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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.

There is an extensive literature on the use of compartmental modeling to understand the distribution and retention of various positron emission tomography (PET) radiotracers (see, e.g., [

Similar to a kinetic PET study, DCE-MRI involves the serial acquisition of images before, during, and after the injection of a contrast agent [

It is important to note that there exists a subtle, though fundamental, difference between the compartmental models employed in quantitative DCE-MRI and dynamic PET analyses. The compartments in kinetic PET modeling typically (^{15}O labeled H_{2}O is one notable exception) refer to biochemical compartments (e.g., bound or free), whereas the compartments in kinetic MRI modeling refer to physical compartments (e.g., the blood, EES, or EIS). Thus, when the compartments extracted from a DCE-MRI analysis are used to separate the PET TAC into different compartments, the TAC is separated into the compartments determined from the DCE-MRI data—and these compartments are fundamentally different than the biochemical compartments. This means that the TACs associated with these compartments, as well as the kinetic parameters describing the movement of the tracer between these compartments, are not the same as those reported in the existing PET literature. More specifically, in this contribution, we develop the formalism required to use DCE-MRI data to extract separate TACs for the blood pool (i.e., the input function), EES, and EIS and then show how these time courses can be used to fit simplified versions (i.e., fewer free parameters with known TACs) of a PET compartmental model to extract kinetic parameters related to the delivery and retention of PET tracer that is distributed amongst the blood space, EES, and EIS. We conclude by discussing how the access to these new physiological parameters may be of use in future dynamic PET studies.

Figure

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.

A typical DCE-MRI study employs an untargeted contrast agent that is distributed from blood into tissue, but is unable to appreciably penetrate cells, so the compartmental model is considerably simpler than the above model for PET tracer kinetics and is given as:

We now show how DCE-MRI data can be used to eliminate a number of the unknown quantities in (

If we take the

To evaluate the theory above, we simulated kinetic PET data over a range of parameter combinations. The simulations were initialized with an arterial input function ^{18}F-fluorothymidine (FLT) PET scan (data not shown as the particular tracer employed is not central to this paper; that is, all that is needed is a reasonable, experimentally measured input function). This time course was then used to drive (

Figure ^{−1}), ^{−1}), and ^{−1}). The solid lines indicate the extracted curves, while the individual points correspond to the true (simulated) data; the filled circles in each panel depict the measured

An example of simulated tissue curves and the fits provided by (

As stated above, two sets of noise realizations were performed. Figures

The concordance correlation coefficient between the estimated and true values of the time courses as a function of noise in the tissue curves for a single set of PET kinetic parameters. If the

The error in the estimated PET kinetic parameters as a function of the noise in the tissue curves. Each panel corresponds to a different set of PET kinetic parameters. For each set of parameters, when the error in

Figure

Figures

The concordance correlation coefficient between the estimated and true values for the time courses as a function of error in the DCE-MRI parameters for a single set of PET kinetic parameters. The method is able to return the time courses faithfully when the DCE-MRI parameter error is less than 5%. With higher error in the DCE-MRI parameters, the CCC remains above 0.95 on average, though some realizations returned CCC values as low as 0.9.

The error in the estimated PET kinetic parameters as a function of the error in the DCE-MRI parameters. Each panel corresponds to a different set of PET kinetic parameters. For each parameter combination, the error in the PET parameters is below 25% provided the error in the DCE-MRI parameters is below 10%. As the DCE-MRI parameter error increases, the error in the PET parameters exceeds 40% in some cases (see panel (d)).

Figure

Since the advent of the first prototype SPECT-CT system in 1990 [

The results from the simulations show that the method returns good estimates for the time courses

As seen in Figures

The method developed by Asllani et al. [

As noted in the Introduction, the parameters ^{15}O]-labeled water studies. Typical modeling of [^{15}O]-labeled water utilizes a two-compartment model with one intravascular compartment and one extravascular compartment [

It should also be noted that performing the analysis described in this work would, of course, not preclude any dynamic modeling with more traditional compartment definitions on the same data. Also, despite the changes in the physical interpretation of the rate constants, the arterial input function derived from the proposed method is identical to that used in more traditional dynamic PET modeling and can be used in implementing these models. Perhaps, the method proposed in this effort has value in merely providing an input function from which a standard dynamic analysis could be performed. Additionally, the input function estimated by this approach comes from the (local) tissue of interest which could potentially eliminate uncertainties related to the delay and dispersion when an input function is estimated from blood samples or ROIs in distant locations.

Future studies with this method will focus on validating the proposed method with

We have presented a method that uses DCE-MRI parameters to separate the whole tissue concentration curves,

The authors thank the National Cancer Institute for funding through R01 CA138599, 1P50 098131, 1U01 CA142565, U24 CA126588, U01 CA174706, and P30 CA068485. The authors thank Dr. Noor Tantawy, Ph.D., and Ms. Clare Osborne, B.S., for technical assistance with the acquisition of the microPET data, and Dr. Lei Xu, Ph.D., Dr. Junzhong Xu, Ph.D., and Dr. Sepideh Shokouhi, Ph.D., for informative discussions. The authors thank Dr. Robert Doot, Ph.D., for reading and offering constructive criticism of an early version of this paper.

^{18}F-fluorothymidine in patients with gliomas

^{15}O-labeled water and PET