Dr Maxime Touzot
email: maxime.touzot@auraparis.org

Pascal Seris

Catherine Maheas

Jill Vanmassenhove

Anne-Lyse Langlois

Kamal Moubakir

Sophie Laplanche

Thierry Petitclerc

Christophe Ridel

Marc Lavielle
email: marc.lavielle@inria.fr

Anne- Lyse Langlois

Affiliations

A mathematical model to predict BNP levels in hemodialysis patients

Keywords: BNP, dialysis, modelling, Cardiovascular disease

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INTRODUCTION

Biomarkers such as Natriuretic peptides (BNP, NT-proBNP) have been established as markers of mortality and cardiac events in Coronary Artery Disease (CAD) and Heart Failure (HF). [START_REF] Mccullough | B-type natriuretic peptides: a diagnostic breakthrough for clinicians[END_REF] Both markers have been correlated with several cardiac parameters (Blood Pressure=BP, Left Ventricular Hypertrophy= LVH or LV systolic function) and non-cardiac parameters (Age, Gender, Diabetes mellitus or Body Mass Index=BMI). [START_REF] Tripepi | Biomarkers of Left Atrial Volume: A Longitudinal Study in Patients With End Stage Renal Disease[END_REF][START_REF] Apple | Multi-biomarker risk stratification of N-terminal pro-B-type natriuretic peptide, high-sensitivity C-reactive protein, and cardiac troponin T and I in end-stage renal disease for all-cause death[END_REF] Furthermore, some authors have also emphasized the utility of "BNP-targeted" heart-failure therapy in clinical practice. [START_REF] Porapakkham | B-Type Natriuretic Peptide-Guided Heart Failure Therapy[END_REF][START_REF] O'donoghue | Natriuretic peptides in heart failure: should therapy be guided by BNP levels?[END_REF] In end stage renal disease (ESRD), especially in hemodialysis patients (HD), Cardiovascular Disease (CVD) is a burden and remains the first cause of mortality. [START_REF] Longenecker | Traditional cardiovascular disease risk factors in dialysis patients compared with the general population: the CHOICE Study[END_REF] If both BNP an NT-Pro BNP are markers of cardiac events in ESRD, their use and interpretation (HD) still remains challenging.

BNP levels are often increased in HD. This can be partially explained by a decreased renal elimination but mainly by multiple factors both intrinsic (variability in measurement, type of BNP) and extrinsic related to patient comorbidity, including CVD or malnutrition. [START_REF] Jacobs | Inflammation, overhydration and cardiac biomarkers in haemodialysis patients: A longitudinal study[END_REF][START_REF] Booth | N-terminal proBNP -Marker of cardiac dysfunction, fluid overload, or malnutrition in hemodialysis patients?[END_REF] . There is considerable variation in BNP levels over time and the cut-off values to define disease are not standardized across heterogeneous groups of patient populations. [START_REF] Chazot | Fluid overload correction and cardiac history influence brain natriuretic peptide evolution in incident haemodialysis patients[END_REF][START_REF] Tapolyai | Volume estimation in dialysis patients: The concordance of brain-type natriuretic peptide measurements and bioimpedance values[END_REF][START_REF] Agarwal | B-type natriuretic peptide is not a volume marker among patients on hemodialysis[END_REF][START_REF] Safley | Changes in B-type natriuretic peptide levels in hemodialysis and the effect of depressed left ventricular function[END_REF][START_REF] Cappuccio | Combinatorial code governing cellular responses to complex stimuli[END_REF][START_REF] Sheen | The use of Btype natriuretic peptide to assess volume status in patients with end-stage renal disease[END_REF] Finally, the potential role BNP as a biomarker for fluid overload (FO) has been disappointing with discrepant results in small studies. [START_REF] Chazot | Fluid overload correction and cardiac history influence brain natriuretic peptide evolution in incident haemodialysis patients[END_REF][START_REF] Tapolyai | Volume estimation in dialysis patients: The concordance of brain-type natriuretic peptide measurements and bioimpedance values[END_REF][START_REF] Agarwal | B-type natriuretic peptide is not a volume marker among patients on hemodialysis[END_REF][START_REF] Safley | Changes in B-type natriuretic peptide levels in hemodialysis and the effect of depressed left ventricular function[END_REF] There is still debate as to whether this cardiac biomarker is more reflective of FO or intrinsic cardiac dysfunction in HD. Taken together, previous studies in HD have revealed that BNP levels can be influenced by many factors that may not have the same impact on BNP levels, and anticipation of a certain "targeted BNP level" to guide fluidremoval therapy is still missing.

