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Abstract

Compartmental modeling analysis of ¹¹C-raclopride (RAC) PET data can be used to measure the dopaminergic response to intra-scan behavioral tasks. Bias in estimates of binding potential (BP_ND) and its dynamic changes (ΔBP_ND) can arise both when head motion is present and when the compartmental model used for parameter estimation deviates from the underlying biology. The purpose of this study was to characterize the effects of motion and model bias within the context of a behavioral task challenge, examining the impacts of different mitigation strategies. Seventy healthy adults were administered bolus plus constant infusion RAC during a simultaneous PET/magnetic resonance (MR) scan with a reward task experiment. BP_ND and ΔBP_ND were estimated using an extension of the Multilinear Reference Tissue Model (E-MRTM2) and a new method (DE-MRTM2) was proposed to selectively discount the contribution of the initial uptake period. Motion was effectively corrected with a standard frame-based approach, which performed equivalently to a more complex reconstruction-based approach. DE-MRTM2 produced estimates of ΔBP_ND in putamen and nucleus accumbens that were significantly different from those estimated from E-MRTM2, while also decoupling ΔBP_ND values from first-pass k₂′ estimation and removing skew in the spatial bias distribution of parametric ΔBP_ND estimates within the striatum.

Keywords

Behavioral task kinetic modeling motion correction PET

Introduction

¹¹C-Raclopride (RAC) positron emission tomography (PET) is a well-established means of imaging dopamine D₂/D₃ receptor binding. It has been used to measure the spatial distribution of receptors,¹ as well as the kinetic properties of their binding.² It has also been used to study the dopaminergic system under blocking and displacement conditions and after pharmacological challenges using amphetamine,^3–5 cocaine,^6,7 and nicotine,^8,9 and behavioral challenges such as reward,^10,11 motor performance,¹² pain,¹³ and cognitive tasks.¹⁴

One of the difficulties in working with behavioral challenge experiments is their modest response magnitudes relative to those of pharmacological challenges. While pharmacological challenges may cause changes in binding potential (BP_ND) of 10–20% or greater,^5,15,16 behavioral challenges produce smaller changes of around 0–10%.^14,17–19 With these smaller effects, measurements of behavioral challenge response are more difficult to discern from noise, while also being more susceptible to different sources of bias,^20,21 including bias arising from head motion¹⁷ and from model selection.²²

Head motion over the course of a PET acquisition can create misalignments between frames and blurring artifacts within frames leading to biased measurements of BP_ND and its change over time (ΔBP_ND: BP_ND-POST – BP_ND). Motion bias is routinely addressed in the field by either rigidly registering PET volumes after reconstruction (i.e. frame-based motion correction)^23,24 or using more advanced methods which require independently estimated motion parameters (e.g. reconstruction-based motion correction²⁵ or event-based rebinning^26,27).

Bias in estimates of RAC BP_ND and ΔBP_ND can also arise from the compartmental models used for analysis when underlying assumptions are violated. Depending on the design of the study, RAC kinetic modeling approaches may utilize a two-tissue compartment model configuration with metabolite-corrected arterial plasma data as an input function. Alternatively, simplifying assumptions may be made to use a one-tissue compartment model configuration and/or a reference-tissue model for which the input function is derived from a region devoid of specific binding.^28,29 One common source of model bias arises when fitting a model with a one-tissue compartment configuration to data that is more accurately represented by two-tissue compartments.^21,22 Single-tissue compartment configurations are often employed to improve model stability and convergence, rendering such bias a necessary tradeoff. This bias may be compounded if the model is further reduced by fixing the rate of efflux from the reference region (k₂′) to constrain the parameter space and thereby facilitate robust parametric mapping.^30,31 These biases can be reduced while maintaining a single-compartment configuration by adjusting the model to better fulfill its simplifying assumptions.

In this work, we build upon an earlier finding of measurable differences in RAC ΔBP_ND between participants grouped by task performance³² to investigate the impact of motion and model biases and to propose an effective approach for addressing them within the context of an intra-scan behavioral challenge. First, we used simulations to estimate the extent of the motion bias and compare frame-based and reconstruction-based approaches to correcting it. Next, we considered the bias that arises when the one-tissue model assumption of fast-exchange between the non-displaceable and specifically bound compartments is violated. To mitigate this bias, we propose a new model: the Debiased Extended Multilinear Reference Tissue Model (DE-MRTM2). DE-MRTM2 eliminates the contribution of the initial uptake period to the estimation of BP_ND and ΔBP_ND, thereby improving model-based bias in estimates of behavioral task response for intra-scan task designs. Simulations were used to estimate the extent of the model bias, the impact of DE-MRTM2, and the relationship between k₂′ selection and ΔBP_ND. The estimates of model bias and motion bias were then compared using simulated challenge responses of different magnitudes. Finally, frame-based motion correction and DE-MRTM2 were applied to the acquired human data and the regional statistical significance of the proposed methods was evaluated.

Material and methods

Participants and data acquisition protocols

Seventy adult participants (female = 34, ages 18–30 years) were retrospectively selected from an adolescent development study performed on an integrated PET/MRI scanner (Biograph mMR, Siemens Healthineers, Erlangen, Germany) at the University of Pittsburgh Medical Center.³³ Healthy volunteers were scanned using RAC while simultaneously performing a functional magnetic resonance imaging (fMRI) task designed to study reward response. All participants gave written informed consent and were studied in accordance with experimental procedures approved by the University of Pittsburgh Institutional Review Board. All participants were imaged in the headfirst supine position and PET data were collected from the start of radiotracer administration.

