Estimating pharmacokinetic parameters in imaging
A method is provided for estimating a parameter of physiological significance. One or more images are provided of a tissue in a subject to whom a dose of a contrast agent (CA) has been administered, using a computer equipped with image processing software, the concentration or relative concentration of the agent in a region or regions of interest in the tissue is determined, thus generating concentration data. The time-based behavior of concentrations of CA within the tissue is determined using a pharmacokinetic model that is based on a set of pharmacokinetic model parameters. Using computer code, the pharmacokinetic model is fit to the concentration data, varying one or more parameters, such that a best fit estimate of a parameter of physiological significance is provided.
1. A method of estimating a parameter of physiological significance, the method comprising:
(a) providing one or more images of a tissue in a subject to whom a dose of a contrast agent (CA) has been administered; and
(b) determining, using a computer equipped with image processing software, the concentration or relative concentration of the agent in a region or regions of interest in the tissue, thereby generating concentration data;
(c) describing the time-based behavior of concentrations of CA within the tissue using a pharmacokinetic model that is based on a set of pharmacokinetic model parameters; and
(d) fitting, using computer code, the pharmacokinetic model to the concentration data, varying one or more parameters, wherein the best fit estimates a parameter of physiological significance,
wherein the pharmacokinetic model for performing the analysis is a distributed model, and wherein the distributed model is based on the Krogh cylinder given by the following equations:
∂
[
C
]
∂
t
=
D
∇
2
[
C
]
-
k
on
ɛ
[
C
]
[
Ag
]
+
k
off
[
B
]
∂
[
B
]
∂
t
=
k
on
ɛ
[
C
]
[
Ag
]
-
k
off
[
B
]
-
k
e
,
B
[
B
]
∂
[
Ag
]
∂
t
=
R
s
-
k
on
ɛ
[
C
]
[
Ag
]
+
k
off
[
B
]
-
k
e
,
Ag
[
Ag
]
∂
[
I
]
∂
t
=
k
e
[
B
}
-
k
resid
[
I
]
∂
[
C
]
∂
r
|
r
=
R
=
0
-
D
∂
[
C
]
∂
r
|
r
=
R
cap
=
P
(
[
C
]
p
-
[
C
]
ɛ
)
[
C
]
|
t
=
0
=
0
[
B
]
|
t
=
0
=
0
[
Ag
]
|
t
=
0
=
Ag
0
[
I
]
|
t
=
0
=
0
wherein ∇ 2 denotes the Laplacian in cylindrical coordinates, [C] denotes the free CA concentration, [B] denotes the bound CA/antigen concentration, [Ag] denotes the unbound antigen concentration, [I] denotes the concentration of intracellular CA, D denotes the CA diffusion coefficient in tissue, k on denotes the CA/antigen association rate constant, k off denotes the CA/antigen dissociation rate constant, ε denotes the CA void fraction in the tissue, k e,B denotes the internalization rate constant of the CA/antigen bound complex, k e,Ag denotes the internalization rate constant of the antigen, k resid denotes the rate of release of CA or CA signal from the intracellular compartment, R S denotes the antigen synthesis rate, R denotes the Krogh cylinder radius, R cap denotes the capillary radius, P denotes the tumor capillary permeability, Ag 0 denotes the initial antigen density, and [C] P denotes the plasma concentration of the contrast agent as a function of time, also sometimes called an arterial input function.
2. The method of claim 1 , wherein the contrast agent includes a positron- or gamma-emitting isotope.
3. The method of claim 2 , wherein the positron- or gamma-emitting isotope is 68Ga, 18F, 89Zr, 64Cu, 86Y, 124I, 123I, 99mTc, 125I, 111In, 67Cu, or 177Lu.
4. The method of claim 1 , wherein the contrast agent comprises paramagnetic or superparamagnetic material.
5. The method of claim 4 , wherein the paramagnetic or superparamagnetic material is gadolinium, iron oxide, iron platinum, or manganese.
6. The method of claim 1 , wherein the contrast agent comprises a fluorescent probe.
7. The method of claim 1 , wherein the one or more images were generated by single photon emission computed tomography (SPECT), positron emission tomography (PET), magnetic resonance imaging (MRI), computed tomography (CT), detecting fluorescence, or a combination thereof.
