RESUMEN
To date, there is no established treatment for heart failure with preserved ejection fraction (HFpEF). Dipeptidyl peptidase-IV (DPP-IV) inhibitors reportedly have improved not only diabetes mellitus but also heart failure with systolic dysfunction in experimental models. We investigated the effects of a DPP-IV inhibitor on HFpEF in rats. Dahl salt-sensitive rats were fed either high-salt (high-salt diet (HSD): 8% NaCl) or low-salt diets (0.3% NaCl) from 6.5â¯weeks of age. They were then treated with or without a DPP-IV inhibitor, vildagliptin (10â¯mg/kg/day, orally), from 11â¯weeks of age for 9â¯weeks and analyzed at the age of 20â¯weeks. HSD rats mimicked the pathophysiology of HFpEF. There were no differences in heart rate, blood pressure, left ventricular (LV) systolic function, or the extent of LV hypertrophy between HSD rats with or without vildagliptin. However, vildagliptin decreased LV end-diastolic pressure, the most reliable hemodynamic parameter of HFpEF in HSD rats. Vildagliptin also decreased the LV distensibility index, a sensitive marker of LV diastolic function in HSD rats. Vildagliptin decreased the expression of collagen genes in HSD hearts and attenuated LV interstitial fibrosis (HSD with vehicle and vildagliptin, 2.9% vs. 1.9%; Pâ¯<â¯0.05). Furthermore, vildagliptin administration reduced both plasma renin activity and aldosterone concentrations in HSD rats. A DPP-IV inhibitor, vildagliptin, improved the severity of LV fibrosis, and thus, diastolic dysfunction of HFpEF in Dahl salt-sensitive hypertensive rats. DPP-IV inhibitors are promising medicines for treatment of HFpEF in patients with diabetes mellitus.
Asunto(s)
Diástole/efectos de los fármacos , Inhibidores de la Dipeptidil-Peptidasa IV/farmacología , Animales , Biomarcadores/metabolismo , Colágeno/genética , Colágeno/metabolismo , Fibrosis , Regulación de la Expresión Génica/efectos de los fármacos , Receptor del Péptido 1 Similar al Glucagón/metabolismo , Glucosa/metabolismo , Insuficiencia Cardíaca/diagnóstico por imagen , Insuficiencia Cardíaca/genética , Insuficiencia Cardíaca/fisiopatología , Pruebas de Función Cardíaca/efectos de los fármacos , Ventrículos Cardíacos/efectos de los fármacos , Ventrículos Cardíacos/fisiopatología , Hipertensión/genética , Hipertensión/fisiopatología , Inflamación/patología , Pruebas de Función Renal , Masculino , Miocardio/patología , Ratas Endogámicas Dahl , Sistema Renina-Angiotensina/efectos de los fármacos , Volumen Sistólico/efectos de los fármacos , Vildagliptina/farmacologíaRESUMEN
BACKGROUND AND AIMS: Diabetes mellitus (DM) can cause left ventricular (LV) diastolic dysfunction, leading to heart failure with preserved ejection fraction (HFpEF). Dipeptidyl peptidase IV (DPP-IV) inhibitors have failed to reduce hospitalization due to HF in type 2 DM (T2D) patients in a large-scale clinical trial, despite their cardiovascular protective effects. Therefore, it is important to investigate whether DPP-IV inhibitors can improve LV diastolic dysfunction in T2D patients. The aim of the study was to evaluate whether teneligliptin, the strongest of the DPP-IV inhibitors, improves LV dysfunction or prevents the worsening of LV diastolic function in T2D patients. METHODS: The TOPLEVEL study is designed as an open-labeled, marker-stratified randomized, parallel-group comparison, standard treatment-controlled multicenter study. TOPLEVEL includes two marker-defined subgroups to give treatment recommendations for T2D patients with normal (E/e' < 8) or impaired LV diastolic function (E/e' ≥ 8), where E/e' is the ratio of peak velocity of early transmitral diastolic filling by echocardiography to early diastolic mitral annular velocity by tissue Doppler echocardiography as LV diastolic function. Patients are randomly assigned to either teneligliptin (20 or 40 mg) or the standard treatment group. All patients are followed up for 2 years. The primary endpoint measure is the change in E/e' from baseline and 2 years after enrollment. CONCLUSION AND PERSPECTIVES: TOPLEVEL is a clinical trial of teneligliptin targeting LV diastolic dysfunction in T2D patients. This study demonstrates the effectiveness of DPP-IV inhibitors on LV diastolic dysfunction, an important surrogate endpoint to predict the cardiovascular outcomes of HFpEF (UMIN000014589).