When considering the interaction of different parameters for a specific outcome, mathematical modelling can be used as a robust method to understand and predict biological response. It has been widely used in pharmacodynamics to predict a drugs response, or in biology to predict cellular response. [START_REF] Cappuccio | Combinatorial code governing cellular responses to complex stimuli[END_REF] We attempted to model the BNP level depending on several clinical and biological parameters in order to predict the "targeted" BNP for a given patient.

The aim of the study was to; (1) assess to which extent each parameter will contribute to the BNP variation, and (2) to define a "targeted BNP" that could be used as a marker of fluid overload and to guide ultrafiltration. We built a mathematical model based on 6 clinical and biological variables that could be easily obtained at the patient bedside. We show for the first time the complex contribution of each variable in the modulation of BNP levels and the limitation in its interpretation such as age, CD and Dry Weight.

MATERIALS AND METHODS

The present study aimed to build a mathematical model, which enables accurate investigation of the relationship between BNP and clinical and biological parameters.

Patient population:

We initiated a single centre, observational, retrospective study of adult (>18 years old) HD. We collected patient epidemiological and laboratory data using our Medical informatics record (Hemodial, PHP developpement, France).

In our centre, BNP measure is performed monthly with the routine blood test, since 2014.

BNP level was performed before dialysis at the midweek session. Midweek measure was used to standardize results as it leads to a relative constant level of BNP. [START_REF] Sheen | The use of Btype natriuretic peptide to assess volume status in patients with end-stage renal disease[END_REF] BNP was measured by immunoassay on the Architect i2000 (Abbot Diagnostic). BNP levels <100 ng/L are considered normal in non-CKD, and the detection limits range from 2 to 5000 ng/L. Albumin and C-reactive protein (CRP) were performed every 3 months. The presence of a stable CAD and/or Atrial Fibrillation (AF) defined cardiac disease (CD).

Data for echocardiography were analysed when available. Echocardiography was performed on a nondialysis day during the year of the study. Left Ventricular Mass Index (LVMI) and Left Ventricular Ejection Fraction (LVEF) were measured by standard techniques.

Estimation of Dry Weight and Fluid Overload

We used two different approaches to estimate the FO: (1) a "clinician approach" based on the dry weight (DW) estimated by the clinician. The clinician FO was defined by c-FO = predialysis weight -DW; (2) a "bio-impedancemetry approach" that estimates the NHW. The bio-impedancemetry FO was defined by the FO = the predialysis weight -NHW. These 2 approaches were implemented into the models construction. The NWH was determined by BCM according to the manufacture's instructions (Fresenius). Bio impedance analysis is a reliable, repetitive, and simple, technique to assess the fluid status of a dialysis patient. [START_REF] Crepaldi | Application of Body Composition Monitoring to Peritoneal Dialysis Patients[END_REF][START_REF] Van Biesen | Fluid Status in Peritoneal Dialysis Patients: The European Body Composition Monitoring (EuroBCM) Study Cohort[END_REF] Modelling BNP level.

We performed a longitudinal study of all biological and clinical parameters measured monthly during 6 months. The asymmetrical distribution of BNP led us to consider a logtransformation for the statistical analyses, assuming a normal distribution for the log-BNP.

We first identified clinical and biological variables that have been shown to be associated Statistical analysis was performed using the computing environment R (R Development Core Team, 2017). Several linear models were fitted to the data, using the ln Function in R software. The best model was selected by minimizing the Bayesian Information Criteria (BIC). [START_REF] Schwarz | Estimating the Dimension of a Model[END_REF] Coefficients a0 to a6 are listed in table 2.

Statistical analysis of demographic or biological characteristics.

