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Formula
In today's discussion we shall address the alveolar gas equation. The composition of the alveolar gas is dependent upon atmospheric air and the exchange of gases from the capillary blood in the lungs. The alveolar gas equation establishes a relationship between alveolar ventilation and PAO₂ and PaCO₂
We will demonstrate the utility of the alveolar gas equation with the following case:
In the care of a patient, the flowmeters show nitrous oxide (N₂0) at 0.5 liters/minute and oxygen (O₂) at 0.5 liter/minute and the vaporizer is set to deliver 1.0 % isoflurane. Your monitoring system closely reflects that the patient is truly receiving what you are attempting to deliver. An arterial line is placed (about 10 minutes after the patient has been receiving the above described general anesthetic) since you expect that the procedure will result in significant blood loss. Immediately after placement of the arterial line you send an arterial sample. The PaO₂ is determined to be 300 mm Hg.
1.Is that what you expected?
2.How does one know what to expect?
公式系列：
今天我们着重讨论肺泡气公式。肺泡气的组成依赖于大气以及肺毛细血管交换的气体。肺泡气公式表明了肺泡通气与P_AO₂和PaCO₂之间的关系。
我们将用下面的病例来证明肺泡气公式的有效性：
某患者，麻醉机流量计N₂0 0.5L/min，O₂ 0.5L/min，异氟醚挥发器浓度为1.0%。监测系统也表明患者接受与麻醉机设定相符的参数。考虑到手术可能出现大出血，上述麻醉后10min患者接受动脉穿刺置管。动脉穿刺后即行动脉血检测，PaO₂为300mmHg.
1.这是你期望的结果吗？
2.你如何看待该结果？

编辑：西门吹血

参考答案：
我们今天的问题是，接受全身麻醉的健康患者，已知其吸入与呼出的气体浓度，其动脉血氧分压（PaO₂）能否计算而引出。答案是可以。
为判断实验室获得的PaO₂是否准确，首先需要看能否计算肺泡气氧分压。
改良肺泡气公式描述了其关系：
P_AO₂=(PB-PH₂O)FIO₂-PaCO₂
这里：P_AO₂为肺泡气氧分压
　　　PB为大气压
　　　PH₂O为在1个大气压和37°C情况下的饱和蒸气压
　　　FIO₂为吸入气的氧分数
　　　PaCO₂为动脉血二氧化碳分压
备注：在该改良肺泡气公式中存在以下几种假设：
１，  PaCO₂=P_ACO₂，因为二者之间常不存在较大差异。
２，  F为校正因子，以呼吸商（R）和FIO₂为基础。当在FIO₂较高（>50%，该方程式常用于此情况下）时，F的影响可忽略不计。
建立在该关系基础上，我们可以看到，P_AO₂倍以下因素所影响：
1，吸入气氧浓度
2，大气压
3，动脉血二氧化碳张力
该关系显示，海拔增加，P_AO₂降低；而环境压力增高，比如处于高压氧舱内，P_AO₂增加。
现在我们再来看P_AO₂的计算，我们必须判断实验室获得的PaO2是否建立在PAO2的基础上。根据改良肺泡气公式：
P_AO₂=(PB-PH₂O )FIO₂-PaCO₂
基础为PB =760 mmHg, PH₂O =47 mmHg, FIO₂ =0.21 (空气)，PaCO₂约为40 mmHg，可计算得出P_AO₂ =102.

然后，PaO₂正常值为多少？
PaO₂正常值通常为80-100 mmHg，这是假设病人在PB =760 mmHg，PaCO₂ =40 mmHg 及呼吸空气(FIO₂ =0.21)情况下。PaO₂正常值随年龄增加而减少。下列方程描述了在海平面呼吸空气情况下年龄与PaO₂正常值的关系：
Normal PaO₂ = 102 - (age in years/3)
然而在吸入氧浓度大于21%的情况下麻醉科医生常可以进行血气分析，因此，需要判断实验室获得的PaO₂是否正常的建立在FIO₂ 基础上。
FIO₂变化时，肺泡-动脉梯度(A-a DO₂=PAO₂ - PaO₂)关系为非线性的，这表明了P_AO₂与PaO₂之间的差别。在海平面呼吸空气情况下A-a梯度正常为5-10 mmHg，但也有学者认为A-a梯度低于25mmHg就为正常。同样，FIO₂ = 1.0时，A-a梯度小于等于100为正常。

综合分析：
接受FIO₂ = 0.5的健康患者（假设为海平面），PaCO₂ =40，改良肺泡气公式为：
P_AO₂=(PB-PH₂O )FIO₂-PaCO₂ = (760-47)(0.5)-40=310 mm Hg.
A-a梯度= A-a DO₂=P_AO₂ - PaO₂ = 310-300 = 10
该数值显然在正常范围，即使FIO₂值较低。