Asunto(s)
Diabetes Mellitus Tipo 2/tratamiento farmacológico , Cardiomiopatías Diabéticas/tratamiento farmacológico , Inhibidores de la Dipeptidil-Peptidasa IV/uso terapéutico , Pirazoles/uso terapéutico , Tiazolidinas/uso terapéutico , Disfunción Ventricular Izquierda/tratamiento farmacológico , Función Ventricular Izquierda/efectos de los fármacos , Adulto , Anciano , Anciano de 80 o más Años , Diabetes Mellitus Tipo 2/complicaciones , Diabetes Mellitus Tipo 2/diagnóstico , Cardiomiopatías Diabéticas/diagnóstico por imagen , Cardiomiopatías Diabéticas/etiología , Cardiomiopatías Diabéticas/fisiopatología , Inhibidores de la Dipeptidil-Peptidasa IV/efectos adversos , Progresión de la Enfermedad , Femenino , Insuficiencia Cardíaca/etiología , Insuficiencia Cardíaca/fisiopatología , Insuficiencia Cardíaca/prevención & control , Humanos , Japón , Masculino , Persona de Mediana Edad , Estudios Multicéntricos como Asunto , Pirazoles/efectos adversos , Ensayos Clínicos Controlados Aleatorios como Asunto , Tiazolidinas/efectos adversos , Factores de Tiempo , Resultado del Tratamiento , Disfunción Ventricular Izquierda/diagnóstico por imagen , Disfunción Ventricular Izquierda/etiología , Disfunción Ventricular Izquierda/fisiopatología , Adulto JovenRESUMEN
PURPOSE: Several lines of evidence suggest that renal dysfunction is associated with cardiovascular toxicity through the action of uremic toxins. The levels of those uremic toxins can be reportedly reduced by the spherical carbon adsorbent AST-120. Because heart failure (HF) causes renal dysfunction by low cardiac output and renal edema, the removal of uremic toxins could be cardioprotective. METHOD: To determine whether blood levels of the uremic toxin indoxyl sulfate (IS) increase in HF and whether AST-120 can reduce those levels and improve HF. We induced HF in 12 beagle dogs by 6 weeks of rapid right ventricular pacing at 230 beats per min. We treated six dogs with a 1-g/kg/day oral dosage of AST-120 for 14 days from week 4 after the start of rapid ventricular pacing. The other six dogs did not receive any treatment (control group). RESULTS: In the untreated dogs, IS levels increased as cardiac function deteriorated. In contrast, plasma IS levels in the treated dogs decreased to baseline levels, with both left ventricular fractional shortening and pulmonary capillary wedge pressure also improving when compared with untreated dogs. Finally, AST-120 treatment was shown to reduce both myocardial apoptosis and fibrosis along with decreases in extracellular signal-regulated kinase phosphorylation, the Bax/Bcl-2 ratio, and TGF-ß1 expression and increases in AKT phosphorylation. CONCLUSIONS: IS levels are increased in HF. AST-120 treatment reduces the levels of IS and improves the pathophysiology of HF in a canine model. AST-120 could be a novel candidate for the treatment of HF.
