Method for estimating haeomodynamic parameters by joint estimation of the parameters of a global perfusion model
The invention relates to a method for estimating haemodynamic perfusion parameters of an elementary volume—termed a voxel—of an organ, from perfusion signals by jointly estimating the parameters of an optionally limited comprehensive perfusion model. The invention moreover relates to a processing unit of a perfusion imaging analysis system, adapted for carrying out such a method and for delivering the estimated parameters according to an appropriate format to a human-machine interface able to represent said estimated parameters for a user.
1. A method for estimating and presenting a representation of one or more haemodynamic perfusion parameters of an elementary volume, referred to as a voxel, of an organ, said method being implemented by a processing unit of a perfusion imaging analysis system, and comprising:
obtaining perfusion signals S(t) derived from images of the organ;
estimating the haemodynamic parameter or parameters using a joint estimation of the parameters Θ of a global perfusion model comprising:
a first relationship between the perfusion signal S(t) and a concentration C(t) of a contrast agent circulating in said voxel over a time t,
a second relationship between the concentration C(t) of a contrast agent, the blood flow BF, a parametric or semiparametric model C a (t,Θ a ) of an arterial input function and a parametric or semiparametric model R(t,Θ R ) of a complementary cumulative distribution function of the transit time in the voxel, Θ a and Θ R being respectively the parameters of the models C a (t,Θ a ) and R(t,Θ R ), and
a third relationship Ψ(Θa)=0 between the parameters Θa of the model of the arterial input function Ca(tΘ a ); and
displaying a graphical representation of the estimated value or values for the parameter or parameters on a human-machine interface for evaluation by a user.
2. A method according to claim 1 , wherein:
the perfusion signal S(t) is obtained from digital images delivered by a magnetic resonance perfusion imaging apparatus:
the first relationship of the global perfusion model is expressed by S(t)=S 0 e −k·TE·C(t) where S 0 is the mean intensity of the signal before the arrival of the contrast agent in the voxel, TE is an echo time and k is a non-zero constant; and
the second relationship of the global perfusion model is expressed by C(t)=η·BF·C a (t,Θ a ){circle around (x)}R(t,Θ R ) where {circle around (x)} designates the convolution product, η is a non-zero constant and BF is the blood flow in the voxel.
3. A method according to claim 1 , wherein:
the perfusion signal S(t) is obtained from digital images delivered by a computed tomography perfusion imaging apparatus;
the first relationship of the global perfusion model is a proportionality equation S(t)=α·C(t) where α where is a non-zero constant; and
the second relationship of the global perfusion model is expressed by C(t)=η·BF·C a (t,Θ a ){circle around (x)}R(t,Θ R ) where {circle around (x)} designates the convolution product, η is a non-zero constant and BF is the blood flow in the voxel.
4. A method according to claim 1 , comprising successive iterations for a plurality of voxels of the organ.
5. A method according to claim 1 , where the joint estimation of the parameters Θ of the global perfusion model used by the processing unit is implemented by means of the Bayes method or the method of Maximum Likelihood methods or the method non-linear least squares.
6. A method according to claim 1 , further including far quantifying the goodness-of-fit of the global perfusion model to experimental perfusion data D=[S(t 1 ), . . . , S(t N )] by a calculation of a probability
p
(
D
|
M
)
=
∫
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p
(
Θ
|
M
)
p
(
D
|
Θ
,
M
)
ⅆ
Θ
of these data given said model.
7. A method according to claim 6 , further comprising iteratively implementing the method by the processing unit for each global perfusion model of the plurality of models.
8. A method according to claim 7 , wherein the estimated parameters according to the perfusion model, whose probability is the greatest, are delivered.
9. A method according to claim 1 , further comprising choosing a global perfusion model from a plurality of models.
10. A method according to claim 1 , wherein the model Ca(t,Θ a ) of an arterial input function is a so-called “tri-gamma” model with twelve parameters defined by:
{
C
a
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t
,
Θ
a
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a
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Γ
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)
:
Euler
gamma
function
.
