Estimating pharmacokinetic parameters in imaging
A method of estimating a parameter of physiological significance in the central nervous system (CNS) is provided. The method comprises (a) providing one or more images of the brain or cerebral spinal fluid (CSF) in a subject to whom a dose of a contrast agent (CA) has been administered; (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 brain or CSF, thereby generating concentration data; (c) describing the time-based behavior of concentrations of CA within the brain or CSF 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 in the CNS.
1. A method of estimating a parameter of physiological significance in the central nervous system (CNS), the method comprising:
(a) providing one or more images of the brain or cerebral spinal fluid (CSF) in a subject to whom a dose of a contrast agent (CA) has been administered;
(b) determining, using a computer equipped with image processing software, the concentration or relative concentration of the CA in a region or regions of interest in the brain or CSF, thereby generating concentration data;
(c) describing the time-based behavior of concentrations of CA within the brain or CSF 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 in the CNS.
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 are 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 pharmacokinetic model for performing the analysis is a distributed model.
9. The method of claim 8 , wherein the distributed model is given by the following equations:
∂
C
(
x
,
t
)
∂
t
=
D
∂
2
C
(
x
,
t
)
∂
x
2
+
PS
V
(
C
p
(
t
)
-
C
(
x
,
t
)
ɛ
)
-
k
on
C
(
x
,
t
)
ɛ
T
(
x
,
t
)
+
k
off
B
(
x
,
t
)
∂
B
(
x
,
t
)
∂
t
=
k
on
C
(
x
,
t
)
ɛ
T
(
x
,
t
)
-
k
off
B
(
x
,
t
)
-
k
int
B
(
x
,
t
)
∂
T
(
x
,
t
)
∂
t
=
R
s
-
k
on
C
(
x
,
t
)
ɛ
T
(
x
,
t
)
+
k
off
B
(
x
,
t
)
-
k
int
,
T
B
(
x
,
t
)
∂
I
(
x
,
t
)
∂
t
=
k
int
B
(
x
,
t
)
-
k
resid
I
(
x
,
t
)
∂
C
CSF
(
t
)
∂
t
=
-
Q
CSF
V
CSF
C
CSF
(
t
)
+
D
E
A
V
CSF
∂
C
(
0
,
t
)
∂
x
+
P
BCSFB
S
BCSFB
V
CSF
(
C
p
(
t
)
-
C
CSF
(
t
)
)
∂
C
(
L
,
t
)
∂
x
=
0
C
CSF
(
t
)
=
C
(
0
,
t
)
wherein C denotes the free CA concentration in the brain parenchyma, B denotes the bound CA/antigen concentration in the brain parenchyma, T denotes the unbound antigen concentration in the brain parenchyma, I denotes the concentration of intracellular CA, C CSF denotes the concentration of CA in the CSF, D denotes the CA diffusion coefficient in brain parenchyma, 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 parenchyma, k int denotes the internalization rate constant of the CA/antigen bound complex, k int,T 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, L denotes the half-distance of the parenchymal thickness, A denotes the ependymal surface area, P denotes the capillary to brain permeability, S denotes the capillary surface area in the brain, V denotes the brain volume, P BCSFB denotes the blood/CSF barrier permeability, S BCSFB denotes the blood/CSF surface area, V CSF denotes the CSF volume, D E denotes the diffusion rate across the ependymal surface, and C p denotes the plasma concentration of the contrast agent as a function of time, also sometimes called an arterial input function.
10. The method of claim 1 , wherein the one or more parameters of physiological significance are the contrast agent affinity K D , the brain permeability surface area over volume PS/V, the CSF to brain transport rate D E A/V CSF , the CA/antigen bound complex internalization rate k int , and/or the antigen concentration T 0 .
11. A method detecting a disease 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 or brain region of interest 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 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 disease lesion based on the concentration data and the estimated parameter or parameters of physiological significance.