Participants received a bolus injection of RAC (661–802 MBq) followed by a constant infusion (KBol = 105 min, 54% of the total dose) for the duration of the 90-minute scan. PET 3D coincidence event data were collected and stored in list-mode format. PET volumes were iteratively reconstructed with a uniform 3-minute framing using the e7 tools (OP-OSEM, 3 iterations, 21 subsets, no filter).^34,35 Attenuation correction was performed using a pseudoCT attenuation map³⁶ generated from a T1-weighted structural sequence (MPRAGE) registered to the PET volume at the start of the task. The simultaneously acquired MRI protocol centered on eight fMRI-BOLD sequences (echo time [TE] = 30 ms, repetition time [TR] = 1500 ms). Six were acquired during the task window (t = 40–75 min) and two were resting state sequences, one at the beginning of the scan (t = 0–10 min) and one after completion of the task (t = 80–90 min). The protocol also included the aforementioned MPRAGE for attenuation correction and region-of-interest label generation, and several sequences used routinely for brain studies (e.g. localizer, gradient-echo field mapping, ultrashort TE, TurboFLASH, diffusion spectrum imaging, and magnetization transfer ratio). For the purpose of PET data analysis, the task was considered as a single block. No pharmacological intervention was performed. Further information about the study design can be found in previous reports.^32,33

Control data from a different bolus RAC study⁵ were utilized exclusively to determine specific simulation input parameters (K₁′, k₂′). These data were acquired on a standalone PET scanner (ECAT EXACT HR+, Siemens, Knoxville, TN) at the University of Pittsburgh. Transmission-mode PET was used to acquire attenuation maps, and arterial blood plasma was sampled as an input function. The maximal injected mass of the RAC bolus was 6 µg and PET data were acquired for 60 minutes post-injection.

Kinetic modeling

The Multilinear Reference Tissue Model (MRTM2)³¹ was used to measure RAC BP_ND in the striatum with the cerebellum as the reference tissue. The efflux rate constant ( $k_{2}^{'})$ was fixed to a first-pass estimate fit by MRTM in a high binding region (putamen).^30,31 This model was E xtended³⁷ to E-MRTM2 (equation (1)) to accommodate a behavioral challenge using the formulation of Alpert et al.,³⁸ but with a unit step at the onset of the task (t = 40 min) as the activation function. This is similar to the approach taken by Normandin et al.,³⁹ though with a simpler challenge encoding.

[\begin{matrix} C_{T} (t) \end{matrix}] = [\int C_{R} (t) d t + \frac{1}{k_{2}^{'}} C_{R} (t) - \int C_{T} (t) d t

- \int C_{T} (t) u (t - 40) d t] [\begin{matrix} k_{2} \\ k_{2 a} \\ {Δ k}_{2 a} \end{matrix}]

(1)

When considering a model with a single-tissue compartment, BP_ND is expressed in terms of a combination of the true efflux rate (k₂), and the apparent efflux rate (k_2a)²⁹ (equation (2)).

{B P}_{N D} = \frac{k_{2}}{k_{2 a}} - 1

(2)

ΔBP_ND is expressed in terms of k₂, k_2a, and the change in the apparent efflux rate (Δk_2a) (equation (3)).

{Δ B P}_{N D} = \frac{- k_{2} {Δ k}_{2 a}}{k_{2 a} (k_{2 a} + {Δ k}_{2 a})}

(3)

Simulation design

Simulated PET data were utilized in three different simulation experiments to investigate bias in ΔBP_ND: estimation of motion bias, estimation of model bias, and comparison of motion and model bias (see the respective sections for each below). This section details the common methods across all simulation experiments.

Simulated PET time activity curves were generated for every voxel in the brain using a two-tissue compartment model configuration. Fully simulating this set of four-dimensional timeseries PET data required values of K₁, k₂, k₃, and k₄ for every voxel in the brain as well as an arterial input function (C_P).

The input parameters to the simulations were deliberately selected to reflect the experimental data to the greatest extent possible without the benefit of known ground truth values. Individual values of K₁, k₂, and k₃ for each voxel were generated using the definitions of their associated macroparameters: R₁ and BP_ND (equations (4) to (6)).²⁹

K_{1} = R_{1} K_{1}^{'}

(4)

k_{2} = R_{1} k_{2}^{'}

(5)

k_{3} = {B P}_{N D} k_{4}

(6)

To determine the most appropriate values of R₁ and BP_ND, voxelwise analysis with MRTM2³¹ was performed on the acquired PET data and maps of R₁ and BP_ND were averaged across all participants to serve as realistic voxel-based maps for input to the simulations.

In contrast to the selection of the other compartmental microparameters, a robust means of assigning voxelwise estimates to k₄ was not available. Therefore, individual simulations fixed k₄ to a single physiologically plausible value reported for RAC (k₄ = 0.07 min⁻¹)^2,22 in order to calculate bias levels.

