Mathematical modeling in chronic kidney disease
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Transcript of Mathematical modeling in chronic kidney disease
Mathematical modeling in chronic kidney disease
Peter Kotanko, MDRenal Research Institute, New York
[email protected], 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
0,11
0,12
0,13
0,14
0,15
0,16
0,17
0,18
0:00
0:06
0:13
0:20
0:26
0:33
0:40
0:46
0:53
1:00
1:06
1:13
1:20
1:26
1:33
1:40
1:46
1:53
2:00
2:06
2:13
2:20
2:26
2:33
2:40
2:46
2:53
3:00
3:06
3:13
3:20
3:26
3:33
3:40
3:46
3:53
4:00
TIME (HRS:MIN)
EC
V (L
)
80
82
84
86
88
90
92
94
96
98
100
0 00:0
9:15
00:1
6:03
00:2
2:48
00:2
9:33
00:3
6:18
00:4
3:03
00:4
9:50
00:5
6:35
01:0
3:21
01:1
0:06
01:1
6:52
01:2
3:37
01:3
0:22
01:3
7:08
01:4
3:53
01:5
0:39
01:5
7:24
02:0
4:09
02:1
0:55
02:1
7:41
02:2
4:27
02:3
1:12
02:3
7:58
02:4
4:43
02:5
1:29
02:5
8:14
03:0
5:00
03:1
1:44
03:1
8:29
03:2
5:14
03:3
2:00
03:3
8:46
03:4
5:31
03:5
2:17
03:5
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
0.7
0.8
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
0.6
0.7
0.8
0.9
1
AJKD, 2006
Systolic Blood Pressure Relates to Mortality
Very simple Markov model of SBP evolution predicts survival
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
6-8 9-11 12-14
15-17
18-20
21-23
24-26
27-29
30-32
33-35
36-38
39-41
42-44
45-47
48-50
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
148
152
156
Follow-up time
Kotanko et al, ISN Nexus, 2007
SBP Evolution by Gender & Race
125
130
135
140
145
150
155
1 4 7
10
13
16
19
22
25
28
31
34
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79
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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