8. The method of claim 1 , wherein the parameter of physiological significance is the contrast agent affinity K D , the Krogh cylinder radius R, the CA/antigen bound complex internalization rate k e,B , and the antigen concentration Ag T =[Ag]+[B], wherein K D represents the ratio of the dissociation rate k off to the association rate k on of contrast agent/antigen binding, R represents the capillary to capillary half-distance (a measure of tumor vascularity), k e,B represents the internalization rate of CA into the intracellular space, and Ag T represents the concentration of target antigen in the tumor.
9. A method of detecting a malignant lesion in a subject, the method comprising:
(a) providing one or more images of a subject to whom a dose of contrast agent (CA) has been administered;
(b) identifying a lesion candidate based on the acquired image or images;
(c) determining, using a computer equipped with image processing software, the concentration or relative concentration of the CA in a region of interest in the tissue, thereby generating concentration data;
(d) describing the time-based behavior of concentrations of the CA within the subject using a pharmacokinetic model that is based on a set of pharmacokinetic model parameters;
(e) fitting, using computer code, the pharmacokinetic model to the concentration data, varying one or more parameters wherein the best fit estimates a parameter or parameters of physiological significance; and
(f) determining whether the lesion candidate is a malignant lesion based on the concentration data and the estimated parameter or parameters of physiological significance,
wherein the pharmacokinetic model for performing the analysis is a distributed model that describes spatial and temporal variations, and wherein the distributed model is based on the Krogh cylinder given by the following equations:
∂
[
C
]
∂
t
=
D
∇
2
[
C
]
-
k
on
ɛ
[
C
]
[
Ag
]
+
k
off
[
B
]
∂
[
B
]
∂
t
=
k
on
ɛ
[
C
]
[
Ag
]
-
k
off
[
B
]
-
k
e
,
B
[
B
]
∂
[
Ag
]
∂
t
=
R
s
-
k
on
ɛ
[
C
]
[
Ag
]
+
k
off
[
B
]
-
k
e
,
Ag
[
Ag
]
∂
[
I
]
∂
t
=
k
e
[
B
}
-
k
resid
[
I
]
∂
[
C
]
∂
r
|
r
=
R
=
0
-
D
∂
[
C
]
∂
r
|
r
=
R
cap
=
P
(
[
C
]
p
-
[
C
]
ɛ
)
[
C
]
|
t
=
0
=
0
[
B
]
|
t
=
0
=
0
[
Ag
]
|
t
=
0
=
Ag
0
[
I
]
|
t
=
0
=
0
wherein ∇ 2 denotes the Laplacian in cylindrical coordinates, [C] denotes the free CA concentration, [B] denotes the bound CA/antigen concentration, [Ag] denotes the unbound antigen concentration, [I] denotes the concentration of intracellular CA, D denotes the CA diffusion coefficient in tissue, k on denotes the CA/antigen association rate constant, k off denotes the CA/antigen dissociation rate constant, ε denotes the CA void fraction in the tissue, k e,B denotes the internalization rate constant of the CA/antigen bound complex, k e,Ag denotes the internalization rate constant of the antigen, k resid denotes the rate of release of CA or CA signal from the intracellular compartment, R S denotes the antigen synthesis rate, R denotes the Krogh cylinder radius, R cap denotes the capillary radius, P denotes the tumor capillary permeability, Ag 0 denotes the initial antigen density, and [C] P denotes the plasma concentration of the contrast agent as a function of time, also sometimes called an arterial input function.
10. A method of detecting a malignant lesion in a subject, the method comprising:
(a) providing one or more images of a subject to whom a dose of contrast agent (CA) has been administered;
(b) identifying a lesion candidate based on the acquired image or images;
(c) determining, using a computer equipped with image processing software, the concentration or relative concentration of the CA in a region of interest in the tissue, thereby generating concentration data;
(d) describing the time-based behavior of concentrations of the CA within the subject using a pharmacokinetic model that is based on a set of pharmacokinetic model parameters;
(e) fitting, using computer code, the pharmacokinetic model to the concentration data, varying one or more parameters wherein the best fit estimates a parameter or parameters of physiological significance; and
(f) determining whether the lesion candidate is a malignant lesion based on the concentration data and the estimated parameter or parameters of physiological significance,
wherein the pharmacokinetic model for performing the analysis is a distributed model that describes spatial and temporal variations, and, where the parameter of physiological significance is the contrast agent affinity K D , the Krogh cylinder radius R, the CA/antigen bound complex internalization rate k e,B , and the antigen concentration Ag T =[Ag]+[B], wherein K D represents the ratio of the dissociation rate k off to the association rate k on of contrast agent/antigen binding, R represents the capillary to capillary half-distance, which is a measure of tumor vascularity, k e,B represents the internalization rate of CA into the intracellular space, and Ag T represents the concentration of target antigen in the tumor.