All data with normal distribution were reported as a mean ± SD or a percentage. Comparisons between patients were performed using a non-parametric test (Whitney test) or chi-square test, and Fisher's exact test, as appropriate. Statistical significance was first established for a p value < 0.05.

RESULTS

Baseline Characteristic of the 2 data set.

Demographic and biological characteristics of cohort 1 and cohort 2 at the beginning of the study (=M0) are shown in Table 1. For cohort 1, the mean age was 67.1 years (range 21-93).

Diabetes mellitus was found in 55/150 (36.6%) patients. Cardiac disease (CD), as defined by the presence of a stable CAD and/or AF was present in 63/150 (42%) patients. Twenty-six patients (17%) had a history of myocardial infarction.

The median dialysis vintage was 59 months (range 6-392). The majority of patients were on hemodiafiltration with a mean dialysis session time of 229±25 min. The mean Kt/v was

Construction and selection of a predictive model

We generated nine models that included the 15 clinical and biological variables (see materials and methods). We then selected among all the possible linear models the one that shows the best predictive performance for the BNP level, according to the Bayesian Information Criteria (BIC) (nine of the models are reported in supplemental Table S1).

Briefly, the model with the lowest BIC is preferred. The best model obtained (=model m2) includes the following variables: Age, sBP, CD, Albumin, NHW and FO. The complete equation is detailed in the materiels and methods section. It should be noted that the model including FO estimated by bio-impedancemetry was considered slightly better than the one based on a "clinician-approach" for predicting the BNP level. Furthermore, diabetes mellitus, BMI and antihypertensive drugs that have been reported to influence BNP levels were not included from the final model. Table 2 summarizes all the variables and their contribution for the m2 model.

Formatted: English (United States)

Formatted: English (United States)
The 3 variables that contribute the most significantly to the model (using the Relative important metrics method) were Age, FO and CD.

To exclude possible interaction between variable (e.g. effect modification by age upon CAD), we performed a test for interaction. Supplementary table 2 summarize the results obtained with the 15 possible interactions (6 variables) are displayed in). None of theses models has a better BIC than the model without interaction, with adjusted p-values> 0.05.

Optimisation of the model

The correlation between the measured log-BNP and the predicted log-BNP was 0.567 in the learning set and was similar to the validation set (r=0.543). However, the multiple R-square, which determines the proportion of variability explained by the model, was low 0.32. This indicates that the 6 variables only explain 1/3 of the log-BNP variability (multiple R-square = 0.32)

To improve the robustness of our model, we added the baseline values for the six variables at M0 as an additional explanatory variable in order to predict the BNP at further time points (M+1). The correlation between the measured log-BNP and the predicted log-BNP then increased to 0.794 (multiple R-square = 0.63) for the learning set and 0.759 for the validation set (Figure 1). It should be note that Age, CD and to a lesser extent NHY won't change between Mx and Mx+1. Thus the addition of BNP and sBP mainly explained the better correlation observed. These results emphasised the fact that a longitudinal screening of the BNP is mandatory.

Assessing the contribution of each variable.

Our model allows us to specifically assess the contribution of each variable for the BNP prediction, and to which extent they modulated BNP levels (Figure 234);. We defined a standard hemodialysis patient, 67 years old, sBP 130/80 mmHg, FO=0, Albumin =36.5 g/l.

By fixing values for 5 out of 6 variables, we could easily assess the effect of the remaining variable on the BNP level. For example, Figure 1 (2) A negative "linear effect" for albumin and NHW (Figure 3). For Each 10 g/l of albumin, BNP decrease with a FC=1.4 (Figure 3A). We observed that BNP levels also decrease with the NHW. The predicted BNP was 360, 260 and 188 ng/ml for a NHW of 45, 70 and 100kg respectively without CD (Figure 3B).

(3) A positive linear effect for CD and FO (Figure 4). CD was one of the top 3 variables that determined BNP levels with a FC of 1.69. Our model confirms also that Fluid Overload positively correlated with BNP independently of the CD. Considering a 67 year old hemodialysis patient (sBP=130/80 mmHg), the predicted BNP for a FO of 0, 2.5 and 5 kg was 221, 304 and 418 ng/ml respectively; or 373, 514 and 707 ng/ml if CD is present.

Define the "right" BNP for a given patient.