To estimate the reference tissue rate constants (K₁′, k₂′), we utilized a control RAC data set acquired in healthy adult volunteers with a bolus injection and arterial blood sampling.⁵ The reference region (cerebellum) time activity curve (TAC) was fit using a nonlinear one-tissue compartmental model and a metabolite-corrected plasma input function. The average estimated values across four participants (K₁′ = 0.22 ± SD 0.02 mL cm⁻³min⁻¹, k₂′ = 0.58 ± SD 0.05 min⁻¹) were selected for use in the simulations. Given these values of K₁′ and k₂′ and the acquired cerebellum TACs averaged across participants in the task-reward study, a suitable parametric bolus plus constant infusion arterial input function (C_P) was selected for use in simulations.

Once the noiseless TACs were simulated, Gaussian noise was added on a voxelwise basis according to the method described in Logan et al.⁴⁰ (equations (7) and (8))

N (t) = s X \sqrt{\frac{e^{- λ t} A (t)}{Δ t}}

(7)

Equation (7) describes the generated noise (N) prior to decay correction, where A(t) is the noiseless activity value at time t, λ is the half-life of ¹¹C (20.4 min), $e^{- λ t} A (t)$ is the activity value with decay applied, Δt is the frame length at time t, X is a Gaussian random variable with a mean of 0 and a standard deviation of 1, and s is a scaling factor. An s value of 500 was selected to match the signal-to-noise ratio of the experimental PET data in the striatum.

A_{N} (t) = A (t) + e^{λ t} N (t)

(8)

Equation (8) shows how the decay-corrected noise ( $e^{λ t} N$ ) is added to the noiseless activity value ( $A$ ) to generate a realization of the noisy activity value ( $A_{N}$ ) at time t.

Motion bias

Frame-based motion correction

The methodology for frame-based motion correction is well established in the field.^23,24,41,42 Briefly, the head was treated as non-deformable, and a linear least squares rigid body registration algorithm (implemented in SPM8⁴³) was applied to track its displacements. This was accomplished by retrospectively coregistering the dynamic volumes⁴⁴ to a reference volume at the onset of the task (t = 40 min).

Reconstruction-based motion correction

To correct for motion during reconstruction, head motion was first estimated from the PET data using a procedure similar to frame-based motion correction. First, the PET list-mode data were split into 1-minute subframes (with the exception of the first subframe, which was 2 minutes to accommodate the rapidly changing spatial contrast associated with delivery). Next, preliminary image reconstructions were performed, accounting for detector normalization and radiofrequency MRI coil array attenuation, but without correcting for head attenuation. The resulting volumes were registered to produce motion estimates, rather than to perform motion correction directly. These motion estimates were measured as a set of three translations and three rotations, which were then encoded into a 4 × 4 transformation matrix and supplied to the reconstruction algorithm for motion correction.

Motion was corrected as part of the iterative PET reconstruction for each dynamic frame using a development version of the e7 tools.²⁵ For each PET volume reconstructed, the associated timeframe was divided into subframes corresponding to the temporal resolution of the motion estimates. During each reconstruction iteration, the current estimate of the PET volume was replicated for each subframe, and the subframe volumes were moved according to the estimated motion before being forward projected into sinogram space. After backprojection, the subframe volumes were motion corrected and averaged to form the subsequent estimate of the reconstructed PET volume. Correction for scatter and randoms was performed using the full sinogram for the given timeframe, with proportional scaling for each subframe.

Motion bias: Experimental task data

To demonstrate the deleterious effects of motion and the compensatory effects of frame- and reconstruction-based motion correction, a comparison was performed between the participants who moved the most and those who moved the least. The high and low motion groups were selected to include individuals whose motion was in the upper and lower quintiles (20%, n = 10 per group) of total cumulative participant motion (Figure S1). For each participant, voxelwise maps of binding potential and the change in binding potential were generated by applying kinetic modeling to motion-corrected image data, using the methods described above. Example regional TACs reconstructed with different motion corrections and fit with E-MRTM2 can be seen in Figure 1(a).

Figure 1.

Example experimental TACs and kinetic model fits. (a) Putamen and nucleus accumbens TACs from a high motion subject reconstructed with no motion correction (No MC), frame-based motion correction (Frame MC), or reconstruction-based motion correction (PET Recon MC) and fit with E-MRTM2. (b) Putamen and nucleus accumbens TACs from a low motion subject reconstructed with frame-based motion correction and fit with E-MRTM2 and DE-MRTM2.

Motion bias: Taskless simulations

To simulate realistic motion at a high temporal resolution, motion was estimated from the simultaneously acquired MR data of the participants in the high motion group. The algorithm for estimating motion from EPI-based MRI sequences has been described previously.^26,45 It follows the same approach as the PET-based approach (Figure S2A), using rigid body registration with a least-squares cost function to estimate motion. The first volume in the first task fMRI sequence was selected as the reference volume, and all other volumes were registered to it in two steps: intra-sequence and inter-sequence. First, volumes within the same sequence were registered, producing a set of motion estimates for each volume. Afterward, the reference volume used for each sequence was registered to the overall reference volume at the start of the task. Final motion estimates were obtained by multiplying the 4 × 4 transformation matrices corresponding to the intra- and inter-sequence estimates (Figure S2B).

Higher temporal resolution estimates were created by substituting the PET- for MR-based estimates wherever they were available, creating unified motion estimates (Figure S2C). However, to avoid discontinuities within the unified motion estimates, instead of using intersequence MR-based estimates for the second transformation, the time-matched PET-based transforms were used (Figure S3).

