Artur Hahn1,2, Julia Krüwel-Bode3, Yannis Seemann2, Sarah Schuhegger2, Johann M. E. Jende1, Anja Hohmann4, Volker J. F. Sturm1, Ke Zhang5, Sabine Heiland1, Martin Bendszus1, Michael O. Breckwoldt1,6, Christian H. Ziener1,5, and Felix T. Kurz1,5
1Department of Neuroradiology, Heidelberg University Hospital, Heidelberg, Germany, 2Department of Physics and Astronomy, University of Heidelberg, Heidelberg, Germany, 3Molecular Mechanisms of Tumor Invasion (V077), German Cancer Research Center (DKFZ), Heidelberg, Germany, 4Department of Neurology, Heidelberg University Hospital, Heidelberg, Germany, 5Department of Radiology (E010), German Cancer Research Center (DKFZ), Heidelberg, Germany, 6Clinical Cooperation Unit Neuroimmunology and Brain Tumor Immunology, German Cancer Research Center (DKFZ), Heidelberg, Germany
Synopsis
Based
on the microvasculature of entire healthy and tumor-bearing mouse brains,
imaged with high-resolution fluorescence microscopy, the transverse relaxation
process within virtual MRI voxels was simulated. Extended parametrizations of
the non-Lorentzian signal decay were used to train support vector machine and
random forest classifiers to differentiate healthy brain and tumor voxel
signals. A proof-of-principle is presented with U87 and GL261 glioblastoma at
different SNR levels. This automated workflow enables the in-silico development
of specialized MRI sequences to maximize classification accuracy with minimal
NMR measurements for experimental analogies.
Introduction
Intravascular
deoxyhemoglobin naturally causes microscopic field inhomogeneities in an external
magnetic field that lead to deviations of the transverse relaxation process with
T2 and T2* from linear exponential decay1. MR signal
decay properties in biological tissue are therefore influenced by the
microvascular architecture, which can be used to describe vascular remodeling
in glioblastoma multiforme (GBM)2. We now present a software framework that trains
statistical classifiers to interpret signals for single-voxel tumor detection
using simulated MR signal decays. We demonstrate the feasibility of learning
endogenous contrasts to classify microvascular pathologies.Methods
The
brain vasculature of n=3 healthy NMRI nu/nu mice, as well as, respectively, n=6
U87 GBM- and GL261 GBM-bearing mice was imaged using single plane illumination
microscopy (SPIM) upon fluorescent endothelial marking through Lectin-FITC
injection and successful tissue clearing at an in-plane resolution of 3.25 µm
and 5 µm between planes3. Vessel segmentation was performed in 3D using
ilastik4, noise removal was applied in Matlab R2018b (Mathworks, Natick, MA,
USA), and manually drawn masks delineated tumor tissue. An MPI-parallelized
program in Python 3 automatically processed cubic subvolumes as virtual MRI
voxels (100, 200, and 300 µm side length after 60% volume shrinkage from
clearing): sub-voxel field inhomogeneities from paramagnetic blood
susceptibility were calculated by a 3D dipole convolution with the vasculature5, assuming constant blood oxygenation Y=60% and hematocrit Hct=0.4 at B0=3
Tesla6, and spin dephasing during free induction decay was simulated in C++11
with OpenMP parallelization, considering water diffusion (D=1 µm2/ms)
in the extravascular space, with time steps dt=0.1 ms up to t=1 s. The
resulting signal attenuation was parametrized with linear least squares fits to
the logarithm of the magnetization magnitude, assuming Lorentzian (t), Gaussian
(t2), and monomial (tb) time dependence for the full time
range, as well as separately for the short- and long-time regimes (before and
after t=200 ms). For each virtual voxel signal, the fit parameters and
respective sum of squared residuals were saved as measurable features to
characterize the transverse decay. These scalar features were used to train
support vector machine (SVM) and random forest classifiers, using open-source
software from the LibSVM library7 and Scikit-Learn8, to differentiate
healthy brain from tumor voxel signals (see Fig. 1 for a workflow
summary). The model parameters for classification were optimized in quick
3-fold cross validation grid searches on the respective training signals.
Different training set sizes were used to predict U87 and GL261 tumor tissue on
previously unused voxels, also from previously blinded mice, with Rician noise
added to the magnitude signal at signal to noise ratios (SNR) between 2 and
500, defined using the first signal time point at t=0.1 ms.Results
All
training scenarios showed that stable classification accuracies around 75-80%
could be attained for the U87 GBM model with feasible training set sizes on the
order of 102 (Fig. 2). For the GL261 tumor model, stable accuracies
above 90% could be maintained with very little training data on the order of 10
signals (Fig. 3), especially with random forests. While SVM classification
suffered at SNR≤4
for small training sets, predictions improved even with very bad SNR at higher
training numbers and random forests performed very robustly under SNR variation
in all cases. Our results also show that the T2*-effects of
tumor-induced vessel remodeling are more pronounced in larger MRI voxels (Figs.
2-3).Discussion
In
all cases, stable peak prediction accuracies were quasi identical using SVM and
random forest classifiers, which is indicative of the valuable information
within the dephasing process, which can be parametrized through diversified fitting.
Random forest classifiers performed better in our initial, fully reproducible
tests, reaching stable prediction accuracies with less training data and showing
higher resilience to strong SNR variations. While our simulations were
performed with simplified constant blood oxygenation, these results strongly motivate
experimental analogies and modeling extensions to the numerical framework to
include more physiological aspects.Conclusion
Extended
sampling of the T2* relaxation process and adequate fitting shows
the potential to facilitate machine-aided voxel-wise interpretations of the MRI
signal without a need for exogenous contrast agents. Through prior training
with transverse relaxation signals and correlated ground-truth measurements of
tumor tissue, the T2* evolution may serve as an abstract, learnable
contrast to classify vascular pathology. In experimental analogies, hypercapnic
and hyperoxic conditions may help emphasize the vascular influence on the
signal decay9. With the developed software framework, suited MRI sequences
and oxygenation manipulations can be explored in silico to optimize
experimental design numerically.Acknowledgements
The authors gratefully acknowledge support with computational resources through the HPC-research cluster bwForCluster MLS&WISO by the state of Baden-Württemberg through bwHPC and the bwHPC-C5 project, as well as the German Research Foundation (DFG) through grant INST 35/1134-1 FUGG, as well as the data storage service SDS@hd, supported by the Ministry of Science, Research and the Arts Baden-Württemberg (MWK) and the DFG through grant INST 35/1314-1 FUGG and INST 35/1503-1 FUGG.
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