Ben R Dickie1,2, Tao Jin3, Rainer Hinz4, Geoff JM Parker5,6, Laura M Parkes1,2, and Julian Matthews1,2
1Division of Neuroscience and Experimental Psychology, Faculty of Biology Medicine and Health, The University of Manchester, Manchester, United Kingdom, 2Geoffrey Jefferson Brain Research Centre, Manchester Academic Health Science Centre, Manchester, United Kingdom, 3Department of Radiology, University of Pittsburgh, Pittsburgh, PA, United States, 4Division of Informatics, Imaging, and Data Sciences, Faculty of Biology, Medicine, and Health, The University of Manchester, Manchester, United Kingdom, 5Centre for Medical Image Computing, Department of Computer Science and Department of Neuroinflammation, University College London, London, United Kingdom, 6Bioxydyn Ltd, Manchester, United Kingdom
Synopsis
Chemical-exchange
spin-lock (CESL) MRI can detect uptake and clearance of intravenously
administered glucose into the brain at high spatial resolution. We apply
quantitative modelling to describe glucoCESL kinetics in tumour-bearing and
healthy rats. Parameters relating to glucose transport (Tmax, Kt,
kd), metabolism (MRglu) and blood volume (vb) were estimated and
compared between tumour and cortical tissue.
Kinetic modelling of glucoCESL MRI data yields meaningful estimates of glucose
transport and metabolism, and our modelling approach holds great promise to
probe glucose transport and metabolism at high spatial resolution.
Introduction
Chemical-exchange
saturation transfer (CEST) and spin-lock (CESL) MRI can non-invasively
detect uptake of intravenously administered glucose into the brain1,2.
However, kinetic modelling to determine quantitative parameters relating to glucose
transport and metabolic rates has not been applied to this type of data. We
introduce the theoretical background for kinetic modelling of glucoCESL data,
and evaluate two models to estimate transport and metabolic parameters in healthy
rats and in a rat glioma model. Theory
Changes in R1,ρ are proportional to changes
in glucose concentration (ΔC)1:
$$\Delta R_{1,\rho} = r_{g}\Delta C$$
where $$$r_{g}$$$ is the R1,ρ relaxivity of glucose.
Two kinetic
models are proposed (Figure 1). Both models assume the metabolic rate
of glucose consumption, MRglu, is not dependent on local glucose availability. Model 1 assumes the influx and efflux rates of glucose across the
blood-brain barrier (BBB), k1
and k2, are governed by Michelis-Menten
kinetics3 and thus dependent on the arterial and tissue glucose concentrations respectively. Model 2 assumes a mixture of Michelis-Menten kinetics and
passive diffusion across the BBB4. The mass transport equation for both models is:
$$\frac{dC(t)}{dt} = k_{1}C_{a}(t) - k_{2}C_{1}(t) - MR_{glu}$$
where all
parameters are defined in Figure 1. The total glucose concentration in tissue is
modelled as:
$$C(t) = v_{b}C_{a}(t) + (1-v_{b})C_{1}(t)$$
where $$$v_{b}$$$ is the fractional blood volume. Methods
Animals: Animal studies were approved by the
Institutional Animal Care and Use Committee at the University of Pittsburgh. Animal preparation and MRI experiments
have been described previously1,5. Fischer 344 rats weighing 252-283
g (n = 4) (Charles River, Wilmington, MA) were inoculated with 9L cells and
imaged 4-5 weeks later. Healthy Sprague-Dawley rats weighing 335-388g (n = 3)
were also imaged.
MRI: Rats were anesthetized with 2% isoflurane in a mixture of O2
and air and the right femoral artery catheterised. SE-EPI CESL images
with and without R1,ρ-weighting
(i.e., spin-lock pulse duration TSL = 0 and 50 ms, B1 ∼
500 Hz) were acquired at 9.4 T in an interleaved manner and data fit using an
exponential model to estimate R1,ρ
time-courses. Scan parameters of CESL images are given in Table 1. A glucose
bolus (1g/kg) was injected after 20 minutes (tumour bearing) and 30 minutes
(healthy) of baseline data over approximately 30-60 seconds, after which R1,ρ was measured for 50
minutes.
Analysis: Voxelwise estimates of ∆R1,ρ(t) were converted to
estimates of ∆C(t) using $$$r_{g}$$$ = 0.067 (s mM)−1
derived from Figure 1D of Jin et al.1. Kinetic models were fit to
measured ∆C(t) time-courses using the
ordinary differential equation solver ode45 and lsqcurvefit function in Matlab
(Mathworks, version 5 2017a). A bi-exponential fit to a population-based input
function given in Figure 4C of Nasrallah et al. was used for Ca(t)6 (Figure 2a). Datapoints for calculation of $$$r_{g}$$$ and Ca(t) were extracted from .png files of the
respective figures using the GrabIt function in Matlab.
Regions of
interest (ROIs) were drawn manually in tumour and cortex regions. Cortical values of
kinetic parameters in healthy rats were combined with cortical
values from tumour-bearing rats, and differences between cortex (n = 7) and tumour (n = 4) evaluated using t-tests for partially overlapping samples. The Akaike
information criterion (AIC) and ∆AIC (∆AIC = AIC1
– AIC2) were computed to compare model fits. Statistical analysis was done
in R (version 4.0.2).Results
Figures 2b-c show sensitivity of ∆R1,ρ to kinetic parameters. Figure 3 shows an example of tumour and cortical ROI definition, and
example ∆C(t) time-courses and model fits. Figure 4 shows parametric maps for a
tumour bearing rat, and mean values of each parameter in cortex and tumour
tissue. Model 1 had a lower AIC
than model 2 in cortex (ΔAIC < 0, p = 0.032). In some tumours, model 2 had
lower AIC than model 1 (ΔAIC > 0), indicating possible BBB disruption,
however overall there was no difference (p = 0.53). Kt and vb
from model 1 were significantly higher in tumour tissue compared to cortex. Discussion
Estimates of Tmax, Kt, MRglu,
kd and vb were
found to lie well within the range of previously published values7. Significant
differences in Kt and vb
were observed between tumour and cortical tissue, demonstrating the potential
of the proposed approach to detect abnormal vascularity and glucose transport in-vivo. Model 2 provided no additional information above model 1 in either cortex
or tumour (Figure 4t). However some tumours had positive ∆AIC (Figure 4s), possibly indicating disruption of the BBB. The half saturation constant Kt
will also trade-off saturable and non-saturable kinetics – higher Kt observed in tumour tissue may also indicate increased passive diffusion8.
Model 2 predicted similar vb in cortex and tumour, whereas
model 1 predicted higher vb in tumour tissue, the latter agreeing with a study investigating 9L
glioma blood volume9. The parameter kd was able to
capture variability associated with Tmax,
Kt and vb, and modelling transport via free diffusion only may provide an adequate descriptive model in tumour tissue.
Validation is now needed to determine the validity of the proposed kinetic
models. Conclusion
We have demonstrated the feasibility of applying kinetic models to glucoCESL
MRI data and show the potential of the approach to probe glucose transport and metabolism
at high spatial resolution. Acknowledgements
We would like to acknowledge the Medical Research Council for funding (MRC Confidence in Concept Round 6, MC_PC_17172). References
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