PET volumes were simulated with a dynamic framing matching the high temporal resolution of these motion estimates and transformed according to them to create intraframe motion. To create a series of volumes with a uniform framing of 3 minutes, the subframe volumes at this higher temporal resolution were averaged. Where motion is simulated between the subframes, the averaging creates a blurring effect in the final volume, simulating intraframe motion.

The relative effects of intra- and interframe motion were compared by simulating intraframe motion with no task challenge and either performing no motion correction or frame-based motion correction before kinetic analysis. Not performing motion correction allowed us to estimate the total motion bias in ΔBP_ND, while correcting for it allowed us to estimate the contribution of the intraframe component alone. Simulated motion was derived from estimates of the participants with the most motion (top 20%), and noise levels were calibrated to match the acquired data.

Model bias

Theory: DE-MRTM2 and model bias in ΔBPND

An analytical approach can be employed to describe the bias that arises from the difference between one-compartment and two-compartment reference tissue models (equation (9)). This difference can be ascribed to a term (E) that depends upon the convolution of the tissue concentration derivative with an exponential function of BP_ND and k₄²² (equation (10)).

[\begin{matrix} C_{T} (t) \end{matrix}] = [C_{R} (t) \int (C_{R} (t) - E) d t

- \int {(C}_{T} (t) - E) d t] [\begin{matrix} R_{1} \\ k_{2} \\ k_{2 a} \end{matrix}]

(9)

E = \frac{d C_{T}}{d t} \otimes e^{- k_{4} (1 + B P_{N D}) t}

(10)

This term is especially pronounced during the uptake period (strong tissue derivative) and in regions with either low binding or low k₄. Applying a one-compartment tissue model—like MRTM and its variations—assumes that E (and therefore the difference between the two models) is negligibly small. Therefore, to mitigate the bias that arises when it is not, we propose an approach to D ebias the contribution of the initial uptake period (DE-MRTM2) where the tissue concentration is changing rapidly. However, to retain kinetic information in the uptake period for estimation of k₂, we discounted the uptake period for BP_ND exclusively by introducing a second “Δk_2a” term (equation (11)).

[\begin{matrix} C_{T} (t) \end{matrix}] = [\int C_{R} (t) d t + \frac{1}{k_{2}^{'}} C_{R} (t) - \int C_{T} (t) d t

- \int C_{T} (t) u (t - 40) d t - \int C_{T} (t) u (t^{D} - t) d t] [\begin{matrix} k_{2} \\ k_{2 a} \\ {Δ k}_{2 a} \\ {Δ k}_{2 a}^{D} \end{matrix}]

(11)

DE-MRTM2 breaks the measurement of $k_{2 a}$ into three periods—initial uptake ( ${Δ k}_{2 a}^{D}$ ), baseline ( $k_{2 a}$ ), task ( ${Δ k}_{2 a}$ )—while employing the full TAC for estimation of k₂. The metric of interest, ΔBP_ND, corresponds to the difference in BP_ND between the task and baseline periods. Therefore, equations (2) and (3) still apply for calculating BP_ND and ΔBP_ND respectively. The additional term ( ${Δ k}_{2 a}^{D}$ ) performs its debiasing function by eliminating all contributions of frames prior to the end of the uptake period from the estimation of BP_ND and ΔBP_ND. Example regional TACs fit with E-MRTM2 and DE-MRTM2 can be seen in Figure 1(b).

Simulations: Estimating model bias in ΔBP_ND

Model bias was estimated by comparing data simulated with a two-tissue compartmental model against kinetic modeling analysis performed with a single compartment. By simulating PET data without a challenge, and fitting a model with a challenge, any resultant estimate of ΔBP_ND can be attributed solely to bias. Voxel maps of ΔBP_ND were produced by fitting both E-MRTM2 and DE-MRTM2 to the simulated data and median averaging across noise realizations (n = 10). These simulations were then compared to human voxel maps of ΔBP_ND fit with E-MRTM2 and DE-MRTM2 and median averaged across all participants.

Experimental: Assessing the impact of k₂′ on ΔBP_ND

To examine the extent to which this approach to bias mitigation is dependent upon the selection of k₂′, DE-MRTM2 and E-MRTM2 were fit while the value of k₂′ was fixed according to one of four estimation methods. In order of highest to lowest estimated value of k₂′, these methods were:

Estimated from blood in control data set (k₂′ = 0.55)

MRTM fit to top 10% of striatum voxels by BP_ND (k₂′ = 0.30)

MRTM fit to putamen (k₂′ = 0.25)

MRTM fit to bottom 10% of striatum voxels by BP_ND (k₂′ = 0.20)

Comparing motion and model bias

To compare the effects of motion bias, model bias, and true task response signal, a series of voxelwise simulations were analyzed, varying the presence of motion and the magnitude of the simulated challenge response ( ${Δ B P}_{N D}$ ) within the striatum (0%, −5%, −10%, −20%). Motion was added to half the simulations by transforming each reconstructed PET volume by a set of motion parameters. Different motion realizations were simulated by using motion parameters estimated from each participant in the high motion group (n = 10). Model bias (present in all simulations) was induced by forward simulating a 2-tissue compartment model and fitting E-MRTM2. The analyses of the motionless and high motion simulations were compared using the parametric maps of ${Δ B P}_{N D}$ . The parametric maps for the high motion group were averaged across motion (including noise) realizations. The parametric maps for the no motion group were averaged across noise realizations (n = 10). Bias was assessed by evaluating the absolute value of error in ΔBP_ND relative to the simulated ground truth at the voxel level. Model bias was estimated from the no motion group and motion bias was estimated by comparing the high motion and no motion simulations. The relative contributions of motion bias, model bias, and true signal were determined by comparing the absolute error maps.