Our model allows us to establish the "right" BNP is for a given patient. It could help clinician to target it for dry weight adjustment (Table 3 andTableS3) resume values of predicted-BNP and the 95% IC according to different values for Age, Weight, FO and CD. We intentionally fixed values for Albumin and sBP to avoid too much information.

DISCUSSION

B-Type Natriuretic peptides have emerged as a useful biomarker in HF or CAD. In HD, BNP may be used as a sensitive marker of mortality but only in stable patients without HF, LVD or complex comorbidities. [START_REF] Madsen | N-terminal pro brain natriuretic peptide predicts mortality in patients with end-stage renal disease in hemodialysis[END_REF][START_REF] Zoccali | Cardiac natriuretic peptides are related to left ventricular mass and function and predict mortality in dialysis patients[END_REF][START_REF] Winkler | Change in Nterminal-pro-B-type-natriuretic-peptide and the risk of sudden death, stroke, myocardial infarction, and all-cause mortality in diabetic dialysis patients[END_REF] However, interpretation of BNP levels is more complex due to the specific pathophysiology of ESRD and the presence of multiple comorbidities. All these confounding factors explain partially why studies fail to demonstrate the clinical use of BNP as a marker of fluid overload or to guide fluid removal. Anticipation of BNP values for a patient according to their clinical characteristics is lacking. In the present study, we built a mathematical model to predict the BNP in hemodialysis according to clinical and biological variables.

In our model, we identified the three variables that contribute the most significantly to BNP levels in dialysis patients: age, CD and FO. All these variables have been already associated with BNP level, but to which extent they contribute to it variation is new. It is known that age is correlated with BNP levels in HF, CAD and dialysis. In our study population. For example, BNP increases with age in a linear manner up to 60 years. After this threshold, age does not influence BNP levels, suggesting that older patients will have similar baseline BNP levels. A similar effect was observed with sBP suggesting that the stretch of Left Ventricle induced by low sBP have minor effects on BNP modulation. However, it should be noted that the relation between blood pressure and BNP might be confounded by the use of medications (e.g RAAS or beta-blockers). [START_REF] Balion | Physiological, pathological, pharmacological, biochemical and hematological factors affecting BNP and NT-proBNP[END_REF] Malnutrition has been associated with BNP levels in HD based on BCM markers but not biomarkers such as albumin. [START_REF] Booth | N-terminal proBNP -Marker of cardiac dysfunction, fluid overload, or malnutrition in hemodialysis patients?[END_REF] Here we emphasized the tight relationship between albumin and BNP. Albumin is not the optimal marker of malnutrition but its level is associated with poor outcome in HD. [START_REF] Foley | Hypoalbuminemia, cardiac morbidity, and mortality in end-stage renal disease[END_REF] Our model also shows that BNP levels decrease according to a patients' weight, similarly to These results correspond to what has been described with BMI and BNP levels, where lower circulating levels are observed in patients with a higher BMI [START_REF] Horwich | B-Type Natriuretic Peptide Levels in Obese Patients With Advanced Heart Failure[END_REF][START_REF] Daniels | How obesity affects the cut-points for B-type natriuretic peptide in the diagnosis of acute heart failure[END_REF][START_REF] Nadruz | Impact of Body Mass Index on the Accuracy of N-Terminal Pro-Brain Natriuretic Peptide and Brain Natriuretic Peptide for Predicting Outcomes in Patients With Chronic Heart Failure and Reduced Ejection Fraction[END_REF][START_REF] Das | Impact of body mass and body composition on circulating levels of natriuretic peptides: results from the Dallas Heart Study[END_REF] . One possible explanation is that BNP clearance is increased due to the presence of the natriuretic peptide Clearance receptor (NPR-C) in adipose tissue.

However, cardiac cachexia might also explain the higher BNP values in cases of low weight.

