# US 10,319,478 B2 · System and method of modeling erythropoiesis and its management

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 10,319,478 B2
- Document ID: US10319478B2
- Status: Granted
- Kind: B2
- Application number: 14/343,464
- Filed: 2012-09-07
- Published: 2014-07-17
- Granted: 2019-06-11
- Earliest claimed: 2011-09-08
- Assignees: Fresenius Medical Care Holdings, Inc.
- Applicants: Doris Helene Fuertinger; Franz Kappel; Peter Kotanko; Nathan W. Levin; Stephan Thijssen
- Inventors: Doris Helene Fuertinger; Franz Kappel; Peter Kotanko; Nathan W. Levin; Stephan Thijssen
- Web page: https://patentgrep.com/patent/US10319478B2

## CPC

- G16H 50/50: for simulation or modelling of medical disorders
- A61K 38/1816: {Erythropoietin [EPO]}
- G16H 50/20: for computer-aided diagnosis, e.g. based on medical expert systems
- G16H 50/80: for detecting, monitoring or modelling epidemics or pandemics, e.g. flu
- G16C 20/30: Prediction of properties of chemical compounds, compositions or mixtures
- G16H 20/17: delivered via infusion or injection
- G16H: HEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
- A61K: PREPARATIONS FOR MEDICAL, DENTAL OR TOILETRY PURPOSES (devices or methods specially adapted for bringing pharmaceutical products into particular physical or administering forms A61J3/00; chemical aspects of, or use of materials for deodorisation of air, for disinfection or sterilisation, or for bandages, dressings, absorbent pads or surgical articles A61L; soap compositions C11D)
- G16C: COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE

## Abstract

A method of adjusting a patient's undesired hematocrit and/or hemoglobin concentration to a value within a desired range at a predetermined time with an erythropoiesis stimulating agent (ESA) regimen includes obtaining patient parameters required for input into a model for predicting the patient's hematocrit and/or hemoglobin concentration at a predetermined time with a selected ESA administration regimen, and employing the patient parameters and an initially selected EPO administration regimen in the model to predict the patient's hematocrit and/or hemoglobin concentration at the predetermined time with the initially selected ESA administration regimen. Optionally, if the patient's hematocrit and/or hemoglobin concentration is not predicted by the model to be in the desired range at the predetermined time, the method includes employing the model with one or more different ESA administration regimens until the model predicts that the patient's hematocrit and/or hemoglobin concentration will be in the desired range at the predetermined time. The method then includes administering ESA to the patient with an ESA administration regimen predicted to adjust the patient's hematocrit and/or hemoglobin concentration to the desired range at the predetermined time. The method can be implemented in a computer system for adjusting a patient's undesired hematocrit and/or hemoglobin concentration to a desired range at a predetermined time with an erythropoiesis stimulating agent (ESA) regimen.