Regional statistical significance

To evaluate the impact of the proposed methods for reducing both motion and model bias, ΔBP_ND values within the most salient striatal subregions (putamen, caudate, nucleus accumbens) were statistically tested across motion and modeling methodologies. Frame-based and reconstruction-based motion correction were compared with a paired t-test using participants’ regional ΔBP_ND values fit with E-MRTM2. E-MRTM2 and DE-MRTM2 were also compared with a paired t-test using participants’ regional ΔBP_ND values with frame-based motion correction.

Results

Regional statistical significance

Comparing regional ΔBP_ND values using frame- and reconstruction-based motion correction showed no significance (p > 0.05) in caudate and nucleus accumbens and significance (p < 0.05) in putamen (Table 1). Differences between ΔBP_ND values fit with E-MRTM2 and DE-MRTM2 were extremely significant (p < 0.001) in putamen and nucleus accumbens, and not significant (p > 0.05) in caudate (Table 1).

Table 1.

Human Data. Regional ΔBP_ND analyzed with different methods and evaluated for statistical significance. %ΔBP_ND is reported with raw ΔBP_ND in parentheses.

	ΔBP_ND
Motion correction	Frame MC	Recon MC	p-value
Region
Putamen	–0.4% (–0.01)	0.9% (0.03)	4.7e-02*
Caudate	–2.9% (–0.07)	–2.1% (–0.05)	9.7e-01
Nucleus Accumbens	1.5% (0.03)	4.7% (–0.09)	1.3e-01
	ΔBP_ND
Model	E-MRTM2	DE-MRTM2	p-value
Region
Putamen	–0.2% (–0.01)	–2.2% (–0.07)	1.3e-07***
Caudate	–3.5% (–0.08)	–4.6% (–0.11)	1.1e-01
Nucleus Accumbens	1.1% (0.02)	–2.1% (–0.05)	4.9e-05***

Top: Comparison of frame-based (Frame MC) and reconstruction-based (Recon MC) motion correction with ΔBP_ND values fit using E-MRTM2. Bottom: Comparison of E-MRTM2 and DE-MRTM2 with motion corrected frame-by-frame (*p < 0.05, **p < 0.01, ***p < 0.001).

Motion bias

The top row of Figure 2 demonstrates how important motion correction can be for the accuracy of ΔBP_ND maps when participant motion is high (n = 10). Even averaged across participants, motion causes a bias pattern in the ΔBP_ND map consistent with a rigid displacement of the head over time. With frame-based motion correction, striatal ΔBP_ND in the voxel map changes from 9.7% to −3.5%. An extended version of the top row of Figure 2, including the low motion group and reconstruction-based motion correction, can be found in Figure S4.

Figure 2.

Motion Bias and Correction (Human Task Data) Parametric maps of task response (ΔBP_ND) averaged across participants with high motion (n = 10) and either without motion correction (No MC) or with frame-based motion correction (Frame MC). (Taskless Simulations) Effect of frame-based motion correction averaged across realizations (n = 10). Top Row: Bias in ΔBP_ND without and with frame-based motion correction. Bottom Row: Absolute value of motion bias in ΔBP_ND without and with frame-based motion correction.

The simulations in the bottom panels of Figure 2 examine the same application of frame-based motion correction in the context of a known ground truth to quantify the extent of the bias present before and after motion correction. With no simulated challenge, all the measured change in BP_ND can be attributed to bias. After frame-based motion correction, striatal bias in ΔBP_ND was reduced from 5.8% to 2.2% (Table 2). With both positive and negative motion bias apparent at the voxel level, absolute bias values were taken at the regional level to capture the variance present in the bias maps. After frame-based motion correction, the absolute value of the total motion bias in striatal ΔBP_ND changed from 0.59 to 0.16 (a decrease in the spatial variance of motion bias of 72.9%). This equates to 20.4% average error in absolute occupancy (|%ΔBP_ND|) in striatum before frame-based motion correction and 5.9% average error afterward (Table 2). For comparison, putamen RAC BP_ND has been shown to have a standard deviation of 10% in test-retest evaluations.⁴⁶

Table 2.

Simulations. Regional values of ΔBP_ND and |ΔBP_ND| extracted from the simulated parametric maps in Figure 2 and Figure 3.

	ΔBP_ND		\|ΔBP_ND\|
Motion Correction	No MC	Frame MC	No MC	Frame MC
Region
Whole Striatum	5.8% (0.17)	2.2% (0.06)	20.4% (0.59)	5.9% (0.16)
Putamen	5.8% (0.19)	2.4% (0.08)	18.9% (0.62)	5.6% (0.17)
Caudate	6.3% (0.15)	1.3% (0.03)	23.5% (0.57)	6.4% (0.14)
Nucleus Accumbens	2.4% (0.05)	3.9% (0.08)	21.2% (0.43)	7.4% (0.15)
	ΔBP_ND		\|ΔBP_ND\|
Model	E-MRTM2	DE-MRTM2	E-MRTM2	DE-MRTM2
Region
Whole Striatum	–0.6% (–0.02)	0.2% (0.01)	10.3% (0.29)	17.4% (0.48)
Putamen	–1.5% (–0.05)	0.03% (0.00)	9.9% (0.32)	16.7% (0.53)
Caudate	0.8% (0.02)	0.9% (0.02)	11.2% (0.25)	18.7% (0.42)
Nucleus Accumbens	2.3% (0.05)	–1.2% (–0.03)	11.5% (0.23)	19.0% (0.40)