11. A method according to claim 1 , wherein the model R(t,Θ R ) of a complementary cumulative distribution function of the transit time in the voxel is a so-called “corrected integral gamma” model with two parameters defined by:
{
R
(
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,
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:
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function
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:
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gamma
function
.
12. A method according to claim 1 , wherein the third relationship Ψ(Θa)=0 of the global perfusion model is expressed as
∫
0
+
∞
C
ca
(
t
,
Θ
ca
)
ⅆ
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=
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0
where C 0 is a non-zero arbitrary constant identical for any voxel of interest.
13. A method according to claim 1 , wherein the third relationship of the global perfusion model Ψ(Θa)=0 is expressed as
∫
0
+
∞
C
ca
(
t
,
Θ
ca
)
ⅆ
t
=
C
0
where C ca (t,Θ ca ) is a component of the model C a (t,Θ a ) modelling the concentration of the contrast agent during its first pass and C 0 is a non-zero arbitrary constant identical for any voxel of interest.
14. A method according to claim 1 , further comprising calculating complementary information in the form of an estimated arterial input function C a (t, ).
15. A method according to claim 14 , further comprising delivering the complementary information to the human-machine interface for display to the user.
16. A method according to claim 1 , further comprising calculating complementary information in the form of an estimated complementary cumulative distribution function R(t, ).
17. A method according to claim 1 , further comprising calculating complementary information in the form of a confidence interval associated with a parameter of the global perfusion model.
18. A method according to claim 1 , further comprising calculating complementary information in the form of a bet associated with a parameter of the global perfusion model.
19. The method of claim 1 , wherein the graphical representation comprises a map of the organ.
20. A processing unit comprising a storage device, an interface for communicating with the outside world and a processor, wherein:
the interface is configured to receive from the outside world a signal S(t) obtained by perfusion imaging;
the storage device stores a global perfusion model, said model comprising:
a first relationship between the perfusion signal S(t) and a concentration C(t) of a contrast agent circulating in a voxel over the course of time t,
a second relationship between the blood flow BF in the voxel, the concentration C(t), a parametric or semiparametric model C a (t,Θ a ) of an arterial input function and a parametric or semiparametric model R(t,Θ R ) of a complementary cumulative distribution function of the transit time in the voxel, Θ a and Θ R being respectively the parameters of the models, and
a third relationship Ψ(Θa)=0 between the parameters Θa of the model of the arterial input function Ca(tΘ a ); and
the processor is configured to implement a method for estimating haemodynamic perfusion parameters according to claim 1 .
21. A processing unit according to claim 20 , wherein the interface delivers one or more estimated parameters according to an appropriate format to a human-machine interface configured to display said estimated parameters to a user.
22. A perfusion imaging analysis system comprising a processing unit according to claim 20 and a human-machine interface configured to display to a user one or more parameters estimated by said processing unit.
23. A processing unit comprising a storage device, an interface for communicating with the outside world and a processor, wherein:
the interface is configured to receive digital perfusion images from the outside world;
the storage device stores a global perfusion model, said model comprising:
a first relationship between a perfusion signal S(t) and a concentration C(t) of a contrast agent circulating in a voxel in the course of time t,
a second relationship between the concentration C(t), the blood flow BF, a parametric or semiparametric model C a (t,Θ a ) of an arterial input function and a parametric or semiparametric model R(t,Θ R ) of a complementary cumulative distribution function of the transit time in the voxel, Θ a and Θ R being respectively the parameters of the models, and
a third relationship Ψ(Θa)=0 between the parameters Θa of the model of the arterial input function Ca(tΘ a ); and
the processor is configured to determine a perfusion signal S(t) from perfusion images received and to implement a method for estimating one or several haemodynamic perfusion parameters according to claim 1 .