This finding raises concern about the interpretation, predictive values and choice of cut-off values for Natriuretic peptides as in HF or reduced LVF. [START_REF] Horwich | B-Type Natriuretic Peptide Levels in Obese Patients With Advanced Heart Failure[END_REF][START_REF] Nadruz | Impact of Body Mass Index on the Accuracy of N-Terminal Pro-Brain Natriuretic Peptide and Brain Natriuretic Peptide for Predicting Outcomes in Patients With Chronic Heart Failure and Reduced Ejection Fraction[END_REF] Our model emphasized that BNP levels are influenced by both intrinsic cardiac pathology HD and FO volume. In our 2 cohorts, even without HF, patients with a history of CAD or an AF had higher BNP levels compared to other HDs, independently of age or FO. This finding could reflect the presence of LVH observed in our patient. However, as HF measures (LVH, LVD) were excluded from the model, we could not definitively conclusion whether BNP is more reflective of FO or intrinsic cardiac dysfunction.

The potential role of BNP as a biomarker of volume excess is controversial [START_REF] Chazot | Fluid overload correction and cardiac history influence brain natriuretic peptide evolution in incident haemodialysis patients[END_REF][START_REF] Tapolyai | Volume estimation in dialysis patients: The concordance of brain-type natriuretic peptide measurements and bioimpedance values[END_REF][START_REF] Agarwal | B-type natriuretic peptide is not a volume marker among patients on hemodialysis[END_REF][START_REF] Safley | Changes in B-type natriuretic peptide levels in hemodialysis and the effect of depressed left ventricular function[END_REF] . Some authors have argued that BNP may only reflect FO in stable hemodialysis patient without underlying cardio-vascular disease. [START_REF] Agarwal | B-type natriuretic peptide is not a volume marker among patients on hemodialysis[END_REF] Our model shows that even when considering various co-morbidities such as CD or diabetes mellitus, FO was one of most important predictors of BNP level. Our model allows us to anticipate the BNP level according to the patient's characteristics including the FO for a given dialysis-session. Comparison of the "predicted BNP" vs the "measured BNP" could give information about FO and help a clinician alter the dry weight adjustment. Estimation of the dry weight is critical is HD to avoid pulmonary oedema or intradialytic Hypotension (IDH) that are both correlated with mortality. [START_REF] Reeves | Mechanisms, Clinical Implications, and Treatment of Intradialytic Hypotension[END_REF] Such "BNP-target" therapy should be assessed by a prospective study. Taken together, our findings demonstrated the complex modulation of BNP levels by each variable included in the model. This complexity may explain the seemingly conflicting results on BNP in dialysis patients.

When including the previous values M-1, our model only explains 2/3 for BNP variation.

Several factors may explain this relative low correlation. First, the variability in the measure of variable such as BNP or sBP may weaken our model. BNP has a reduced half-life (20 min) as compare to NT-Pro-BNP (60-120 min), which will result in a higher variability of measure.

We used a third generation kit for BNP measure that was different for previous reports. [START_REF] Booth | N-terminal proBNP -Marker of cardiac dysfunction, fluid overload, or malnutrition in hemodialysis patients?[END_REF][START_REF] Chazot | Fluid overload correction and cardiac history influence brain natriuretic peptide evolution in incident haemodialysis patients[END_REF][START_REF] Agarwal | B-type natriuretic peptide is not a volume marker among patients on hemodialysis[END_REF] Even if the performance of all Third generation kit showed similar result in HF or CAD with mild CKD (Stage 3-4), it is not known if their predictive values can be extrapolated to HD patient.

Secondly, the lack of inclusion of measure of LVH or LVD that are correlated well with BNP measure is also a major limitation. We also focused on clinical and biological variables that could be easily retrieve at bedside, which introduced bias. Finally, we acknowledged that the robustness of our model may be limited by it intrinsic properties. Several mathematical models (multiple linear regression, Polynomal regression or artificial network...) may be considered to predict a specific outcome. Each of them has their own advantage or limits.

Our study has however several limitations. First, it is retrospective mono-centre study without external validation. As mentioned earlier, variability in BNP measure and lack of echocardiographic measures weaken our results. The latter were excluded for 2 main reasons:

1/ data were not available for all patients at the beginning of the observational study and 2/ Echocardiography were also performed during the 6 months observational study at various time point by at least 5 different operators. The latter could also give rise to residual cofounding in our model.

Finally we did not perform quantification of diuresis in our patients because of the retrospective analysis, and the absence of consensus for diuresis estimation in hemodialysis.