## Claims

### Claim 1

A method of adjusting a patient's undesired hematocrit and/or hemoglobin concentration to a value within a desired range at a predetermined time with an erythropoiesis stimulating agent (ESA) regimen comprising:
a) obtaining patient parameters required for input into a model for predicting the patient's hematocrit and/or hemoglobin concentration at a predetermined time with a selected ESA administration regimen;
b) employing the patient parameters and an initially selected ESA administration regimen in the model to predict the patient's hematocrit and/or hemoglobin concentration at the predetermined time with the initially selected ESA administration regimen, wherein the model comprises the functions:
⁢
∂
∂
t
⁢
p
⁡
(
t
,
μ
p
)
+
∂
∂
μ
p
⁢
p
⁡
(
t
,
μ
p
)
=
β
p
⁢
p
⁡
(
t
,
μ
p
)
,
⁢
⁢
∂
∂
t
⁢
q
⁡
(
t
,
μ
q
)
+
∂
∂
μ
q
⁢
q
⁡
(
t
,
μ
q
)
=
(
β
q
-
α
q
⁡
(
E
⁡
(
t
)
)
)
⁢
q
⁡
(
t
,
μ
q
)
,
⁢
⁢
∂
∂
t
⁢
r
⁡
(
t
,
μ
r
)
+
∂
∂
μ
r
⁢
r
⁡
(
t
,
μ
r
)
=
β
r
⁢
r
⁡
(
t
,
μ
r
)
,
⁢
⁢
∂
∂
t
⁢
s
⁡
(
t
,
μ
s
)
+
v
s
⁡
(
E
⁡
(
t
)
)
⁢
∂
∂
μ
s
⁢
⁢
s
⁡
(
t
,
μ
s
)
=
-
α
s
⁢
s
⁡
(
t
,
μ
s
)
,
⁢
⁢
∂
∂
t
⁢
m
⁡
(
t
,
μ
m
)
+
∂
∂
μ
m
⁢
m
⁡
(
t
,
μ
m
)
=
-
α
m
⁡
(
E
⁡
(
t
)
,
μ
m
)
⁢
m
⁡
(
t
,
μ
m
)
,
⁢
⁢
and
⁢
d
d
⁢
⁢
t
⁢
E
.
end
⁡
(
t
)
=
1
TBV
⁢
E
i
⁢
⁢
n
end
⁡
(
t
)
-
c
deg
end
⁢
E
end
⁡
(
t
)
⁢
d
d
⁢
⁢
t
⁢
E
ex
⁡
(
t
)
=
1
TBV
⁢
E
i
⁢
⁢
n
ex
⁡
(
t
)
-
c
deg
ex
⁢
E
ex
⁡
(
t
)
,
⁢
⁢
where
⁢
⁢
⁢
α
q
⁡
(
E
⁡
(
t
)
)
=
a
1
-
b
1
1
+
e
k
1
⁢
E
⁡
(
t
)
-
c
1
+
b
1
⁢
α
q
⁡
(
E
⁡
(
t
)
)
=
a
1
-
b
1
1
+
e
-
k
1
⁢
E
⁡
(
t
)
-
c
1
+
b
1
,
⁢
α
m
⁡
(
E
⁡
(
t
)
,
μ
m
)
=
{
γ
m
+
min
(
c
E
E
⁡
(
t
)
k
E
,
b
E
)
for
⁢
⁢
E
⁡
(
t
)
<
τ
E
,
⁢
μ
m
⁢
⁢
i
⁢
⁢
n
m
,
n
≤
μ
m
≤
μ
ma
⁢
⁢
x
m
,
n
,
γ
m
otherwise
,
⁢
⁢
⁢
where
⁢
⁢
⁢
M
~
⁡
(
t
)
=
10
-
8
⁢
M
⁡
(
t
)
/
TBV
,
⁢
⁢
M
⁡
(
t
)
=
∫
0
μ
ma
⁢
⁢
x
m
⁢
m
⁡
(
t
,
μ
m
)
⁢
d
⁢
⁢
μ
m
,
and
⁢
⁢
⁢
TBV
=
total
⁢
⁢
blood
⁢
⁢
volume
,
wherein p(t,μp) is a population density of a BFU-E cell class at time t with maturity μp, βp is a proliferation rate for BFU-E cells, q(t,μq) is a population density of a CFU-E cell class at time t with maturity μq, βq is a proliferation rate for CFU-E cells, αq(E(t)) is an apoptosis rate for CFU-E cells which depends on erythropoietin(EPO)-concentration E(t) at time t, r(t,μr) is a population density of an erythroblast class at time t with maturity μr, βr is a proliferation rate for erythroblasts, s(t,μs) is a population density of a marrow reticulocytes class at time t with maturity μs, vs(E(t)) is a maturation velocity of cells leaving the erythroblast class an entering the reticulocytes population class which depends on EPO-concentration E(t) at time t, αs is an apoptosis rate for marrow reticulocytes, m(t, μm) is a population density of an erythrocyte class at time t with maturity μm, αm(E(t), μm) is an apoptosis rate for erythrocytes which depends on EPO-concentration E(t) at time t and maturity μm, Eend(t) is an endogenous EPO concentration at time t, Einend(t) is an amount of EPO released by a patient's kidneys, cdegend is a degradation rate of endogenous EPO, Eex(t) is an exogenous EPO concentration at time t, Einex(t) is an amount of EPO administered to the patient, cdegex is a degradation rate of exogenous EPO, a1, b1, c1 and k1 are constants for the apoptosis rate for CFU-E cells, a2, b2, c2, and k2 are constants for the maturation velocity for marrow reticulocytes, γm is a mortality rate of erythrocytes, bE, cE, and kE are constants in the mortality rate of erythrocytes, τE is a threshold beneath which neocytolysis is triggered, μm is a erythrocyte maturity; μminm,n is a lower bound of erythrocytes which are possibly exposed to neocytolysis, μmaxm,n is an upper bound of erythrocytes which are possibly exposed to neocytolysis, M(t) is a total population of erythrocytes;
c) employing the model with one or more different ESA administration regimens until the model predicts that the patient's hematocrit and/or hemoglobin concentration will be in the desired range at the predetermined time; and
d) administering ESA to the patient according to the different ESA administration regimen predicted to adjust the patient's hematocrit and/or hemoglobin concentration to a value within the desired range at the predetermined time.