Model bias

To find an appropriate time for ending the uptake period ( $t^{D})$ , a series of kinetic analyses were performed, using PET simulations with a k₄ value within the literature range (0.07 min⁻¹)². BP_ND-dependent TACs were created by sorting voxels within the striatum into bins based on their BP_ND values. These TACs were then analyzed using DE-MRTM2 with t^D values varied in 3-minute increments consistent with the PET framing of the participant data (21 min, 24 min, 27 min, 30 min, 33 min). The value of t^D was selected to minimize bias in ΔBP_ND across values of BP_ND in simulations (Figure S5). The absolute minimum of ΔBP_ND bias occurred at t^D between 27 and 30 minutes post-injection. Therefore, t^D was selected to be 27 minutes post-injection to reduce the variance by allowing for one additional frame in estimating baseline BP_ND.

The top row of Figure 3 shows the effect of applying DE-MRTM2 to the acquired task-reward data. Median averaging across participants was applied to parametric maps of ΔBP_ND, reducing the influence of spurious outlier voxels. While the regional ΔBP_ND values in the striatum remain similar (E-MRTM2: −3.1%, DE-MRTM2: −3.3%), differences can be observed in the surrounding areas. Specifically, the “halo” of positive values around the striatum becomes less spatially distinct, and positive and negative ΔBP_ND values are no longer strongly associated with white and gray matter respectively.

Figure 3.

Model Bias and Correction (Human Task Data) Voxel maps of ΔBP_ND median averaged across all 70 study participants. DE-MRTM2 produces noticeable differences in the spatial distribution of ΔBP_ND both extrastriatally and around the edges of the striatum. (Taskless Simulations) Top Row: Bias becomes more balanced between positive and negative directions after applying DE-MRTM2 in simulations. Of particular note is the elimination of the ‘halo’ pattern of positive bias around the edges of the striatum. Bottom Row: The absolute value of the bias in ΔBP_ND is increased after applying DE-MRTM2.

Similar spatial effects can be observed in the simulated ΔBP_ND maps averaged across noise realizations (n = 10) in the lower half of Figure 3. Positive bias around the edges of the striatum is mitigated and extrastriatal bias becomes more balanced. Within the striatum, ΔBP_ND bias changes modestly (from −0.6% to 0.2%) after deweighting. However, striatal variance in absolute ΔBP_ND bias (|ΔBP_ND|) increases from 0.29 to 0.48 (an increase in the spatial variance of model bias of 65.5%) (Table 2). Another way to interpret this effect is by examining histograms of ΔBP_ND voxels within the striatum (Figure S6). The histogram of striatal voxels fit with E-MRTM2 has a standard deviation of 0.17 and a skewness of -0.78, while the histogram of striatal voxels fit with DE-MRTM2 has a standard deviation of 0.23 and a skewness of −0.25.

Figure 4 shows the relationship between DE-MRTM2 and the selection of k₂′ in the context of a representative participant data set. The E-MRTM2 ΔBP_ND fits are highly dependent on the value of k₂′ fixed prior to analysis. The conventional method for selecting the value of k₂′ (MRTM fit to a high binding region like putamen)³¹ produces ΔBP_ND maps that are most similar to DE-MRTM2—albeit with some dependence on the average level of BP_ND used for the calibration—while setting the value of k₂′ either too high or too low causes higher and lower estimates of ΔBP_ND respectively. DE-MRTM2 however, produces consistent ΔBP_ND maps independent of the selection of k₂′.

Figure 4.

Effect of debiasing at different levels of k₂′. E-MRTM2 estimates of ΔBP_ND are highly dependent on k₂′ selection, while DE-MRTM2 estimates of ΔBP_ND are not. Each row selects k₂′ using a different method: k₂′ = 0.55, estimated from blood plasma fits in control data set. k₂′ = 0.30, estimated from MRTM fits of top 10% of striatum voxels by BP_ND. k₂′ = 0.25, estimated from MRTM fit to regional putamen TAC. k₂′ = 0.20, estimated from MRTM fits of bottom 10% of striatum voxels by BP_ND.

Comparing motion and model bias

Figure 5 compares the relative effects of high motion bias and model bias at different levels of task response. Independent of the task magnitude, bias in whole striatum ΔBP_ND ranges from 0.5% to 5%, while in the nucleus accumbens subregion, it can range from 2% to 12%. Examining the absolute value bias maps in the bottom half of Figure 5, as task response increases, model bias increases only slightly and motion bias decreases only slightly. When there is no task response (0%), motion accounts for 63% of the bias effect in the striatum (model bias: 37%). At high magnitudes of task response (20%) however, motion bias contributes 50% of the observed effect (model bias: 50%).

Figure 5.

Simulations to compare motion and model bias in ΔBP_ND. Each column depicts the simulation of a different level of challenge response in terms of change in BP_ND. The top two rows depict the ΔBP_ND levels in high motion and motionless simulations respectively. The bottom three rows show the absolute value of the error in ΔBP_ND after accounting for the simulated response magnitude for each column. Total bias is derived from the high motion simulations, model bias from the motionless simulations, and motion bias from the difference between them.

