氧离曲线的数学模式与临床意义

The mathematical model of the oxygen dissociation curve and clinical evaluation

目的为判定氧离曲线的偏移,推导了氧离曲线的数学方程,并测定了氧离曲线位移常数(SC)。方法应用生物数学原理,将氧离曲线用自然对数底数e的负指数函数方程表达,并在坐标图上测定氧离曲线位移常数。结果PaO220～100mmHg区间氧离曲线的数学方程为SaO2(%)=100-67.7×e-[(PaO2-20)/SC],标准状况下的氧离曲线SC=20.5。由氧离曲线方程计算一定PaO2所对应的SaO2,与标准状况下实测的PaO2所对应的SaO2实测值十分接近,其误差(-x±s)仅为(0.56±0.45)%。推导出氧离曲线位移常数SC的计算公式,SC=(20-PaO2)/ln[(100-SaO2)/67.7]。由血气分析所测的PaO2与SaO2可用此公式计算SC。结论PaO220～100mmHg区间氧离曲线的数学方程可用自然对数底数e的负指数函数方程表达。测定氧离曲线位移常数SC是判定氧离曲线偏移的理想方法。氧离曲线无偏移时SC=20.5,氧离曲线右移时SC值增大,氧离曲线左移时SC值降低。SC值偏离越大,则氧离曲线偏移越重。

Objective For judgments of shift of oxygen dissociation curve （ODC）, the mathematical equation of ODC was conducted and shift constant （SC） of ODC was detected. Methods The ODC is expressed with equation of negative index function of nature logarithms e （ e = 2. 718 28 ） by biomathematics. The shift constant of ODC was detected at squared paper. Results The mathematical equation of ODC when PaO2 20 to 100 mm Hg is SaO2 （ % ） = 100 - 67.7×e^-[（PaO2-20）/SC]. At standard state, shift constant of ODC SC = 20.5. The PaO2 and SaO2 was calculated with equation of ODC and the calculated values is also close to the detected values with deflective values of both （ x^-2 ± s ） as （ 0. 56 ± 0. 45 ） %. The calculated formula of shift constant of ODC is SC = （ 20 - PaO2 ）/In [ （ 100 - SaO2 ）/67. 7 ]. The SC was calculated by detected values of PaO2 and SaO2 with formula of SC. Conclusions In the range of PaO2 from 20 to 100 mm Hg,the mathematical equation of ODC is expressed with equations of negative index function of nature logarithme. The detection of shift constant of ODC is a good method for judgment of shift of ODC. When ODC do not shift,SC = 20.5. When ODC shift to right, SC value increases. When ODC shift to left,SC value decreases. More the SC value shifts,more the ODC shifts.