Fig 2 - available via license: Creative Commons Attribution 4.0 International
Content may be subject to copyright.
Left: neuron pair under fluorescence microscope. Image credit: Wierda and Sorensen (2014) , "Innervation by a GABAergic neuron depresses spontaneous release in glutamatergic neurons and unveils the clamping phenotype of synaptotagmin-1 " by K.D.B. Wierda and J.B Sorensen, 2014, J. Neurosci., 34(6), 2100-2110, (DOI: https://doi.org/10.1523/JNEUROSCI.3934-13.2014 ). CC BY-NC-SA 3.0 . Right: schematic representation of neural cell structure. Cell bodies are approximated by spherical geometries (blue) and cellular projections are approximated by cylindrical segments (green). Spatial information of cellular structures within a voxel is not encoded in the MRI measurement. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Source publication
Diffusion MRI is a valuable tool for probing tissue microstructure in the brain noninvasively. Today, model-based techniques are widely available and used for white matter characterisation where their development is relatively mature. Conversely, tissue modelling in grey matter is more challenging, and no generally accepted models exist. With advan...
Contexts in source publication
Context 1
... assume that T2 relaxation is comparable inside cellular structures and in the extra-cellular volume ( Clark and Le Bihan, 2000;Niendorf et al., 1996 ). Thus, brain tissue is modelled to consist of three distinct components, such that í µí±£ cyl + í µí±£ sph + í µí±£ ext = 1 where í µí±£ í µí± represents the volume fraction of component í µí± . Fig. 2 shows a schematic representation of grey matter morphology composed of quasi-spherical cell bodies and quasi-cylindrical segments of neural ...
Context 2
... fast and robust estimation of model parameters, we developed a neural network consisting of three fully connected layers with rectified linear unit activation functions ( Goodfellow et al., 2016 ). The threelayer neural network is able to capture the complexity of the biophysical model sufficiently well (Supplementary Material, Fig. S2) and gives similar results to traditional model fitting techniques (Supplementary Material, Figs. S3 and S4). Our implementation is based on the PyTorch deep-learning platform ( https://pytorch.org ...
Context 3
... only slight improvements may be seen for SNR > 50 . The reason for this is that the three-layer neural network has limited capacity and further layers should be added to observe increased accuracy for higher SNR, as Supplementary Fig. S2 suggests. ...
Context 4
... diffusion encoding STE and LTE waveforms used in this work have different spectral content, which could lead to unwanted timedependence effects ( Grebenkov, 2010;Jespersen et al., 2019 ). Indeed, the Monte-Carlo simulations we show in the Supplementary Material (Fig. S12B) demonstrate that in impermeable spherical compartments, STE and LTE signals have substantially different apparent diffusivity, consistent with findings in Lundell et al. (2019) . However, we do not observe the same effect in in-vivo measurements, as shown by signal decay curves in Fig. S12A. Based on simulation results with ...
Context 5
... simulations we show in the Supplementary Material (Fig. S12B) demonstrate that in impermeable spherical compartments, STE and LTE signals have substantially different apparent diffusivity, consistent with findings in Lundell et al. (2019) . However, we do not observe the same effect in in-vivo measurements, as shown by signal decay curves in Fig. S12A. Based on simulation results with quasi-spherical meshes containing quasi-cylindrical protrusions in Fig. S12C, we suggest that the discrepancy between in-vivo measurements and a restriction model may be due to exchange processes between cell bodies and projections. This result motivates the use of an apparent spherical compartment ...
Context 6
... STE and LTE signals have substantially different apparent diffusivity, consistent with findings in Lundell et al. (2019) . However, we do not observe the same effect in in-vivo measurements, as shown by signal decay curves in Fig. S12A. Based on simulation results with quasi-spherical meshes containing quasi-cylindrical protrusions in Fig. S12C, we suggest that the discrepancy between in-vivo measurements and a restriction model may be due to exchange processes between cell bodies and projections. This result motivates the use of an apparent spherical compartment diffusivity which encapsulates multiple properties of cell bodies, including cell size, bulk diffusivity and water ...
Citations
... Fitting models to powder-averaged signals is often referred to as the "spherical mean technique" (SMT), a term introduced by Kaden et al. (2016b). While powder-averaging enables the estimation of various microstructural parameters (Jespersen et al., 2013;Lasič et al., 2014;Kaden et al., 2016a,b;Szczepankiewicz et al., 2016;Henriques et al., 2020;Palombo et al., 2020;Gyori et al., 2021), a significant amount of information is lost during averaging. Therefore, it may be beneficial to estimate the parameters directly from full data without powder-averaging. ...