Asunto(s)
Carbono/administración & dosificación , Síndrome Cardiorrenal/terapia , Insuficiencia Cardíaca/terapia , Indicán/sangre , Enfermedades Renales/prevención & control , Óxidos/administración & dosificación , Desintoxicación por Sorción/métodos , Uremia/prevención & control , Adsorción , Animales , Apoptosis , Proteínas Reguladoras de la Apoptosis/metabolismo , Síndrome Cardiorrenal/sangre , Síndrome Cardiorrenal/fisiopatología , Estado de Conciencia , Modelos Animales de Enfermedad , Perros , Fibrosis , Insuficiencia Cardíaca/sangre , Insuficiencia Cardíaca/complicaciones , Insuficiencia Cardíaca/fisiopatología , Hemodinámica , Enfermedades Renales/sangre , Enfermedades Renales/etiología , Enfermedades Renales/fisiopatología , Mitocondrias Cardíacas/metabolismo , Mitocondrias Cardíacas/patología , Miocardio/metabolismo , Miocardio/patología , Transducción de Señal , Uremia/sangre , Uremia/etiología , Uremia/fisiopatología , Función Ventricular IzquierdaRESUMEN
BACKGROUND AND AIMS: Sodium-dependent glucose transporter-2 (SGLT-2) inhibitors, which are anti-diabetic drugs, reportedly decrease the incidence of cardiovascular events in high-risk patients with cardiovascular diseases, and thus chronic heart failure (CHF). SGLT-2 inhibitors also decrease albuminuria in patients with type 2 diabetes mellitus (T2D). Since albuminuria is a biomarker of not only chronic kidney disease but also cardiovascular events, we hypothesized that, among T2D patients with CHF, SGLT-2 inhibitors will decrease the extent of albuminuria and also improve CHF concomitantly. METHODS: DAPPER (UMIN000025102) is a multicenter, randomized, open-labeled, parallel-group, standard treatment-controlled study, which is designed to evaluate whether dapagliflozin, one of the SGLT-2 inhibitors, decreases albuminuria in T2D patients with CHF and exerts cardioprotective effects on the failing heart. The patients are randomized to either of the dapagliflozin (5 or 10 mg, once daily orally) or control group (administration of anti-diabetic drugs administered other than SGLT 2 inhibitors). The estimated number of patients that need to be enrolled is 446 in total (223 in each group). The primary objective is the changes in the urinary albumin-to-creatinine ratio from the baseline after 2-year treatment. The key secondary objectives are (1) the safety of dapagliflozin and (2) the cardiovascular and renal efficacies of dapagliflozin. CONCLUSION AND PERSPECTIVES: DAPPER study investigates whether dapagliflozin decreases albuminuria and exerts beneficial effects on the failing heart in T2D patients. (UMIN000025102).
Asunto(s)
Albuminuria/prevención & control , Compuestos de Bencidrilo/uso terapéutico , Diabetes Mellitus Tipo 2/tratamiento farmacológico , Nefropatías Diabéticas/prevención & control , Glucósidos/uso terapéutico , Insuficiencia Cardíaca/tratamiento farmacológico , Inhibidores del Cotransportador de Sodio-Glucosa 2/uso terapéutico , Albuminuria/diagnóstico , Albuminuria/epidemiología , Diabetes Mellitus Tipo 2/diagnóstico , Diabetes Mellitus Tipo 2/epidemiología , Nefropatías Diabéticas/diagnóstico , Nefropatías Diabéticas/epidemiología , Insuficiencia Cardíaca/diagnóstico , Insuficiencia Cardíaca/epidemiología , Insuficiencia Cardíaca/fisiopatología , Humanos , Japón/epidemiología , Estudios Multicéntricos como Asunto , Ensayos Clínicos Controlados Aleatorios como Asunto , Factores de Riesgo , Factores de Tiempo , Resultado del TratamientoRESUMEN
Although the important role of fibroblast growth factor (FGF)23 on cardiac remodeling has been suggested in advanced chronic kidney disease (CKD), little is known about serum (s)FGF23 levels in patients with heart failure (HF) due to nonischemic cardiac disease (NICD) and early CKD. The present study aimed to investigate sFGF23 levels in NICD patients and identify the responsible factors for the elevation of sFGF23 levels. We prospectively measured sFGF23 levels in consecutive hospitalized NICD patients with early CKD (estimated glomerular filtration rate ≥ 40 ml·min(-1)·1.73 m(-2)) and analyzed the data of both echocardiography and right heart catheterization. Of the 156 NICD patients (estimated glomerular filtration rate range: 41-128 ml·min(-1)·1.73 m(-2)), the most severe HF symptom (New York Heart Association class III-IV, 53% vs. 33%, P = 0.015) was found in the above median sFGF23 (39.1 pg/ml) group compared with the below median sFGF23 group. sFGF23 levels were higher in patients with HF hospitalization history compared with those without HF [median: 46.8 (interquartile range: 38.8-62.7) vs. 34.7 (interquartile range: 29.6-42.4) pg/ml, P < 0.0001]. In the multivariate analysis, HF hospitalization was independently related to elevated sFGF23 levels (P = 0.022). Both systolic dysfunction and high plasma aldosterone concentration were identified as predictors of high sFGF23 levels (P < 0.05). Among the neurohormonal parameters, elevated sFGF23 levels were the only factor to predict a declining left ventricular ejection fraction (P = 0.001). These findings suggest that the progression of HF per se contributes to the elevation of sFGF23 levels even in the early stages of CKD, which leads to further myocardial dysfunction, potentially creating a vicious cycle.