12. The method of claim 11 , wherein the pharmacokinetic model for performing the analysis is a distributed model.
13. The method of claim 12 , wherein the distributed model is given by the following equations:
∂
C
(
x
,
t
)
∂
t
=
D
∂
2
C
(
x
,
t
)
∂
x
2
+
PS
V
(
C
p
(
t
)
-
C
(
x
,
t
)
ɛ
)
-
k
on
C
(
x
,
t
)
ɛ
T
(
x
,
t
)
+
k
off
B
(
x
,
t
)
∂
B
(
x
,
t
)
∂
t
=
k
on
C
(
x
,
t
)
ɛ
T
(
x
,
t
)
-
k
off
B
(
x
,
t
)
-
k
int
B
(
x
,
t
)
∂
T
(
x
,
t
)
∂
t
=
R
s
-
k
on
C
(
x
,
t
)
ɛ
T
(
x
,
t
)
+
k
off
B
(
x
,
t
)
-
k
int
,
T
B
(
x
,
t
)
∂
I
(
x
,
t
)
∂
t
=
k
int
B
(
x
,
t
)
-
k
resid
I
(
x
,
t
)
∂
C
CSF
(
t
)
∂
t
=
-
Q
CSF
V
CSF
C
CSF
(
t
)
+
D
E
A
V
CSF
∂
C
(
0
,
t
)
∂
x
+
P
BCSFB
S
BCSFB
V
CSF
(
C
p
(
t
)
-
C
CSF
(
t
)
)
∂
C
(
L
,
t
)
∂
x
=
0
C
CSF
(
t
)
=
C
(
0
,
t
)
wherein C denotes the free CA concentration in the brain parenchyma, B denotes the bound CA/antigen concentration in the brain parenchyma, T denotes the unbound antigen concentration in the brain parenchyma, I denotes the concentration of intracellular CA, C CSF denotes the concentration of CA in the CSF, D denotes the CA diffusion coefficient in brain parenchyma, 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 parenchyma, k int denotes the internalization rate constant of the CA/antigen bound complex, k int,T 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, L denotes the half-distance of the parenchymal thickness, A denotes the ependymal surface area, P denotes the capillary to brain permeability, S denotes the capillary surface area in the brain, V denotes the brain volume, P BCSFB denotes the blood/CSF barrier permeability, S BCSFB denotes the blood/CSF surface area, V CSF denotes the CSF volume, D E denotes the diffusion rate across the ependymal surface, and C p denotes the plasma concentration of the contrast agent as a function of time, also sometimes called an arterial input function.
14. The method of claim 11 , where the one or more parameters of physiological significance are the contrast agent affinity K D , the brain permeability surface area over volume PS/V, the CSF to brain transport rate D E A/V CSF , the CA/antigen bound complex internalization rate k int , and/or the antigen concentration T 0 .
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 or brain region of interest 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.
16. The computer system of claim 15 , wherein the pharmacokinetic model for performing pharmacokinetic analysis is a distributed model.
17. The method of claim 16 , wherein the distributed model is given by the following equations:
∂
C
(
x
,
t
)
∂
t
=
D
∂
2
C
(
x
,
t
)
∂
x
2
+
PS
V
(
C
p
(
t
)
-
C
(
x
,
t
)
ɛ
)
-
k
on
C
(
x
,
t
)
ɛ
T
(
x
,
t
)
+
k
off
B
(
x
,
t
)
∂
B
(
x
,
t
)
∂
t
=
k
on
C
(
x
,
t
)
ɛ
T
(
x
,
t
)
-
k
off
B
(
x
,
t
)
-
k
int
B
(
x
,
t
)
∂
T
(
x
,
t
)
∂
t
=
R
s
-
k
on
C
(
x
,
t
)
ɛ
T
(
x
,
t
)
+
k
off
B
(
x
,
t
)
-
k
int
,
T
B
(
x
,
t
)
∂
I
(
x
,
t
)
∂
t
=
k
int
B
(
x
,
t
)
-
k
resid
I
(
x
,
t
)
∂
C
CSF
(
t
)
∂
t
=
-
Q
CSF
V
CSF
C
CSF
(
t
)
+
D
E
A
V
CSF
∂
C
(
0
,
t
)
∂
x
+
P
BCSFB
S
BCSFB
V
CSF
(
C
p
(
t
)
-
C
CSF
(
t
)
)
∂
C
(
L
,
t
)
∂
x
=
0
C
CSF
(
t
)
=
C
(
0
,
t
)
wherein C denotes the free CA concentration in the brain parenchyma, B denotes the bound CA/antigen concentration in the brain parenchyma, T denotes the unbound antigen concentration in the brain parenchyma, I denotes the concentration of intracellular CA, C CSF denotes the concentration of CA in the CSF, D denotes the CA diffusion coefficient in brain parenchyma, 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 parenchyma, k int denotes the internalization rate constant of the CA/antigen bound complex, k int,T 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, L denotes the half-distance of the parenchymal thickness, A denotes the ependymal surface area, P denotes the capillary to brain permeability, S denotes the capillary surface area in the brain, V denotes the brain volume, P BCSFB denotes the blood/CSF barrier permeability, S BCSFB denotes the blood/CSF surface area, V CSF denotes the CSF volume, D E denotes the diffusion rate across the ependymal surface, and C p denotes the plasma concentration of the contrast agent as a function of time, also sometimes called an arterial input function.
18. The computer system of claim 17 , wherein the one or more parameters of physiological significance are is the contrast agent affinity K D , the brain permeability surface area over volume PS/V, the CSF to brain transport rate D E A/V CSF , the CA/antigen bound complex internalization rate k int , and/or the antigen concentration T 0 .