气体部分（即死腔，以V_D 表示）。可以简单的表达式描述该关系：
V_E = V_A + V_D 　　　　　　　　　　　　　　　　　　　　（1）
注：正常呼吸期间V_T （潮气量）等于V_E 。
2.请叙述死腔量的定义，并叙述总死腔量两个不同部分的区别。
因此死腔量可以定义为不参与气体交换的气体量。实际中肺并非理想状态，部分肺泡并未参与气体交换，因为其肺血流少甚至没有。因此，气体进出这些部位时，无氧气摄入或二氧化碳排出。因此，存在总的或生理的死腔：解剖（通气道）和肺泡（低灌注或无灌注肺泡）。
波尔方程可用于计算V_D /V_T ，以及总的呼出潮气量中死腔量的百分比。其表明了死腔与呼出气及动脉血CO₂ 间的关系：
V_D/V_T = (PaCO₂ - PECO₂ )/PaCO₂
PaCO₂ ：动脉血CO₂ 分压
PECO₂ ：呼出气CO₂ 分压
3.V_D/V_T 的正常值？
正常人V_D/V_T 小于0.30。许多导致肺灌注不佳增高的肺部疾病中该分数增加。如果体内CO₂产生量不变，VD/V_T 增加表明，需要增加通气量以排出CO₂。如果机械通气增加不充分，PaCO₂将增高，因为肺泡通气与PaCO₂成反比：
VA = K x VCO₂/PaCO₂ 　　　　　　　　　　　　　　　　（2）
4.试推导波尔方程。
该推导过程并不复杂，建立在质量守恒基础之上。离开肺的全部CO₂必须来自于气体交换区域，而非死腔区域，因此，呼出的气体实际上被死腔气稀释的肺泡气。呼出气中CO₂浓度与呼气量相乘必然等于肺泡产生的CO₂总量：
V_E x F_E = V_A x F_A 　　　　　　　　　　　　　　　　　　（3）
FE和FA分别为呼出气与肺泡气中的CO₂百分比。
从公式1，V_A = V_E - V_D，因此
V_E x F_E = (V_E - V_D) x F_A 　　　　　　　　　　　　　　　（4）
转化方程：
V_D/V_E = (F_A - F_E)/F_A 　　　　　　　　　　　　　　　　（5）
最后，与波尔方程类似，用V_T代替V_E，变换气体分数为分压：
V_D/V_T = (PaCO₂ - PECO₂)/PaCO₂

英文参考答案：

What is the Bohr equation for calculating dead space (VD/VT)?
We begin with an ideal lung, in which there are alveoli that perform gas exchange and conducting airways that do not. The volume of gas exhaled from the lungs with each breath, VE, is comprised of a portion that has come from the gas-exchanging portions of the lung (the alveolar gas), VA, and a portion that has come from conducting airways that do not participate in any gas exchange, called the dead space and denoted VD. We can write a simple expression that illustrates this:
VE = VA + VD  [Equation 1]
Note: VT (tidal volume) is equal to VE during normal breathing.

Define dead space, and identify the two components of total dead space.
Dead space can be defined, therefore, as the volume of gas that does not participate in gas exchange. In practice, lungs are not ideal, and some of the alveoli don't in fact participate in gas exchange because they have no (or very low) pulmonary blood flow. Gas moves in and out of them, but since there is no blood passing through the capillaries, no oxygen is absorbed or carbon dioxide excreted. There are therefore two components of total, or physiological, dead space: anatomic (conducting airways) and alveolar (under- or unperfused alveoli).
The Bohr equation can be used to calculate VD/VT, the fraction of dead space to total expired tidal volume. It relates dead space to expired and arterial CO2:
VD/VT = (PaCO2 - PECO2)/PaCO2
where
PaCO2 = arterial partial pressure of CO2
PECO2 = partial pressure of CO2 in the mixed expired gas

What is the normal value of VD/VT?
Normal humans have a VD/VT of less than 0.30. Many pulmonary diseases which increase the number of poorly perfused alveoli can increase this fraction. If CO2 production by the body does not change, then an increased VD/VT implies that more total ventilation will be required to eliminate this CO2. If ventilation does not increase sufficiently, then PaCO2 will increase, since alveloar ventilation and PaCO2are inversely proportional:
VA = K x VCO2/PaCO2  [Equation 2]

Derive the Bohr equation.
This really isn't that difficult! It is simply based on conservation of mass. All the CO2 that leaves the lungs must have come from gas-exchanging areas, not dead space. So the gas that is exhaled is essentially alveolar gas diluted by dead space gas. The concentration of CO2 in the expired gas multiplied by expired volume must equal all the CO2 produced in the alveoli (concentration multiplied by the volume of alveolar gas):
VE x FE = VA x FA  [Equation 3]
where
FE and FA are the proportions of CO2 in the expired and alveolar gases, respectively
From equation 1, above, VA = VE - VD. Substituting this into equation 3 gives
VE x FE = (VE - VD) x FA  [Equation 4]
Simply rearranging to solve equation 4 for VD/VE yields
VD/VE = (FA - FE)/FA  [Equation 5]
Finally, substituting VT for VE and changing fractions of gas into partial pressures gives the familiar form of the Bohr equation:
VD/VT = (PaCO2 - PECO2)/PaCO2
References:
1.  Nunn JF. Nunn's Applied Respiratory Physiology, 4th ed. Oxford: Butterworth-Heinemann, 1993, pp. 169-78.

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