Asunto(s)
Factores de Crecimiento de Fibroblastos/sangre , Insuficiencia Cardíaca/sangre , Insuficiencia Renal Crónica/sangre , Adulto , Anciano , Aldosterona/sangre , Biomarcadores/sangre , Estudios Transversales , Femenino , Factor-23 de Crecimiento de Fibroblastos , Tasa de Filtración Glomerular , Insuficiencia Cardíaca/diagnóstico , Insuficiencia Cardíaca/etiología , Insuficiencia Cardíaca/fisiopatología , Hospitalización , Humanos , Estimación de Kaplan-Meier , Modelos Lineales , Masculino , Persona de Mediana Edad , Análisis Multivariante , Valor Predictivo de las Pruebas , Pronóstico , Estudios Prospectivos , Insuficiencia Renal Crónica/diagnóstico , Insuficiencia Renal Crónica/fisiopatología , Factores de Riesgo , Índice de Severidad de la Enfermedad , Volumen Sistólico , Sístole , Regulación hacia Arriba , Función Ventricular IzquierdaRESUMEN
Background: Sodium-glucose cotransporter 2 (SGLT2) inhibitors reduce the urinary albumin-to-creatinine ratio (UACR) in patients with elevated levels of albuminuria in the presence or absence of heart failure (HF) or type 2 diabetes mellitus (T2D). However, these effects have not yet been reported in the presence of both HF and T2D. This lack of evidence prompted us to conduct a clinical trial on the effects of dapagliflozin on UACR in patients with HF and T2D. Methods: DAPPER is a multicentre, randomised, open-labeled, parallel-group, standard treatment-controlled trial that enrolled patients at 18 medical facilities in Japan. Eligible participants with both HF and T2D and aged between 20 and 85 years were randomly assigned to a dapagliflozin or control (anti-diabetic drugs other than SGLT 2 inhibitors) group with a 1:1 allocation. The primary outcome was changes in UACR from baseline after a two-year observation, and secondary endpoints were cardiovascular (CV) events and parameters related to HF. This trial was registered with the UMIN-CTR registry, UMIN000025102 and the Japan Registry of Clinical Trials, jRCTs051180135. Findings: Between 12 May 2017 and 31 March 2020, 294 patients were randomly assigned to the dapagliflozin group (n = 146) or control group (n = 148). The mean age of patients was 72.1 years and 29% were female. The mean glycated hemoglobin value was 6.9%, mean NT-proBNP was 429.1 pg/mL, mean estimated GFR was 65.7 mL/min/1.73 m2, and median UACR was 25.0 (8.8-74.6) mg/g Cr in the dapagliflozin group and 25.6 (8.2-95.0) mg/g Cr in the control group. Of the 146 patients in the dapagliflozin group, 122 completed the study, and 107 (87.7%) were taking 5 mg of dapagliflozin daily at the end of the observation period. The primary outcome did not significantly differ between the dapagliflozin and control groups. Among the secondary endpoints, the mean decrease in left ventricular end-diastolic dimensions as one of the echocardiographic parameters was larger in the dapagliflozin group than in the control group. The composite endpoint, defined as CV death or hospitalisation for CV events, hospitalisation for HF events, hospitalisation for all causes, and an additional change in prescriptions for heart failure in a two-year observation, was less frequent in the dapagliflozin group than in the control group. Interpretation: Although dapagliflozin at a dose of 5 mg daily did not reduce urinary albumin excretion in patients with HF and T2D from that in the controls, our findings suggest that dapagliflozin decreased CV events and suppressed left ventricular remodeling. Funding: AstraZeneca KK, Ono Pharmaceutical Co., Ltd.
