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Using dynamic contrast-enhanced magnetic resonance imaging data to constrain a positron emission tomography kinetic model: theory and simulations.

Fluckiger JU, Li X, Whisenant JG, Peterson TE, Gore JC, Yankeelov TE - Int J Biomed Imaging (2013)

Bottom Line: We show how dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data can constrain a compartmental model for analyzing dynamic positron emission tomography (PET) data.We first develop the theory that enables the use of DCE-MRI data to separate whole tissue time activity curves (TACs) available from dynamic PET data into individual TACs associated with the blood space, the extravascular-extracellular space (EES), and the extravascular-intracellular space (EIS).The parameters returned by this approach may provide new information on the transport of a tracer in a variety of dynamic PET studies.

View Article: PubMed Central - PubMed

Affiliation: Department of Radiology, Northwestern University, Chicago, IL 60611, USA.

ABSTRACT
We show how dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data can constrain a compartmental model for analyzing dynamic positron emission tomography (PET) data. We first develop the theory that enables the use of DCE-MRI data to separate whole tissue time activity curves (TACs) available from dynamic PET data into individual TACs associated with the blood space, the extravascular-extracellular space (EES), and the extravascular-intracellular space (EIS). Then we simulate whole tissue TACs over a range of physiologically relevant kinetic parameter values and show that using appropriate DCE-MRI data can separate the PET TAC into the three components with accuracy that is noise dependent. The simulations show that accurate blood, EES, and EIS TACs can be obtained as evidenced by concordance correlation coefficients >0.9 between the true and estimated TACs. Additionally, provided that the estimated DCE-MRI parameters are within 10% of their true values, the errors in the PET kinetic parameters are within approximately 20% of their true values. The parameters returned by this approach may provide new information on the transport of a tracer in a variety of dynamic PET studies.

No MeSH data available.


Related in: MedlinePlus

A schematic representation of the three-compartment model used with the dynamic PET imaging. From left to right, the three compartments represent the blood plasma, the extracellular-extravascular space, and the extracellular-intravascular space.
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fig1: A schematic representation of the three-compartment model used with the dynamic PET imaging. From left to right, the three compartments represent the blood plasma, the extracellular-extravascular space, and the extracellular-intravascular space.

Mentions: Figure 1 depicts the compartmental model that we will use for this study; from left to right, the compartments are the plasma, extravascular-extracellular space, and extravascular-intracellular space, respectively. We again note that these compartments are not those identified in a typical PET kinetic modeling, which consider the three (biochemical) compartments of radiotracer distribution as plasma, free and nonspecifically bound in tissue, and specifically bound [1]. Rather, the (physical) compartments chosen here reflect those typically identifiable in a dynamic contrast-enhanced MRI acquisition described below. The set of compartments described by this model provides access to other potentially useful compartments and rate constants. Thus, while the mathematical description of the tracer concentrations is unchanged, it does change the interpretation of the parameter values; we return to this important point in Section 4. The following set of first-order, ordinary, linear differential equations describe the system depicted in Figure 1:(1)dCp(t)dt=k2CEES(t)−K1Cp(t),dCEES(t)dt=K1Cp(t)−k2CEES(t)−k3CEES(t)+k4CEIS(t),dCEIS(t)dt=k3CEES(t)−k4CEIS(t),where Cp, CEES, and CEIS are the concentrations of the tracer in the blood plasma, extravascular-extracellular, and extravascular-intracellular spaces, respectively. There are four unknown rate constants and three unknown concentration-of-tracer time courses. The problem is compounded by the fact that a typical PET study measures only the total concentration of the tracer in a given voxel or region of interest, Ctissue, which is determined by the concentration of the tracer in each compartment and the relative volume contributions of each compartment:(2)Ctissue(t)=vbCb(t)+vEESCEES(t)+vEISCEIS(t),where vb, vEES, and vEIS are the blood, extravascular-extracellular, and extravascular-intracellular volume fractions, respectively. Solving the second two relations in (1) yields(3)CEES(t)=K1α2−α1Cp(t)⊗[(k4−α1)e−α1t+(α2−k4)e−α2t],CEIS(t)=K1k3α2−α1Cp(t)⊗[e−α1t−e−α2t],α1,2=(k2+k3+k4)±(k2+k3+k4)2−4k2k42.If we note that vb + vEES + vEIS = 1, vp = vb · (1 − hematocrit) and assume that the plasma free fraction is 1, then the solution (i.e., (2) and (3)) has six unknown parameters and three unknown concentration-of-tracer time courses. If the arterial input function can be measured reliably, this is reduced to two unknown concentration time courses. After briefly introducing the relevant aspects of DCE-MRI modeling, we proceed to show how DCE data can constrain this PET model by eliminating unknown parameters and determining unknown concentration-of-tracer time courses.


