title: Non-linear Equation using Plasma Brain Natriuretic Peptide Levels to Predict Cardiovascular Outcomes in Patients with Heart Failure.
abstract: 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|y) was the probability of cardiovascular events occurring after >t, the probability on t was given as p(t|y) = -dP(t|y)/dt, and p(t|y) = pP(t|y) = αyβP(t|y), along with p = αyβ(α and β were constant); the solution was p(t|y) = αyβexp(-αyβt). We fitted this equation to the data set of Protocol I using the maximum likelihood principle, and we obtained the model p(t|y) = 0.000485y0.24788exp(-0.000485y0.24788t). The cardiovascular event-free rate was computed as P(t) = 1/60Σi=1,…,60exp(-0.000485yi0.24788t), based on this model and the BNP levels yiin 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.
authors.affiliation: Department of Cardiovascular Medicine, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.|Department of Cell Biology, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.
authors.forename: Hiroki
authors.initials: H
authors.lastname: Fukuda
authors.affiliation: Department of Cardiovascular Medicine, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.
authors.forename: Hideaki
authors.initials: H
authors.lastname: Suwa
authors.affiliation: Department of Cardiovascular Medicine, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.|Department of Clinical Research and Development, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.
authors.forename: Atsushi
authors.initials: A
authors.lastname: Nakano
authors.affiliation: Department of Cardiovascular Medicine, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.|Department of Cell Biology, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.
authors.forename: Mari
authors.initials: M
authors.lastname: Sakamoto
authors.affiliation: Department of Cardiovascular Medicine, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.|Department of Cell Biology, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.
authors.forename: Miki
authors.initials: M
authors.lastname: Imazu
authors.affiliation: Department of Cardiovascular Medicine, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.
authors.forename: Takuya
authors.initials: T
authors.lastname: Hasegawa
authors.affiliation: Department of Cardiovascular Medicine, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.
authors.forename: Hiroyuki
authors.initials: H
authors.lastname: Takahama
authors.affiliation: Department of Cardiovascular Medicine, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.
authors.forename: Makoto
authors.initials: M
authors.lastname: Amaki
authors.affiliation: Department of Cardiovascular Medicine, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.
authors.forename: Hideaki
authors.initials: H
authors.lastname: Kanzaki
authors.affiliation: Department of Cardiovascular Medicine, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.
authors.forename: Toshihisa
authors.initials: T
authors.lastname: Anzai
authors.affiliation: Department of Cell Biology, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.
authors.forename: Naoki
authors.initials: N
authors.lastname: Mochizuki
authors.affiliation: The institute of Scientific and Industrial Research, Osaka University, 1-1 Yamadaoka, Suita, Osaka, Japan.
authors.forename: Akira
authors.initials: A
authors.lastname: Ishii
authors.affiliation: Department of Clinical Research and Development, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.|Department of Cardiovascular Medicine, Kyoto Prefectural University of Medicine, Kyoto, Japan.
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Asanuma
authors.affiliation: Department of Cardiovascular Medicine, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.|Department of Clinical Research and Development, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.
authors.forename: Masanori
authors.initials: M
authors.lastname: Asakura
authors.affiliation: The institute of Scientific and Industrial Research, Osaka University, 1-1 Yamadaoka, Suita, Osaka, Japan.
authors.forename: Takashi
authors.initials: T
authors.lastname: Washio
authors.affiliation: Department of Cardiovascular Medicine, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.|Department of Clinical Research and Development, National Cerebral and Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka, Japan.
authors.forename: Masafumi
authors.initials: M
authors.lastname: Kitakaze
mesh_terms: D000368:Aged; D000369:Aged, 80 and over; D015415:Biomarkers; D002908:Chronic Disease; D005260:Female; D006333:Heart Failure / Q000097:blood* / Q000503:physiopathology*; D006801:Humans; D008297:Male; D008875:Middle Aged; D008955:Models, Cardiovascular; D020097:Natriuretic Peptide, Brain / Q000097:blood*; D011237:Predictive Value of Tests
chemical_list: D015415:Biomarkers; D020097:Natriuretic Peptide, Brain