Notwithstanding, our study has however several strengths including, the number of patients (N=150) and data implemented in the model (Number of observation = 840), and the validation of the model in an independent cohort.

To conclude, we built a mathematical model based on 6 parameters, which allows the prediction of the BNP level in hemodialysis patient for clinical practice. Our study emphasized the fact that the BNP level for a given hemodialysis patient, is influenced by 3 main factors: Age, CD and FO. Whilst our model could be currently used for dry weight adjustment and prevent IDH, a further prospective study is required.

Contribution

MT and ML contributed to the conception of the study. MT, ALL, CM and KM collected the data. MT and ML analysed the data. MT drafted the manuscript. MT, ML, TP and CR contributed to writing the article.

Conflict-of-interest disclosure:

The authors declare no competing financial interest.

LEGEND Figure 1

Correlation between predicted BNP and measured BNP for the learning set (A), and the validation set (B).

Cohort 1 N=150

Cohort

Inclusion criteria included; ( 1 )

 1 Patient on hemodialysis > 6 months, (2) six consecutive monthly measures of BNP and haemoglobin, and (3) a minimum of two measures of the Normo-Hydrated Weight (NHW) by Body Composition Monitoring (BCM) during the 6 months observational period. Exclusion criteria included; (1) measure of BNP for a specific cause (e.g acute congestive heart failure, acute coronary syndrome), and (2) patients with a pacemaker, implanted defibrillator or amputee because of the contraindication for BCM. Two data sets were used: (1) Cohort 1 that included 150 (screened for eligibility from March 2015 to March 2016), to build the model and estimate its parameters; (2) Cohort 2 that included 62 75 HD that started dialysis or were transferred to our centre from March 2016 to March December 2017. The latter was used to validate the proposed mathematical model.

  Schwarz's BIC is a criterion for model selection among a finite set of models. If a model is estimated on a particular data set (training set), BIC score gives an estimate of the model performance on a new fresh data set (=testing set). The lower BIC score signals a better model. It is based, in part, on the likelihood function. A test for interaction was performed for all variables. Benjamini-Hochberg procedure to was used properly take into account the multiple comparisons The equation of the Final model is = log(BNP) = a0 + a1* FO + a2/(0.02 + exp(-Age/10)) + a3/(1e-05 + exp(-sBP/15)) + a4*NHW + a5*CD + a6*Alb

Figure 2 Predicted

 2 Figure 2Predicted BNP according to Age (A), and systemic Blood Pressure, mmHg (sBP). Values were calculated for a 67 year old male patient, sBP 130/80 mmHg, Albumin 36g/l, NHW = 67 kg and FO = 2 kg. Blue and red curves indicate the absence and presence of a Cardiac disease (CD) respectively.

Figure 3 Predicted

 3 Figure 3 Predicted BNP according to NormoHydrated Weight (NHW, kg) (A), and Albumin (Alb, g/l) (B). Values were calculated for a 67 year old male patient, sBP 130/80 mmHg, Albumin 36g/l, NHW = 67 kg and FO = 2 kg. Blue and red curves indicate the absence and presence of a Cardiac disease (CD) respectively.

Figure 4 Predicted

 4 Figure 4 Predicted BNP according to the Fluid Overload (FO): Values were calculated for a 67 year old male patient, sBP 130/80 mmHg, Albumin 36g/l, NHW = 70 kg. Blue and red curves indicate the absence and presence of a Cardiac disease (CD).

Abbreviations:

  Abbreviations: BIC: Bayesian information criterion; sBP: systolic Blood Pressure; CD: Cardiac disease; NHW: Normo-Hydrated Weight; FO: Fluid Overload assessed by bioimpedancemetry.Benjamini-Hochberg multiple comparison test was used for the p-value adjusted.

Formatted:

  Font: (Default) Times New Roman, English (United Kingdom)

  1.89±0.38. The c-FO was 2.65±1.33 kg and the FO, 1.8±1.88 kg. The sBP was 142/69 mmHg. Half of patients were taking anti-hypertensive drugs: 61 (40%) patients received betablockers, 70 (46%) received RAAS blockers. The mean hemoglobin was 11.2±1.3 g/dl. Mean BNP was 630 ± 717 ng/ml. Echocardiography data were available for 125/150 (83%) patients. The mean LVEF was 65±8% and the mean LVMI was 133±38 g/m 2 .

