Mathematical modeling in chronic kidney disease

Peter Kotanko, MDRenal Research Institute, New York

pkotanko@rriny.comBangalore, March 2008

Pastan S and Bailey J. N Engl J Med 1998;338:1428-1437

Life Expectancy at 45 to 54 and 55 to 64 Years of Age in the U.S. Resident Population and among Persons with Selected

Chronic Diseases

Meyer T and Hostetter T. N Engl J Med 2007;357:1316-1325

Uremic Solutes

Hemodialysis Circuit

Ifudu O. N Engl J Med 1998;339:1054-1062

Hemodialysis Vascular Access by Native Arteriovenous Fistula

Vascular Access (Shunt)

Forni L and Hilton P. N Engl J Med 1997;336:1303-1309

Hemodialysis: Combination of Diffusive & Convective Transport

Meyer T and Hostetter T. N Engl J Med 2007;357:1316-1325

Blood Urea Nitrogen Levels in Two Theoretical Patients Undergoing Conventional Thrice-Weekly Hemodialysis for 3 Hours on Monday,

Wednesday, and Friday

Overhydration in dialysis patients

• During each dialysis session the amount of fluid taken on in the inter-dialytic period has to be removed (as much as 6 L/4 hrs)

• Chronic overhydration results in cardiovascular disease (high blood pressure, left ventricular hypertrophy, …)

Pathophysiology of chronic volume overload

Chronic volume overload

Increased blood pressure

End organ damage

Left ventricular hypertrophy Vascular disease

Cerebro-vascular disease

Cardiovascular disease

TIA; stroke

Arrhythmia; myocardial infarction; sudden death

Removal of Fluid and Solutes by Ultrafiltration with the Goal to Achieve

“Dry Weight” (the “Holy Grail” in dialysis)

Blood Compartment

(venous)

Interstitial Fluid

CapillaryBed

Removal of Plasma WaterDuring Dialysis by Ultrafiltration

But there is are problems …

• There is no uniform definition of “dry weight”

• There is no universally accepted method to determine “dry weight”

• Determination of “dry weight” by bioimpedance (BIA) of the calf is a potential means

• Multifrequency BIA determines the extracellular volume in a given segment

Subject IT70926

0,1

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4:00

TIME (HRS:MIN)

EC

V (L

)

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82

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100

0 00:0

9:15

00:1

6:03

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2:48

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6:35

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3:21

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0:06

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6:52

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3:37

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0:22

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7:08

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3:53

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0:39

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7:24

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4:09

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0:55

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7:41

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4:27

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1:12

02:3

7:58

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4:43

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1:29

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8:14

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5:00

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1:44

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9:03

Rel

. Blo

od

Vo

lum

e C

han

ge

(%)

ECV Delta RBV

Concomitant Recording of Relative Blood Volume Changeand Calf ECV change

Dry weight monitor

Blood volume monitor (BVM)

Questions: Can the dynamics of interstitial fluid be modeled in order to determine “dry weight” without the need of frequent BIA

measurements?What we know:

ultrafiltration rate (HD machine)

relative change in blood volume (BVM)

change in calf ECV (Dry Weight Monitor)

serum albumin level

What we don’t know:

capillary pressure

interstitial protein conc.

Goal

• Bringing the patient to dry weight,

• avoiding the deleterious consequences of overhydration,

• reducing the need for uncomfortable measurements

Body composition in dialysis patients: implications for outcomes

Background

• There is convincing evidence that in contrast to findings in the general population high body mass index (BMI; weight [kg] / (height [m])2) in dialysis patients is associated with improved survival

• But: BMI does not differentiate between various components of body composition

BMI and survival in the general and the HD population

Kalantar-Zadeh, 2006

Same BMI – Different Body Composition

RRI Hypothesis

• Uremic toxin generation occurs predominantly in the visceral organs (“high metabolic rate compartment”; HMRC). The mass of key uremiogenic viscera (gut, liver) is relative to body weight or BMI larger in small people

• Uremic toxins (both lipophilic and hydrophilic) are taken up by adipose and muscle tissues and metabolized and/or stored

• The amount of in-tissue metabolism of uremic toxins depends on the fat and muscle mass

• Most important: Since dialysis dose is prescribed per urea distribution volume (=total body water), small patients may be at an increased risk of under-dialysis

Levin, Gotch, JASN 2001 Sarkar, KI 2006Kotanko, Blood Purif 2007

Predictions made by the RRI model

• Concentration of uremic toxins relate inversely to body size

• Production rate of uremic toxins per unit of body mass is higher in small subjects

• Large patients may have better surrogate outcomes

• Small patients experience better outcomes with higher dialysis doses

Sarkar, Semin Dial 2007

High Metabolic Rate Compartment and BMI are inversely related

Sarkar, Kidney Int 2006

Body size, gut, muscle, fat, and uremic toxins

Uremic ToxinGeneration

Small patient

Large patient

Uremic ToxinGeneration

Muscle Fat

Muscle Fat

VisceralOrgans

Sarkar, KI 2006Kotanko, Blood Purif 2007

3-compartment model

of (hydrophilic) uremic toxin kinetics

(Cronin-Fine, IJAO 2007)