编者按：A-a梯度随FIO2变化间的非线性关系尤其明显的临床局限性。比较而言，PaO₂ /FIO₂ 与a/A ratio (a/A=PaO₂ /P_AO₂)更有意义。有学者报道了使用其替代A-a梯度的优点[2]。
因为血红蛋白对于氧运输是决定性的，大家可参考最近的关于血红蛋白对于氧运输影响的文章，该文章也讨论了这种关系的临床和生理学变化[3]。

英文参考答案：
Our questions for today are directed to elicit if an approximation of PaO2 (arterial partial pressure of oxygen) can be calculated for a healthy patient undergoing general anesthesia, when the inspired and expired concentrations of gases are approximately known. The answer is yes.
To determine if our laboratory derived PaO2 is appropriate , we will first need to see if we can determine the, the alveolar partial pressure of oxygen.
An equation called the "modified alveolar gas equation" describes such a relationship (1):
PAO2=(PB-PH2O)FIO2-PaCO2
Where
PAO2 is the partial pressure of oxygen in the Alveolus,
PB is the barometric pressure,
PH2O is saturated vapor pressure of water at 1 atmosphere and 37°C,
FIO2 is the fraction of inspired oxygen, and
PaCO2 is the arterial partial pressure of carbon dioxide.
Of note, several assumptions are made when deriving the "modified alveolar gas equation." Some such assumptions are:
1. PaCO2 equals PACO2 since a large gradient between the two ususally does not exist.
2. F, the correction factor based on the respiratory quotient (R) and the FIO2, is ignored since at high FIO2 (>50%, when this equation is typically called into use), the impact of F becomes negligible.

One immediately observes, based on this relationship, that the PAO2 is affected by:
1. The inspired concentration of oxygen
2. The barometric pressure
3. The arterial carbon dioxide tension.
The relationship reveals that increasing altitude decreases PAO2, while increasing ambient pressure, such as that employed in an hyperbaric oxygen chamber, would increase PAO2.
Now that we see there exists a means for calculating the PAO2 , we must determine if our laboratory derived PaO2 is appropriate based on the just calculated PAO2. From the modified alveolar gas equation we see:
PAO2=(PB-PH2O )FIO2-PaCO2
Based on PB =760 mm Hg, PH2O =47 mm Hg, FIO2 =0.21 (room air), and PaCO2 approximately 40 mm Hg, the values result in a PAO2 =102.

Next, what is a normal PaO2 ?
Normal PaO2 is usually defined as 80 to 100 mm Hg, which assumes that PB =760 mm Hg, PaCO2 =40 mm Hg and that the patient is breathing room air (FIO2 =0.21). The normal PaO2 decreases with age. A formula exists that provides a rough estimate of age depedent normal PaO2 for individuals breathing room air at sea level:
Normal PaO2 = 102 - (age in years/3)

However anesthesiologists usually have blood gas analysis performed on patients receiving inspired oxygen concentrations greater than 21% (room air). As thus, a need exists to determine if a laboratory derived PaO2 is "normal" based on the FIO2 .
The "A-a Gradient" (A-a DO2=PAO2 - PaO2) is a non-linear relationship over varying FIO2 values which expresses the difference in Alveloar PO2 (PAO2) and arterial PO2 (PaO2). For a healthy patient breathing room air at sea level an A-a gradient of 5-10 mm Hg is considered normal --however some authors regard an A-a gradient less than 25 as normal. For the same healthy patient breathing 100% oxygen (FIO2 = 1.0) an A-a gradient of 100 or less is considered normal.

Let's now put all the information together.

Our healthy patient was breathing a gas mixture with an FIO2 = 0.5. Assuming the patient was at sea level, with a PaCO2 =40, the modified alveolar air equation yields:
PAO2=(PB-PH2O )FIO2-PaCO2 = (760-47)(0.5)-40=310 mm Hg.
Our patient's calculated A-a gradient = A-a DO2=PAO2 - PaO2 = 310-300 = 10.
This value is clearly within the normal range for A-a gradient, at this and even at lower FIO2 values.

Editors note: The A-a gradient, which is non-linear with varying FIO2 has obvious limited clinical utility. The PaO2 /FIO2 and the a/A ratio (a/A=PaO2 /PAO2), give numbers useful for comparison. Some authors have addressed advantages of their use instead of the A-a gradient (2).
Bonus: Because hemoglobin is crucial for oxygen transport, the reader is referred to a recent excellent article that addressses how hemoglobin regulates oxyfgen transport. The article also discusses the interesting clinical and physiologic consequences of this regulation (3).
References:
1.  Bowe EA, Klein EF. Acid Base, Blood Gas, Electrolytes. In: Barash PG, Cullen BF, Stoelting RK, eds. Clinical Anesthesia. Philadelphia: J.B. Lippincott, 1989:680-682.
2.  Gross R, Israel RH. A graphic approach for prediction of arterial oxygen tension at different concentrations of inspired oxygen. Chest 1981; 79:311.
3.  Hsia CCW. Respiratory function of hemoglobin. New Eng J Med 1998; 338:239-47.

本周公式系列总结：
祥见附件幻灯。

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编辑：西门吹血