Cohort 2 (=validation set) contained 62 75 new incident patients (Table

1

). No statistically significant differences were observed between the learning and validation set, except for dialysis vintage, kt/v, c-FO, CRP, Prior myocardial infarction and the haemoglobin level. The latter reflects the presence of anemia usually observed at the beginning of dialysis.

[START_REF] Hörl | Anaemia management and mortality risk in chronic kidney disease[END_REF]

  represents the predicted BNP according to age when sBP =130/80 mmH, FO=0 kg and albumin=36.5 g/l respectively. Effect of age and sBP mimic a dose-response curve (Sigmoid Curve) suggesting a minimal and maximal. Our model reveals BNP levels increase with age from 30 to 60 years

	We observed 3 different kinds of BNP modulation
	(1)

old from 95 to 249 ng/ml (Fold Change FC = 2.83), before reaching a plateau (Fig

2A

). From 60 to 80 years, BNP levels only increase from 249 to 268 ng/ml. A similar effect was observed for the sBP (Fig

2B

). For a sBP< 150 mmHg, we observed a small variation of BNP level from 251 to 287 ng/ml. However, BNP increases from 287 to 487 ng/ml if sBP rises to 200 mmHg (FC = 1.69). The effect observed here was independent of the FO.

Table I :

 I Demographic and biological characteristics of the learning and validation set at M0

	Coefficient	SD	N=75 T value	2 P-value	P-values lmg
	Age (mean, range) Intercept (=a0)	5.610e -00	67.1 (21-93) 5.33e -3	64.1 (19-97) 11.064 <2e -16	0.208 0.32813
	Sex (F/M)			61/89		29/46		0.885
	-Caucasian Ethnicity (N) Age (=a2)	3.175e-2	76 Cohort 1 3 4.719e-	41 Cohort 2 6.728 5.17e-11	0.671 P-values 0.32813
	-Maghreb -Afro-American -Chinese BNP ng/ml (Mean, SD) CD (=a5)	5.243e-1	41 22 6 630±717 2 N=150 9.549e-	5.49	4 12 5 563±592 N=75 6.67e-8	0.135 0.512 0.770 0.844 0.21161
	-Indian FO (=a1)	1.227e-1	5 2.59e-2	4.926	4	1.17e-7	0.485 0.15700
	Nephropathy (N%) Hemoglobin g/dl (Mean, SD)	11.2 ±1.3		10.5±1.6	<0.0001
	-Glomerular * Diabetes * Others Systolic Blood Pressure (mmHg) sBP (=a3)	7.79e-6	83 (55.3%) 42 (28%) 41 (27.3%) 142±27 6 1.954e-	38 (51%) 25 (33.3%) 13 (17.3%) 144.3 ± 27 3.986 7.83e-5	0.571 0.441 0.135 0.432 0.10271
	-Vascular Diastolic Albumin (=a6)		-3.4e-2	35 (23.3%) 69±15 1.152e-	14 (18.6%) 71.1 ± 18.2 -2.954 3.29e-3	0.494 0.705 0.09544
	-TIN Fluid estimation (kg)			17 (11.3%) 3	4 (5.3%)	0.223
	-APKD -Unknown Comorbidities c-FO FO (impendancemetry) Patient weight (kg) NHW (=a4)	-1.182e-2	9 (0.6%) 6 (0.04%) 2.65 ±1.33 1.8 ± 1.88 3 2.931e-	4 (5.3%) 15 (20%) 2.07±1.57 1.52 ± 2.1 -4.03 6.5e-5	1 < 0.001 0.002 0.329 0.08406
	-Diabetes Dry Weight		55 (36.6%) 67.5 (38.5-113)	22 (29.3%) 69.9 (41-123)	0.299 0.690
	-BMI (kg/m 2) NHW			25.9±4.9 68.3 (37-113)	24.9±4.5 70.1 (39.7-122.2)	0.381 0.530
	Cardiovascular disease CRP mg/l (mean, SD)			63 (42%) 9.3 ±10.2	30 (40%) 8.2±9.5	0.886 0.016
	CAD Atrial Fibrillation Albumin g/dl (Mean, SD)	43 (29%) 33 (22%) 36.5 ± 3.9	17 (22.6%) 16 (21.3%) 35.2±6.5	0.424 1 0.074
	Prior Myocardial Infarction	26 (17%)	4 (5.3%)	0.012
	Cardiac Surgery			10 (7%)	4 (5.3%)	0.778
	Valvular disease			16 (11%)	15 (20%)	1
	Echocardiography
	Available (N)		125/150 (83%)	56/75 (75%)
	LVEF (%)			65± 8		62±13		0.412
	LVMI (g/m 2 )			133±38	132±45	0.762
	Treatment
	B-Blockers Abbreviation: F: female; M: male; TIN: Tubulo-interstital Nephropathy; APKD: Autosomic 61 (40%) 41 (55%) 0.064
	RAAS Blockers Calcium Channel Blocker dominant Adult Polycystic Kidney Disease; BMI: Body Mass Index; cFO: clinical Fluid 70 (46%) 42 (28%) 38 (51%) 26 (34%) 0.575 0.335
	RTT Overload; FO: Fluid Overload assessed by bioimpendancemetry; RAAS Blockers: Renin-
	-Time (months, median-range) -Type: HD/HDF angiotensin-aldosterone System blockers; CRP: C-reactive Protein; RRT: Renal Replacement 59 (6-392) 3/147 16 (6-97) 12/63 <0.0001 <0.0001
	-Kt/v Therapy; HD: Hemodialysis; HDF: Hemodiafiltration; NHW: NormoHydrated Weight. 1.89±0.38 1.38±0.43 <0.0001
	-Dialysis time (min) LFEV: Left Ventricular Ejection Fraction; LVMI: Left Ventricular Masse Index, Kt/V : K= 229±25 224±61 <0.0001
	Dialyzer clearance, T= Time, V = Volume of water a patient's body contains.