Discussion

An examination of motion bias and model bias has been presented in the context of an intra-scan behavioral challenge response paradigm. Motion was shown to cause a bias pattern of large adjacent positive and negative regions, while model bias was shown to cause a spatial bias pattern dependent on BP_ND. Frame-based motion correction decreased ΔBP_ND bias globally while also decreasing its variance as shown by |ΔBP_ND|. DE-MRTM2 removed the dependence of ΔBP_ND on first-pass selection of k₂′ and rebalanced the spatial distribution of positive and negative ΔBP_ND bias in exchange for increased variance in ΔBP_ND bias as shown by |ΔBP_ND|. Both sources of bias remained relatively consistent as simulated task response increased.

Frame-based motion correction is considered the standard in the field, making its favorable impact on ΔBP_ND bias unsurprising. The alternative that was considered here, reconstruction-based motion correction, did not considerably improve performance relative to standard frame-based motion correction. Although statistical significance between the two methods was observed in putamen, this difference achieved far less significance than the impact of DE-MRTM2 and would not have appeared significant if ‘no motion correction’ had been included in the statistical comparison. ‘No motion correction’ was excluded from the formal statistical test because the differences it produced in ΔBP_ND, relative to either motion correction method, were both clear (Figure 2) and expected. While more advanced motion-correction did not provide a clear benefit to the quantification of ΔBP_ND in this study, it might be better utilized in others that require finer temporal resolution.^25,27,47

One of the clearest benefits of DE-MRTM2 is markedly reducing the contingency of first-pass global k₂′ selection, which can vary depending on precisely which regions are included in the initial ‘high-binding’ fit. Reduction of 3-parameter MRTM to 2-parameter MRTM2 by fixing k₂′³⁰ is necessary because E-MRTM fits of ΔBP_ND yield far noisier parametric maps and corresponding increases in the variance of regional fits. In our previous work, we observed that fixing k₄ to the optimal value resulted in both a decoupling of the correlation between BP_ND and k₂′ and a reduction in BP_ND bias.²² By fitting estimates of BP_ND and ΔBP_ND only after the end of the initial uptake period (t^D), we were able to mitigate the bias introduced by the selection of k₂′ even when using a single-compartment model.

The other benefit of DE-MRTM2 is a reduction in bias by rebalancing the distribution of voxels with positive and negative bias. It does, however, come with an increase in |ΔBP_ND|, evoking the familiar noise/bias tradeoff. This is best illustrated by Figure S6, where DE-MRTM2 increases the standard deviation of the histogram but decreases the skewness relative to E-MRTM2. This increase in variance could potentially be mitigated in future studies by setting the task start time later. In this work, we used a t^D of 27 min and a task start time of 40 min, allowing only 13 min for the estimation of BP_ND before starting to fit ΔBP_ND. A more even balance between the baseline and task phases of the scan could lead to more robust parametric estimates of ΔBP_ND.

Finally, it is useful to consider the impacts of motion and model bias in the context of informed estimates of the dopamine-induced displacement due to challenge. Here, the total measured change in regional BP_ND was less than 5% (Table 1), and simulations estimated that unmitigated motion and model biases can be around 3% and 1% respectively (Table 2). As positive and negative biases can counteract one another within a given region, Figure 5 uses absolute values to examine the magnitude of motion and model bias relative to one another and as simulated task response increases. Motion accounts for a greater proportion of the absolute bias at low task response rates, while motion and model bias contribute equally at high task response rates. The difference between the two bias effects lies more in their skews and spatial distributions than their overall magnitudes. Also of note is that the total bias is relatively consistent and even decreases slightly as task response increases. These observations—that motion and model bias produce comparable errors that are only weakly dependent on the simulated magnitude of displacement—underscore the notion that sources of bias pose a greater challenge when the elicited task-response effect is small.

Our study had several limitations. The results presented here are specific to RAC and to the context of an intra-scan task challenge paradigm. Pharmacological challenges administered within-scan that produce larger responses may be amenable to more complex models capable of observing greater temporal detail in the responses.⁸ Models fit to data acquired using slower tracers may be more greatly impacted by bias arising from the violation of the fast-exchange assumption between the specific and non-displacable compartments, which is dependent upon the value of k₄. Tracers that exhibit more non-specific binding, receptor internalization, specific binding in the reference region, or signal attributable to blood volume may be more biased by those sources²¹ than by the discrepancy between one and two compartment configurations. We have also limited the scope of our inquiry to motion and model bias specifically and have not considered other potential sources of bias that may have as great an impact, such as bias arising from the PET reconstruction or from attenuation-emission mismatch. Another limitation of our debiasing model is that it may not easily generalize to other behavioral RAC studies, which employ smaller subject cohorts. DE-MRTM2 accepts the trade-off of additional variance in its ΔBP_ND maps in order to better balance positive and negative biases. For reference, a one-sample t-test power calculation (R v3.6.1)⁴⁸ based on the data analyzed here suggests that, at a significance level of α = 0.05 and a power level of β = 0.80, in order to detect a 5% change in putamen BP_ND, E-MRTM2 (µ₀ ΔBP_ND = 0, µ₁ ΔBP_ND = 0.1600, σ ΔBP_ND = 0.0666) would require 4 participants and DE-MRTM2 (µ₀ ΔBP_ND = 0, µ₁ ΔBP_ND = 0.1609, σ ΔBP_ND = 0.1469) would require 9 participants. Likewise, the smaller nucleus accumbens would require 9 participants for E-MRTM2 and 19 participants for DE-MRTM2. For comparison, Martin-Soelch et al.¹⁰ scanned 24 participants and observed a 5.6% decrease in BP_ND in right ventral striatum using the equilibrium method. Studies with a low participant count, lower dose, or a bolus-only infusion paradigm may not be able to accept greater noise without sacrificing detectability of the signal. We have also not yet evaluated the debiasing capacity of DE-MRTM2 in the context of other potentially applicable models such as rFRTM²² or forward-model implementations.