### Claim 2 (depends on 1)

The method of claim 1, wherein the patient parameters include starting hematocrit and/or hemoglobin concentration in the patient's blood, total blood volume of the patient, lifespan of red blood cells (RBCs) of the patient, mean corpuscular volume of the RBCs, and rate of neocytolysis in the patient's blood.

### Claim 3 (depends on 1)

The method of claim 1, wherein the predetermined time is in a range of between about 5 days and about 200 days into the ESA administration regimen.

### Claim 4 (depends on 1)

The method of claim 1, wherein the patient is a dialysis patient and the desired hematocrit is in the range of between about 28 percent and about 36 percent and the desired hemoglobin concentration is in a range of between about 9.5 g/dL and about 12 g/dL.

### Claim 5

A system for adjusting a patient's undesired hematocrit and/or hemoglobin concentration to a value within a desired range at a predetermined time with an erythropoiesis stimulating agent (ESA) regimen the system comprising:
a) an input means for determining patient parameters of the patient;
b) a digital processor coupled to receive determined patient data from the input means, wherein the digital processor executes a modeling system in working memory, wherein the modeling system is configured to:
i) employ the patient parameters and an initially selected ESA administration regimen in the model to predict the patient's hematocrit and/or hemoglobin concentration at the predetermined time with the initially selected ESA administration regimen, wherein the model comprises the functions:
⁢
∂
∂
t
⁢
p
⁡
(
t
,
μ
p
)
+
∂
∂
μ
p
⁢
p
⁡
(
t
,
μ
p
)
=
β
p
⁢
p
⁡
(
t
,
μ
p
)
,
⁢
⁢
∂
∂
t
⁢
q
⁡
(
t
,
μ
q
)
+
∂
∂
μ
q
⁢
q
⁡
(
t
,
μ
q
)
=
(
β
q
-
α
q
⁡
(
E
⁡
(
t
)
)
)
⁢
q
⁡
(
t
,
μ
q
)
,
⁢
⁢
∂
∂
t
⁢
r
⁡
(
t
,
μ
r
)
+
∂
∂
μ
r
⁢
r
⁡
(
t
,
μ
r
)
=
β
r
⁢
r
⁡
(
t
,
μ
r
)
,
⁢
⁢
∂
∂
t
⁢
s
⁡
(
t
,
μ
s
)
+
v
s
⁡
(
E
⁡
(
t
)
)
⁢
∂
∂
μ
s
⁢
s
⁡
(
t
,
μ
s
)
=
-
α
s
⁢
s
⁡
(
t
,
μ
s
)
,
⁢
⁢
∂
∂
t
⁢
m
⁡
(
t
,
μ
m
)
+
∂
∂
μ
m
⁢
m
⁡
(
t
,
μ
m
)
=
-
α
m
⁡
(
E
⁡
(
t
)
,
μ
m
)
⁢
m
⁡
(
t
,
μ
m
)
,
⁢
⁢
and
⁢
d
d
⁢
⁢
t
⁢
E
.
end
⁡
(
t
)
=
1
TBV
⁢
E
i
⁢
⁢
n
end
⁡
(
t
)
-
c
deg
end
⁢
E
end
⁡
(
t
)
⁢
d
d
⁢
⁢
t
⁢
E
ex
⁡
(
t
)
=
1
TBV
⁢
E
i
⁢
⁢
n
ex
⁡
(
t
)
-
c
deg
ex
⁢
E
ex
⁡
(
t
)
,
⁢
⁢
where
⁢
α
q
⁡
(
E
⁡
(
t
)
)
=
a
1
-
b
1
1
+
e
k
1
⁢
E
⁡
(
t
)
-
c
1
+
b
1
⁢
v
s
⁡
(
E
⁡
(
t
)
)
=
a
2
-
b
2
1
+
e
-
k
2
⁢
E
⁡
(
t
)
+
c
2
+
b
2
,
⁢
α
m
⁡
(
E
⁡
(
t
)
,
μ
m
)
=
{
γ
m
+
min
⁡
(
c
E
E
⁡
(
t
)
k
E
,
b
E
)
for
⁢
⁢
E
⁡
(
t
)
<
τ
E
,
⁢
μ
m
⁢
⁢
i
⁢
⁢
n
m
,
n
≤
μ
m
≤
μ
ma
⁢
⁢
x
m
,
n
,
γ
m
otherwise
,
⁢
⁢
⁢
where
⁢
⁢
⁢
M
~
⁡
(
t
)
=