VisceralOrgans

ExtracellularFluid

MuscleMass

Uremic Toxin Concentration Relates to Body Size

(Cronin-Fine, IJAO 2007)

The Plasma Concentration of Pentosidine Relates Inversely to BMI

80

70

30

20

10

60

40

50

To

tal

pen

tosi

din

e p

lasm

a co

nce

ntr

atio

n(p

mo

l/m

g p

rote

in)

14 26 30 34 38 4218 22

BMI (kg/m2)

R = - 0.55P < 0.001

(Slowik-Zylka, 2006)

Body size, gut, muscle, fat, and uremic toxins

Uremic ToxinGeneration

Small patient

Large patient

Uremic ToxinGeneration

Muscle Fat

Muscle Fat

VisceralOrgans

Sarkar, KI 2006Kotanko, Blood Purif 2007

Relation of Total Organ Mass to Relation of Total Organ Mass to Body Weight in 2.004 HD PatientsBody Weight in 2.004 HD Patients

MALES FEMALES

Total organ mass was calculated using regression models byGallagher et al (Am J Clin Nutr. 2006, 83:1062)

Kotanko & Levin Int J Artif Organs, 2007

HM

RO

mas

s [%

of

Bod

y W

eigh

t]

BMI [kg/m2] BMI [kg/m2]

N=1.093 N=911

Survival Stratified by Tertiles of Race- and Sex-Specific Visceral Organ Mass (% of Weight)

Mean Survival (days)Low Tertile: 1031Middle Tertile: 935High Tertile: 876

N = 2004P = 0.0001(log-rank test)

Kotanko, IJAO 2007

Question: is it possible to model the dynamics of uremic toxins

with a model including estimates of fat and visceral mass?

• What we know: estimates of body composition (fat, muscle, total body water, visceral mass, blood levels of toxins)

• What we don’t know: tissue concentrations of uremic toxins, exchange rates

Goal down the road ….

• Future dialysis prescription may account for aspects of body composition beyond urea distribution volume and thus improve the care independent of body composition (females/males; small/large)

High Systolic Blood Pressure

CardiovascularDisease

Inflammation Malnutrition

Infection

Low Systolic Blood Pressure

AntihypertensiveTherapy

Hypothesis: Low SBP is the Terminal Pathway of Various Pathological Processes

Incident Patients

Days since day 30 after first hemodialysis

Surv

ival p

roba

blity

SBP, mmHg

<120

<140

<160

<180

<200

>=200

0 30 60 90 120 150 180 210 240 270 300 330 360

0.5

0.6

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0.9

1

Prevalent Patients

Days since January 1, 2002

Surv

ival p

roba

blity

SBP, mmHg

<120

<140

<160

<180

<200

>=200

0 30 60 90 120 150 180 210 240 270 300 330 360

0.5

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1

AJKD, 2006

Systolic Blood Pressure Relates to Mortality

Very simple Markov model of SBP evolution predicts survival

50%

55%

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100%

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51-53

Months from First Date of Dialysis

Su

rviv

al (

%)

KM Curve (Estimated by Grouping into 3 Mns Grps)

Markov

Kotanko, EDTA 2008

Evolution of pre-HD SBP in surviving HD patients(total N=39.969 HD patients)

SBP means for all patients who kept HD during 1st HD 3 years (not exclusively)

Week when SBPs were measured

SB

P m

eans

of w

eekl

y-m

edia

n

HD kept - time

2, 2nd 6-month

3, 3rd 6-month

4, 4th 6-month

5, 5th 6-month

6, 6th 6-month

7, 7th 6-month

0 24 48 72 96 120 144 168

140

144

148

152

156 Follow-up time

Kotanko et al, ISN Nexus, 2007

Evolution of pre-HD SBP in non-survivors

SBP means for all HD patients who died in first 3 year since HD started

Week when SBPs were measured

SB

P M

eans

of w

eekl

y-m

edia

n

Died Time

2, 2nd 6-month

3, 3rd 6-month

4, 4th 6-month

5, 5th 6-month

6, 6th 6-month

7, 7th 6-month

0 24 48 72 96 120 144 168

140

144

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156

Follow-up time

Kotanko et al, ISN Nexus, 2007

SBP Evolution by Gender & Race

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Weeks Prior to Death

pre

s-S

BP

(m

mH

g)

Black FemaleBlack MaleWhite FemaleWhite MaleAllLog. (White Male)Log. (White Female)Log. (All)Log. (Black Male)Log. (Black Female)

Question: what is the best way to model correlated longitudinal SBP data taking covariates into account ?Ultimate goal: development of an automated alarm system to trigger early diagnostic & therapeutic intervention in deteriorating patients.

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