11. The method of claim 10 , wherein the contrast agent includes a positron- or gamma-emitting isotope.
12. The method of claim 10 , wherein the contrast agent comprises paramagnetic or superparamagnetic material.
13. The method of claim 10 , wherein the contrast agent comprises a fluorescent probe.
14. The method of claim 10 , wherein the one or more images were generated by single photon emission computed tomography (SPECT), positron emission tomography (PET), magnetic resonance imaging (MRI), computed tomography (CT), detecting fluorescence, or a combination thereof.
15. A computer system comprising: a processor; and a program storage device readable by the computer system, embodying a program instructions executable by the processor to perform method steps for performing pharmacokinetic analysis in image(s), the method comprising:
(a) providing one or more images of a subject to whom a contrast agent (CA) has been administered;
(b) identifying a lesion candidate based on the one or more images;
(c) determining, using a computer equipped with image processing software, the concentration or relative concentration of the CA in a region of interest in the tissue, thereby generating concentration data;
(d) describing the time-based behavior of concentrations of CA within the subject using a pharmacokinetic model that is based on a set of pharmacokinetic model parameters; and
(e) fitting, using computer code, the pharmacokinetic model to the concentration data, varying one or more parameters, wherein the best fit estimates a parameter or parameters of physiological significance,
wherein the pharmacokinetic model for performing pharmacokinetic analysis is a distributed model, wherein the distributed model is based on the Krogh cylinder given by the following equations:
∂
[
C
]
∂
t
=
D
∇
2
[
C
]
-
k
on
ɛ
[
C
]
[
A
g
]
+
k
off
[
B
]
∂
[
B
]
∂
t
=
k
on
ɛ
[
C
]
[
A
g
]
-
k
off
[
B
]
-
k
e
,
B
[
B
]
∂
[
A
g
]
∂
t
=
R
S
-
k
on
ɛ
[
C
]
[
A
g
]
+
k
off
[
B
]
-
k
e
,
Ag
[
Ag
]
∂
[
I
]
∂
t
=
k
e
[
B
]
-
k
resid
[
I
]
∂
[
C
]
∂
r
❘
r
=
R
=
0
-
D
∂
[
C
]
∂
r
❘
r
=
R
cap
=
P
(
[
C
]
p
-
[
C
]
ɛ
)
[
C
]
❘
t
=
0
=
0
[
B
]
❘
t
=
0
=
0
[
A
g
]
❘
t
=
0
=
A
g
0
[
I
]
❘
t
=
0
=
0
wherein ∇ 2 denotes the Laplacian in cylindrical coordinates, [C] denotes the free CA concentration, [B] denotes the bound CA/antigen concentration, [Ag] denotes the unbound antigen concentration, [I] denotes the concentration of intracellular CA, D denotes the CA diffusion coefficient in tissue, k on denotes the CA/antigen association rate constant, k off denotes the CA/antigen dissociation rate constant, ε denotes the CA void fraction in the tissue, k e,B denotes the internalization rate constant of the CA/antigen bound complex, k e,Ag denotes the internalization rate constant of the antigen, k resid denotes the rate of release of CA or CA signal from the intracellular compartment, R S denotes the antigen synthesis rate, R denotes the Krogh cylinder radius, R cap denotes the capillary radius, P denotes the tumor capillary permeability, Ag 0 denotes the initial antigen density, and [C] P denotes the plasma concentration of the contrast agent as a function of time, also sometimes called an arterial input function.
16. The computer system of claim 15 , wherein the one or more parameters of physiological significance are the contrast agent affinity K D , the Krogh cylinder radius R, the CA/antigen bound complex internalization rate k e,B , and the antigen concentration Ag T =[Ag]+[B], wherein K D represents the ratio of the dissociation rate k off to the association rate k on of contrast agent/antigen binding, R represents the capillary to capillary half-distance, which is a measure of tumor vascularity, k e,B represents the internalization rate of CA into the intracellular space, and Ag T represents the concentration of target antigen in the tumor.