10
-
8
⁢
M
⁡
(
t
)
/
TBV
,
⁢
⁢
M
⁡
(
t
)
=
∫
0
μ
ma
⁢
⁢
x
m
⁢
m
⁡
(
t
,
μ
m
)
⁢
d
⁢
⁢
μ
m
,
and
⁢
⁢
⁢
TBV
=
total
⁢
⁢
blood
⁢
⁢
volume
,
wherein p(t,μp) is a population density of a BFU-E cell class at time t with maturity μp, βp is a proliferation rate for BFU-E cells, q(t,μq) is a population density of a CFU-E cell class at time t with maturity μq, βq is a proliferation rate for CFU-E cells, αq(E(t)) is an apoptosis rate for CFU-E cells which depends on erythropoietin(EPO)-concentration E(t) at time t, r(t,μr) is a population density of an erythroblast class at time t with maturity μr, βr is a proliferation rate for erythroblasts, s(t,μs) is a population density of a marrow reticulocytes class at time t with maturity μs, vs(E(t)) is a maturation velocity of cells leaving the erythroblast class an entering the reticulocytes population class which depends on EPO-concentration E(t) at time t, αs is an apoptosis rate for marrow reticulocytes, m(t, μm) is a population density of an erythrocyte class at time t with maturity μm, αm(E(t), μm) is an apoptosis rate for erythrocytes which depends on EPO concentration E(t) at time t and maturity μm, Eend(t) is an endogenous EPO concentration at time t, Einend(t) is an amount of EPO released by a patient's kidneys, cdegend is a degradation rate of endogenous EPO, Eex(t) is an exogenous EPO concentration at time t, Einex(t) is an amount of EPO administered to the patient, cdegex is a degradation rate of exogenous EPO, a1, b1, c1 and k1 are constants for the apoptosis rate for CFU-E cells, a2, b2, c2, and k2 are constants for the maturation velocity for marrow reticulocytes, γm is a mortality rate of erythrocytes, bE, cE, and kE are constants in the mortality rate of erythrocytes, τE is a threshold beneath which neocytolysis is triggered, μm is a erythrocyte maturity; μminm,n is a lower bound of erythrocytes which are possibly exposed to neocytolysis, μmaxm,n is an upper bound of erythrocytes which are possibly exposed to neocytolysis, M(t) is a total population of erythrocytes; and
ii) employ the model with one or more different ESA administration regimens until the model predicts that the patient's hematocrit and/or hemoglobin concentration will be a value within in the desired range at the predetermined time; and
c) a dialysis machine coupled to the digital processor, wherein the digital processor is further configured to control administration of the ESA according to an ESA administration regimen that adjusts the patient's hematocrit and/or hemoglobin concentration to a value that is within the desired range at the predetermined time.