Using dynamic contrast-enhanced magnetic resonance imaging data to constrain a positron emission tomography kinetic model: theory and simulations.

Fluckiger JU, Li X, Whisenant JG, Peterson TE, Gore JC, Yankeelov TE - Int J Biomed Imaging (2013)

A schematic representation of the three-compartment model used with the dynamic PET imaging. From left to right, the three compartments represent the blood plasma, the extracellular-extravascular space, and the extracellular-intravascular space.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3814089&req=5

fig1: A schematic representation of the three-compartment model used with the dynamic PET imaging. From left to right, the three compartments represent the blood plasma, the extracellular-extravascular space, and the extracellular-intravascular space.
Mentions: Figure 1 depicts the compartmental model that we will use for this study; from left to right, the compartments are the plasma, extravascular-extracellular space, and extravascular-intracellular space, respectively. We again note that these compartments are not those identified in a typical PET kinetic modeling, which consider the three (biochemical) compartments of radiotracer distribution as plasma, free and nonspecifically bound in tissue, and specifically bound [1]. Rather, the (physical) compartments chosen here reflect those typically identifiable in a dynamic contrast-enhanced MRI acquisition described below. The set of compartments described by this model provides access to other potentially useful compartments and rate constants. Thus, while the mathematical description of the tracer concentrations is unchanged, it does change the interpretation of the parameter values; we return to this important point in Section 4. The following set of first-order, ordinary, linear differential equations describe the system depicted in Figure 1:(1)dCp(t)dt=k2CEES(t)−K1Cp(t),dCEES(t)dt=K1Cp(t)−k2CEES(t)−k3CEES(t)+k4CEIS(t),dCEIS(t)dt=k3CEES(t)−k4CEIS(t),where Cp, CEES, and CEIS are the concentrations of the tracer in the blood plasma, extravascular-extracellular, and extravascular-intracellular spaces, respectively. There are four unknown rate constants and three unknown concentration-of-tracer time courses. The problem is compounded by the fact that a typical PET study measures only the total concentration of the tracer in a given voxel or region of interest, Ctissue, which is determined by the concentration of the tracer in each compartment and the relative volume contributions of each compartment:(2)Ctissue(t)=vbCb(t)+vEESCEES(t)+vEISCEIS(t),where vb, vEES, and vEIS are the blood, extravascular-extracellular, and extravascular-intracellular volume fractions, respectively. Solving the second two relations in (1) yields(3)CEES(t)=K1α2−α1Cp(t)⊗[(k4−α1)e−α1t+(α2−k4)e−α2t],CEIS(t)=K1k3α2−α1Cp(t)⊗[e−α1t−e−α2t],α1,2=(k2+k3+k4)±(k2+k3+k4)2−4k2k42.If we note that vb + vEES + vEIS = 1, vp = vb · (1 − hematocrit) and assume that the plasma free fraction is 1, then the solution (i.e., (2) and (3)) has six unknown parameters and three unknown concentration-of-tracer time courses. If the arterial input function can be measured reliably, this is reduced to two unknown concentration time courses. After briefly introducing the relevant aspects of DCE-MRI modeling, we proceed to show how DCE data can constrain this PET model by eliminating unknown parameters and determining unknown concentration-of-tracer time courses.

Bottom Line: We show how dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data can constrain a compartmental model for analyzing dynamic positron emission tomography (PET) data.We first develop the theory that enables the use of DCE-MRI data to separate whole tissue time activity curves (TACs) available from dynamic PET data into individual TACs associated with the blood space, the extravascular-extracellular space (EES), and the extravascular-intracellular space (EIS).The parameters returned by this approach may provide new information on the transport of a tracer in a variety of dynamic PET studies.

View Article: PubMed Central - PubMed

Affiliation: Department of Radiology, Northwestern University, Chicago, IL 60611, USA.

ABSTRACT
We show how dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data can constrain a compartmental model for analyzing dynamic positron emission tomography (PET) data. We first develop the theory that enables the use of DCE-MRI data to separate whole tissue time activity curves (TACs) available from dynamic PET data into individual TACs associated with the blood space, the extravascular-extracellular space (EES), and the extravascular-intracellular space (EIS). Then we simulate whole tissue TACs over a range of physiologically relevant kinetic parameter values and show that using appropriate DCE-MRI data can separate the PET TAC into the three components with accuracy that is noise dependent. The simulations show that accurate blood, EES, and EIS TACs can be obtained as evidenced by concordance correlation coefficients >0.9 between the true and estimated TACs. Additionally, provided that the estimated DCE-MRI parameters are within 10% of their true values, the errors in the PET kinetic parameters are within approximately 20% of their true values. The parameters returned by this approach may provide new information on the transport of a tracer in a variety of dynamic PET studies.

No MeSH data available.


Related in: MedlinePlus