RESUMEN
BACKGROUND: The distal radial approach (DRA) is a novel catheter cannulation technique to access the distal radial artery for coronary angiography (CAG). It is associated with less occurrence of puncture site occlusion than the conventional transradial approach. However, cannulation failure occasionally occurs due to difficulty in puncturing the smaller distal radial artery. Nitroglycerin is expected to improve the rate of successful DRA via its vasodilative and vasospasm-preventive effects. METHODS: The DRA in CAG using transdermal NitroGlycerin patch (DRANG) study is a single-center, double-arm, parallel-assignment, double-blinded, randomized, controlled trial. Eligible patients with angina pectoris who are scheduled to receive CAG via DRA at the National Cerebral and Cardiovascular Center will be enrolled and allocated to the nitroglycerin group (n = 46) or the no-treatment group (n = 46). The nitroglycerin group will receive a transdermal nitroglycerin patch pre-integrated with a covering material that completely conceals the patch on their upper arm on the puncture side. The no-treatment group will receive only the covering material. Applications are performed 2-8 h before puncture while the patient wears an eye mask. Physicians who are blinded to the allocation and have similar experience with DRA puncture will perform DRA using the Seldinger technique with a 22-gauge needle. The primary outcome is the rate of successful palpation-guided distal radial artery cannulation with the first puncture. The secondary outcomes are the rate of successful distal radial artery cannulation, number of punctures, procedure time, use of ultrasound guidance, diameter of the distal radial artery and changes before and after patch application, and occurrence of arterial vasospasm, occlusion, or hypotension. CONCLUSIONS: This study will allow us to determine the impact of a transdermal nitroglycerin patch on the rate of successful DRA and validate its effectiveness as a DRA pretreatment. TRIAL REGISTRATION: jRCTs051210128.
Asunto(s)
Nitroglicerina , Arteria Radial , Angiografía Coronaria/métodos , Estudios de Factibilidad , Humanos , Nitroglicerina/efectos adversos , Punciones , Arteria Radial/diagnóstico por imagen , Ensayos Clínicos Controlados Aleatorios como AsuntoRESUMEN
Indoxyl sulfate (IS) is associated with either chronic kidney disease or renal failure, which may predict cardiovascular events via cardiorenal syndrome. The present study aimed to elucidate whether the plasma levels of IS can predict the occurrence of cardiovascular events in patients with chronic heart failure (CHF) and investigate which causes of CHF leading to cardiovascular events are highly influenced by plasma IS levels. We measured the plasma IS levels in 165 patients with CHF [valvular disease: 78, dilated cardiomyopathy: 29, hypertrophic cardiomyopathy (HCM): 25 and others: 33] admitted to our hospital in 2012, and we followed up these patients for more than 5 years (the median follow-up period: 5.3 years). We measured the plasma IS level in 165 patients with CHF, and Kaplan-Meier analyses showed that high plasma IS levels (≥ 0.79 µg/mL, the median value) could predict the occurrence of cardiovascular events, i.e., cardiovascular death or rehospitalization due to the worsening of CHF. The sub-analyses showed that the high IS level could predict cardiovascular events in patients with CHF due to HCM and that the plasma IS levels were closely associated with left ventricular (LV) dimension, LV systolic dysfunction, and plasma B-type natriuretic peptide levels, rather than LV diastolic dysfunction. Plasma IS level predicts cardiovascular events in patients with CHF, especially those with HCM along with cardiac dysfunction. Besides, IS may become a proper biomarker to predict cardiovascular events in patients with CHF.