### Claim 6 (depends on 5)

The system of claim 5, wherein the patient parameters include starting hemoglobin concentration in the patient's blood, total blood volume of the patient, lifespan of red blood cells (RBCs) of the patient, mean corpuscular volume of the RBCs, and rate of neocytolysis in the patient's blood.

### Claim 7 (depends on 5)

The system of claim 5, wherein the predetermined time is in a range of between about 5 days and about 200 days into the ESA administration regimen.

### Claim 8 (depends on 5)

The system of claim 5, wherein the patient is a dialysis patient and the desired hematocrit is in the range of between about 28 percent and about 36 percent and the desired hemoglobin concentration is in a range of between about 9.5 g/dL and about 12 g/d L.

### Claim 9

A method of determining an erythropoiesis stimulating agent (ESA) administration regimen to bring a patient's hematocrit and/or hemoglobin concentration into a desired range at a predetermined time comprising:
a) obtaining patient parameters required for input into a model for predicting the patient's hematocrit and/or hemoglobin concentration at a predetermined time with a selected ESA administration regimen;
b) employing the patient parameters and an initially selected ESA administration regimen in the model to predict the patient's hematocrit and/or hemoglobin concentration at the predetermined time with the initially selected ESA administration regimen, wherein the model comprises the functions:
⁢
∂
∂
t
⁢
p
⁡
(
t
,
μ
p
)
+
∂
∂
μ
p
⁢
p
⁡
(
t
,
μ
p
)
=
β
p
⁢
p
⁡
(
t
,
μ
p
)
,
⁢
⁢
∂
∂
t
⁢
q
⁡
(
t
,
μ
q
)
+
∂
∂
μ
q
⁢
q
⁡
(
t
,
μ
q
)
=
(
β
q
-
α
q
⁡
(
E
⁡
(
t
)
)
)
⁢
q
⁡
(
t
,
μ
q
)
,
⁢
⁢
∂
∂
t
⁢
r
⁡
(
t
,
μ
r
)
+
∂
∂
μ
r
⁢
(
t
,
μ
r
)
=
β
r
⁢
r
⁡
(
t
,
μ
r
)
,
⁢
⁢
∂
∂
t
⁢
s
⁡
(
t
,
μ
s
)
+
v
s
⁡
(
E
⁡
(
t
)
)
⁢
∂
∂
μ
s
⁢
s
⁡
(
t
,
μ
s
)
=
-
α
s
⁢
s
⁡
(
t
,
μ
s
)
,
⁢
⁢
∂
∂
t
⁢
m
⁡
(
t
,
μ
m
)
+
∂
∂
μ
m
⁢
m
⁡
(
t
,
μ
m
)
=
-
α
m
⁡
(
E
⁡
(
t
)
,
μ
m
)
⁢
m
⁡
(
t
,
μ
m
)
,
and
⁢
d
dt
⁢
E
.
end
⁡
(
t
)
=
1
TBV
⁢
E
i
⁢
⁢
n
end
⁡
(
t
)
-
c
deg
end
⁢
E
end
⁡
(
t
)
⁢
d
dt
⁢
E
ex
⁡
(
t
)
=
1
TBV
⁢
E
i
⁢
⁢
n
ex
⁡
(
t
)
-
c
deg
ex
⁢
E
ex
⁡
(
t
)
,
where
⁢
α
q
⁡
(
E
⁡
(
t
)
)
=
a
1
-
b
1
1
+
e
k
1
⁢
E
⁡
(
t
)
-
c
1
+
b
1
⁢
α
q
⁡
(
E
⁡
(
t
)
)
=
a
1
-
b
1
1
+
e
k
1
⁢
E
⁡
(
t
)
-
c
1
+
b
1
α
m
⁡
(
E
⁡
(
t
)
,
μ
m
)
=
{
γ
m
+
min
⁡
(
c
E
E
⁡
(
t
)
k
E
,
b
E
)
for
⁢
⁢
E
⁡
(
t
)
<
τ
E
,
μ
m
⁢
⁢
i
⁢
⁢
n
m
,
n
≤
μ
m
≤
μ
m
⁢
⁢
a
⁢
⁢
x
m
,
n
,
γ
m
otherwise
,
⁢
⁢
where
⁢
⁢
⁢
M
~
⁡
(
t
)
=
10
-
8
⁢
M
⁡
(
t
)
/
TBV
,
⁢
⁢
M
⁡
(
t
)
=
∫
0
μ
m
⁢
⁢
a
⁢
⁢
x
m
⁢
m
⁡
(
t
,
μ
m
)
⁢
d
⁢
⁢
μ
m
,
and
⁢
⁢
⁢
TBV
=
total
⁢
⁢
blood
⁢
⁢
volume
,