Table II :

 II Variables included in the final model

	Model	Variables	BIC
	m1	Age, sBP, CD, NHW, FO	1304.2
	m2	m1+ Albumin	1301.6
	m3	Age, sBP, CD, DW, c-FO	1304.8
	m4	Age, sBP, CD, BMI, FO, Albumin	1304.9
	m5	m2 + CRP	1306.7
	m6	m2 + anti hypertensive drugs	1316.9
	m7	m2 + diabetes mellitus	1306.8
	m8	m2 + sex	1307.7
	m9	m2 + ethnies	1319.0
	Supplemental

Abbreviation: FO: Fluid Overload assessed by Bioimpedancemetry; sBP: systolic Blood Pressure; CD: Cardiovascular disease; NHW: NormoHydrated Weight, lmg: relative important metric.

Table 1 : Model list Abbreviations

 1

	Variable 1	Variable 2	BIC	p-value	p-value adjusted
	sBP	Albumin	1301.9	0.016	0.139
	sBP	Age	1302.4	0.022	0.139
	FO	Age	1302.9	0.030	0.139
	FO	NHW	1303.7	0.046	0.139
	NHW	Albumin	1303.7	0.046	0.139
	FO	CD	1304.5	0.077	0.190
	NHW	CD	1304.8	0.089	0.190
	sBP	CD	1305.0	0.101	0.190
	NHW	Age	1305.4	0.135	0.225
	Albumin	CD	1306.0	0.200	0.299
	Age	CD	1306.6	0.294	0.401
	Age	Albumin	1307.3	0.520	0.627
	sBP	NHW	1307.3	0.55	0.627
	FO	sBP	1307.4	0.585	0.627
	FO	Albumin	1307.6	0.782	0.782
	Supplementary

: BIC: Bayesian information criterion; sBP: systolic Blood Pressure; Hb: hemoglobin, CD: Cardiac disease; NHW: Normo-Hydrated Weight; FO: Fluid Overload assessed by bio-impedancemetry; CRP: C reactive protein; DW: Clinician Dry Weight; c-FO : clinical Fluid overload; BMI: Body mass Index.

Table 2 :

 2 test of interaction for all variables