Asunto(s)
Insuficiencia Cardíaca/fisiopatología , Indicán/análisis , Adulto , Anciano , Biomarcadores/sangre , Cardiomiopatía Dilatada/complicaciones , Cardiomiopatía Hipertrófica/complicaciones , Fenómenos Fisiológicos Cardiovasculares/genética , Enfermedad Crónica , Femenino , Insuficiencia Cardíaca/metabolismo , Humanos , Indicán/sangre , Indicán/metabolismo , Estimación de Kaplan-Meier , Masculino , Persona de Mediana Edad , Plasma/química , Pronóstico , Disfunción Ventricular Izquierda/complicacionesRESUMEN
Beta-blockers are recommended as a standard therapy for patients with heart failure (HF). However, beta-blockers are reportedly less effective in HF patients with atrial fibrillation (Af) compared with those with sinus rhythm (SR). Here, we investigated whether HR at discharge determined the cardiovascular outcomes in HF patients with Af treated with beta-blockers. In this analysis, we enrolled 97 HF patients with concomitant Af. These patients were divided into 6 groups according to beta-blocker use and tertiles of discharge HR: lowest <60 beats per minute (bpm), middle 61-70 bpm and highest >71 bpm. The primary endpoint was defined as a composite of rehospitalization due to worsening of HF and all-cause mortality. During a median follow-up of 772 days after discharge, the composite cardiovascular outcome occurred in 37 (61%) and 25 (69%) patients with or without beta-blockers, respectively. In the Cox proportional hazard analysis, the lowest HR tertile in patients with beta-blockers was associated with an increased risk of the composite outcome compared with the middle and highest tertiles in both the unadjusted model (hazard ratio: 2.568, 95% confidence interval (CI): 1.089-6.057, p = 0.031; hazard ratio: 2.024, 95% CI: 0.921-4.447, p = 0.079, respectively) and the model adjusted for potential confounders (hazard ratio: 2.631, 95% CI: 1.078-6.421, p = 0.034; hazard ratio: 2.876, 95% CI: 1.147-7.207, p = 0.024, respectively). In patients with HF and Af receiving beta-blockers, low HR adversely increased the risk of cardiovascular events. This fact may blunt the beneficial effects of beta-blockers in patients with HF and Af.
Asunto(s)
Antagonistas Adrenérgicos beta/uso terapéutico , Fibrilación Atrial/complicaciones , Insuficiencia Cardíaca/tratamiento farmacológico , Frecuencia Cardíaca , Anciano , Femenino , Insuficiencia Cardíaca/complicaciones , Humanos , Masculino , Persona de Mediana Edad , Estudios RetrospectivosRESUMEN
Recently, fibroblast growth factor 23 (FGF23), a phosphate-regulating hormone, has been linked to the pathophysiology of heart failure (HF), thus encouraging us to examine which hemodynamic abnormalities of HF are linked to either serum FGF23 or plasma B-type natriuretic peptide (BNP) levels. We measured both the serum FGF23 and plasma BNP levels in 154 consecutive prospectively enrolled hospitalized HF patients, with an estimated glomerular filtration rate >40 ml min-1 1.73 m-2, who underwent heart catheterizations and an echocardiogram. The serum FGF23 levels correlated with the diameter of the inferior vena cava and its respiratory changes, whereas the plasma BNP levels did not. Both the plasma BNP and serum FGF23 levels were moderately correlated with the mean pulmonary artery (PA) pressure and pulmonary capillary wedge (PCW) pressure. Interestingly, in patients with an above-median right-atrial (RA) pressure (4 mm Hg), FGF23 levels were correlated with both PA and PCW pressures, but the levels were not correlated in patients with a below-median RA pressure. In contrast, the plasma BNP levels were correlated with both PA and PCW pressures. Finally, serum FGF23 levels, compared with the plasma BNP levels, were more strongly associated with the clinical outcomes in patients with above-median RA pressure. These findings suggested that serum FGF23 levels are predominantly correlated with clinical outcomes, may serve as a biomarker for HF in patients with higher RA pressure, may provide beneficial information for patients with right-sided HF and may represent different clinical information than that provided only by plasma BNP levels.
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Presión Sanguínea/fisiología , Factores de Crecimiento de Fibroblastos/sangre , Insuficiencia Cardíaca/etiología , Péptido Natriurético Encefálico/sangre , Vena Cava Inferior/diagnóstico por imagen , Anciano , Ecocardiografía , Femenino , Factor-23 de Crecimiento de Fibroblastos , Insuficiencia Cardíaca/sangre , Insuficiencia Cardíaca/diagnóstico por imagen , Hemodinámica/fisiología , Humanos , Masculino , Persona de Mediana Edad , Presión Esfenoidal PulmonarRESUMEN
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) = αyßP(t|y), along with p = αyß (α and ß were constant); the solution was p(t|y) = αyß exp(-αyßt). We fitted this equation to the data set of Protocol I using the maximum likelihood principle, and we obtained the model p(t|y) = 0.000485y0.24788 exp(-0.000485y0.24788t). The cardiovascular event-free rate was computed as P(t) = 1/60Σi=1, ,60 exp(-0.000485yi0.24788t), based on this model and the BNP levels yi 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.