wherein p(t,μp) is a population density of a BFU-E cell class at time t with maturity μp, βp is a proliferation rate for BFU-E cells, q(t,μq) is a population density of a CFU-E cell class at time t with maturity μq, βq is a proliferation rate for CFU-E cells, αq(E(t)) is an apoptosis rate for CFU-E cells which depends on erythropoietin(EPO)-concentration E(t) at time t, r(t,μr) is a population density of an erythroblast class at time t with maturity μr, βr is a proliferation rate for erythroblasts, s(t,μs) is a population density of a marrow reticulocytes class at time t with maturity μs, vs(E(t)) is a maturation velocity of cells leaving the erythroblast class an entering the reticulocytes population class which depends on EPO-concentration E(t) at time t, αs is an apoptosis rate for marrow reticulocytes, m(t, μm) is a population density of an erythrocyte class at time t with maturity μm, αm(E(t), μm) is an apoptosis rate for erythrocytes which depends on EPO-concentration E(t) at time t and maturity μm, Eend(t) is an endogenous EPO concentration at time t, Einend(t) is an amount of EPO released by a patient's kidneys, cdegend is a degradation rate of endogenous EPO, Eex(t) is an exogenous EPO concentration at time t, Einex(t) is an amount of EPO administered to the patient, cdegex is a degradation rate of exogenous EPO, a1, b1, c1 and k1 are constants for the apoptosis rate for CFU-E cells, a2, b2, c2, and k2 are constants for the maturation velocity for marrow reticulocytes, γm is a mortality rate of erythrocytes, bE, cE, and kE are constants in the mortality rate of erythrocytes, τE is a threshold beneath which neocytolysis is triggered, μm is a erythrocyte maturity; μhd minm,n is a lower bound of erythrocytes which are possibly exposed to neocytolysis, μmaxm,n is an upper bound of erythrocytes which are possibly exposed to neocytolysis, M(t) is a total population of erythrocytes; and
c) employing the model with one or more different ESA administration regimens until the model predicts that the patient's hematocrit and/or hemoglobin concentration will be in the desired range at the predetermined time; and
d) administering ESA to the patient according to the different ESA administration regimen predicted to adjust the patient's hematocrit and/or hemoglobin concentration to a value within the desired range at the predetermined time.

### Claim 10 (depends on 1)

The method of claim 1, wherein the patient undergoes a medical procedure prior to, during, or after initiation of the ESA administration regimen, the medical procedure selected from the group consisting of blood donation, surgery, and dialysis, or any combination thereof.