血氧饱和度计算函数异常：结果为负值问题求助

实现血氧饱和度计算函数时出现异常：采用公认的科学公式计算，返回结果为负值，且绝对值与正确值相差数个百分点，预期结果应为0-100之间的正值，推测问题出在血氧系数计算或常量使用上。

原问题代码 #

private float _calculate_blood_oxygen_saturation(
    float inspiredPartialPressure_kPa,
    float arterialPartialPressure_kPa,
    float temperature_C
)
{
    // Constants for the oxygen-hemoglobin dissociation curve coefficients
    const float _A = -173.4292f;
    const float _B = 248.3763f;
    const float _C = 0.7102f;
    const float _D = -0.9959f;
    const float _E = -0.2337f;

    // Calculate the oxygen saturation curve coefficient
    float temperature_K = temperature_C + 273.15f;

    float oxygenSaturationCurveCoefficient =
        _A +
        ( _B / temperature_K ) +
        ( _C * Mathf.Log( temperature_K ) ) +
        ( _D * Mathf.Pow( 10.0f, _E * ( temperature_K - 50 ) ) );

    // Calculate the oxygen saturation percentage
    float saturationPercentage = ( inspiredPartialPressure_kPa / arterialPartialPressure_kPa ) * 100.0f;
    float saturation           = ( saturationPercentage / oxygenSaturationCurveCoefficient ) * 100.0f;

    return saturation;
}

补充输入参数 #

• arterialPartialPressure 为常量（95 mmHg * 0.133322f）
• 环境温度接近20℃
• inspiredPartialPressure 取值约为20

参考生理资料与重实现代码 #

参考生理资料：

• 血氧饱和度：血红蛋白中氧合血红蛋白的占比，可通过血氧测定仪直接测量
• 血氧容量：血红蛋白能结合的最大氧量，计算公式为患者血红蛋白值 × 1.34，单位为mL/100mL

基于上述资料修订公式与计算逻辑，简化使用平均生理常量以生成合理输出，更新后代码如下：

private float _calculate_blood_oxygen_content(
    float inspiredPartialPressure, 
    float arterialPartialPressure) {

    // Calculate the partial pressure of oxygen in arterial blood via alveolar gas
    // using the formula PaO2 = PIO2 - (PaCO2 / R) - (F * (P - PaH2O))
    // Note: we are intentionally disregarding:
    //      F: the fraction of inspired gas which is not oxygen
    //      PaH2O: and the partial pressure of water vapor in the inspired gas

    float PaCO2 = 5.25f; // partial pressure of CO2 in alveolar gas, in kPa 
                         // (widely variable, but distilled to an average until 
                         // a working model to correctly calculate this is built)

    float R = 0.8f; // respiratory exchange ratio (overly simplified)

    float PaO2 = inspiredPartialPressure - (PaCO2 / R);

    // Calculate the oxygen-hemoglobin dissociation curve,
    // using the formula S = (1 / (1 + 10^((p50 - log(P)) / n))) ^ m

    const float p50 = 3.5463652f; // kPa
    const float n = 2.25f;
    const float m = 2.5f;

    float x = 1f + Mathf.Pow(10f, (p50 - Mathf.Log(arterialPartialPressure)));
    float S = Mathf.Pow(1f / x / n, m);

    // Calculate oxygen content of bound and dissolved oxygen,
    // using the formula CaO2 = (SaO2 x Hb x 1.34) + (PaO2 x 0.003)

    const float oxygenSolubility = 0.003f;
    const float Hb = 14f;  // average hemoglobin concentration in g/dL
    float SaO2 = S * 100f;

    float CaO2 = (SaO2 * Hb * 1.34f) + (PaO2 * oxygenSolubility);  // mL O2 / dL blood

    return CaO2;
}

内容的提问来源于stack exchange，提问作者szsleepy