Non-linear Equation using Plasma Brain Natriuretic Peptide Levels to Predict Cardiovascular Outcomes in Patients with Heart Failure

作者：Fukuda Hiroki; Suwa Hideaki; Nakano Atsushi; Sakamoto Mari; Imazu Miki; Hasegawa Takuya; Takahama Hiroyuki; Amaki Makoto; Kanzaki Hideaki; Anzai Toshihisa; Mochizuki Naoki; Ishii Akira; Asanuma Hiroshi; Asakura Masanori; Washio Takashi; Kitakaze Masafumi^*

来源：Scientific Reports, 2016, 6(1): 37073.

DOI：10.1038/srep37073

Brain natriuretic peptide (BNP) is the most effective predictor of outcomes in chronic heart failure (CHF). This study sought to determine the qualitative relationship between the BNP levels at discharge and on the day of cardiovascular events in CHF patients. We devised a mathematical probabilistic model between the BNP levels at discharge (y) and on the day (t) of cardiovascular events after discharge for 113 CHF patients (Protocol I). We then prospectively evaluated this model on another set of 60 CHF patients who were readmitted (Protocol II). P(t vertical bar y) was the probability of cardiovascular events occurring after >t, the probability on t was given as p(t vertical bar y) = -dP(t vertical bar y)/dt, and p(t vertical bar y) = pP(t vertical bar y) = alpha y(beta)P(t vertical bar y), along with p = alpha y(beta) (alpha and beta were constant); the solution was p(t vertical bar y) = alpha y(beta) exp(-alpha y(beta)t). We fitted this equation to the data set of Protocol I using the maximum likelihood principle, and we obtained the model p(t vertical bar y) = 0.000485y(0.24788) exp(-0.000485y(0.24788)t). The cardiovascular event-free rate was computed as P(t) = 1/60 Sigma(i=1,...,60) exp(-0.000485y(i)(0.24788)t), based on this model and the BNP levels y(i) in a data set of Protocol II. We confirmed no difference between this model-based result and the actual event-free rate. In conclusion, the BNP levels showed a non-linear relationship with the day of occurrence of cardiovascular events in CHF patients.

• 出版日期2016-11-15