In conclusion, the effects of motion bias and model bias on behavioral task response have been investigated and characterized in the context of an intrascan RAC fMRI challenge study, and methods have been proposed to mitigate the negative effects of each. For motion correction, frame-to-frame correction performed as well as a more complex reconstruction-based method. For model selection, DE-MRTM2 both decoupled ΔBP_ND bias from first-pass k₂′ estimation and rebalanced its spatial distribution.

Supplemental Material

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Supplemental material, sj-pdf-6-jcb-10.1177_0271678X221078616 for Assessment of motion and model bias on the detection of dopamine response to behavioral challenge by Michael A Levine, Joseph B Mandeville, Finnegan Calabro, David Izquierdo-Garcia, Daniel B Chonde, Kevin T Chen, Inki Hong, Julie C Price, Beatriz Luna and Ciprian Catana in Journal of Cerebral Blood Flow & Metabolism

Supplemental Material

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Supplemental material, sj-pdf-7-jcb-10.1177_0271678X221078616 for Assessment of motion and model bias on the detection of dopamine response to behavioral challenge by Michael A Levine, Joseph B Mandeville, Finnegan Calabro, David Izquierdo-Garcia, Daniel B Chonde, Kevin T Chen, Inki Hong, Julie C Price, Beatriz Luna and Ciprian Catana in Journal of Cerebral Blood Flow & Metabolism

Footnotes

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was partly supported by National Institute of Biomedical Imaging and Bioengineering Grant 5R01EB014894-02, National Institute of Mental Health Grant Number R01MH080243, National Institute of General Medical Sciences Grant T32 GM008313, NIH Blueprint for Research Science Grant T90DA022759/R90DA023427, and NIH Shared Instrumentation Grant S10RR023043.

Acknowledgments

We would like to thank Rajesh Narendran for making available to us a set of previously published RAC data with arterial blood sampling⁵ for comparison.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Authors’ contributions

Design and acquisition of imaging protocol: FC, JCP, BL

Design and execution of analysis: MAL, JBM, DIG, DBC, KTC, IH, CC

Drafting of manuscript: MAL

Editing of manuscript: MAL, JBM, FC, DIG, DBC, KTC, IH, JCP, BL, CC

ORCID iDs

Michael A Levine

Joseph B Mandeville

Daniel B Chonde

Kevin T Chen

Supplemental material

Supplemental material for this article is available online.

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Supplementary Material

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Assessment of motion and model bias on the detection of dopamine response to behavioral challenge

Abstract

Keywords

Introduction

Material and methods

Participants and data acquisition protocols

Kinetic modeling

Simulation design

Motion bias

Frame-based motion correction

Reconstruction-based motion correction

Motion bias: Experimental task data

Motion bias: Taskless simulations

Model bias

Theory: DE-MRTM2 and model bias in ΔBPND

Simulations: Estimating model bias in ΔBPND

Experimental: Assessing the impact of k2′ on ΔBPND

Comparing motion and model bias

Regional statistical significance

Results

Regional statistical significance

Motion bias

Model bias

Comparing motion and model bias

Discussion

Supplemental Material

sj-pdf-1-jcb-10.1177_0271678X221078616 - Supplemental material for Assessment of motion and model bias on the detection of dopamine response to behavioral challenge

Supplemental Material

sj-pdf-2-jcb-10.1177_0271678X221078616 - Supplemental material for Assessment of motion and model bias on the detection of dopamine response to behavioral challenge

Supplemental Material

sj-pdf-3-jcb-10.1177_0271678X221078616 - Supplemental material for Assessment of motion and model bias on the detection of dopamine response to behavioral challenge

Supplemental Material

sj-pdf-4-jcb-10.1177_0271678X221078616 - Supplemental material for Assessment of motion and model bias on the detection of dopamine response to behavioral challenge

Supplemental Material

sj-pdf-5-jcb-10.1177_0271678X221078616 - Supplemental material for Assessment of motion and model bias on the detection of dopamine response to behavioral challenge

Supplemental Material

sj-pdf-6-jcb-10.1177_0271678X221078616 - Supplemental material for Assessment of motion and model bias on the detection of dopamine response to behavioral challenge

Supplemental Material

sj-pdf-7-jcb-10.1177_0271678X221078616 - Supplemental material for Assessment of motion and model bias on the detection of dopamine response to behavioral challenge

Footnotes

Funding

Acknowledgments

Declaration of conflicting interests

Authors’ contributions

ORCID iDs

Supplemental material

References

Supplementary Material

Simulations: Estimating model bias in ΔBP_ND

Experimental: Assessing the impact of k₂′ on ΔBP_ND