... In recent years, microstructural parameter estimation using machine learning (ML) has received significant attention as a potential solution to issues with conventional fitting, such as slow convergence, poor noise robustness, and terminating at local minima (Golkov et al., 2016;Barbieri et al., 2020;Palombo et al., 2020;de Almeida Martins et al., 2021;Elaldi et al., 2021;Gyori et al., 2021Gyori et al., , 2022Karimi et al., 2021;Sedlar et al., 2021a,b;Kerkelä et al., 2022). ML models can be trained to predict microstructural parameter values from data using supervised or self-supervised learning. ...
... The trained model was then applied to MRI data acquired in a clinical setting to generate microstructural maps. Furthermore, to highlight the fact that the sCNN and training pipeline are applicable to any Gaussian compartment model, the network was trained to estimate the parameters of a constrained three-compartment model by Gyori et al. (2021) that enables the estimation of apparent neural soma density using tensor-valued diffusion encoding (Topgaard, 2017). ...
Diffusion magnetic resonance imaging is sensitive to the microstructural properties of brain tissue. However, estimating clinically and scientifically relevant microstructural properties from the measured signals remains a highly challenging inverse problem that machine learning may help solve. This study investigated if recently developed rotationally invariant spherical convolutional neural networks can improve microstructural parameter estimation. We trained a spherical convolutional neural network to predict the ground-truth parameter values from efficiently simulated noisy data and applied the trained network to imaging data acquired in a clinical setting to generate microstructural parameter maps. Our network performed better than the spherical mean technique and multi-layer perceptron, achieving higher prediction accuracy than the spherical mean technique with less rotational variance than the multi-layer perceptron. Although we focused on a constrained two-compartment model of neuronal tissue, the network and training pipeline are generalizable and can be used to estimate the parameters of any Gaussian compartment model. To highlight this, we also trained the network to predict the parameters of a three-compartment model that enables the estimation of apparent neural soma density using tensor-valued diffusion encoding.
... This is consistent with analyses showing that genes associated with autism are more active during prenatal cerebellar development, when these cortical projections are established [46]. Fetal MRI could potentially reveal more microscopic increases in neuronal density [47] at this developmental time-point and whether these are associated with later autistic traits. The difference in findings between the above-mentioned studies could be attributed to a potential 'sensitive' period of influence during the prenatal period where observable changes in fetal brain structure are apparent. ...
Background
Structural differences exist in the brains of autistic individuals. To date only a few studies have explored the relationship between fetal brain growth and later infant autistic traits, and some have used fetal head circumference (HC) as a proxy for brain development. These findings have been inconsistent. Here we investigate whether fetal subregional brain measurements correlate with autistic traits in toddlers.
Methods
A total of 219 singleton pregnancies (104 males and 115 females) were recruited at the Rosie Hospital, Cambridge, UK. 2D ultrasound was performed at 12-, 20- and between 26 and 30 weeks of pregnancy, measuring head circumference (HC), ventricular atrium (VA) and transcerebellar diameter (TCD). A total of 179 infants were followed up at 18–20 months of age and completed the quantitative checklist for autism in toddlers (Q-CHAT) to measure autistic traits.
Results
Q-CHAT scores at 18–20 months of age were positively associated with TCD size at 20 weeks and with HC at 28 weeks, in univariate analyses, and in multiple regression models which controlled for sex, maternal age and birth weight.
Limitations
Due to the nature and location of the study, ascertainment bias could also have contributed to the recruitment of volunteer mothers with a higher than typical range of autistic traits and/or with a significant interest in the neurodevelopment of their children.
Conclusion
Prenatal brain growth is associated with toddler autistic traits and this can be ascertained via ultrasound starting at 20 weeks gestation.
... In biomedical imaging, there are multiple examples of ML applications like automatic image segmentation, data processing, MRI reconstruction, etc. In DW-MRI, ML techniques have been used for data pre-processing [13,14], estimation of diffusion parameters [15][16][17][18][19], automatic white matter bundle segmentation [20], among other applications (for a review, see [21]). There are still, however, several opportunities for clinical applications and improvements in the detection of histopathology. ...
Diffusion-weighted magnetic resonance imaging (DW-MRI) is a non-invasive technique that is sensitive to microstructural geometry in neural tissue and is useful for the detection of neuropathology in research and clinical settings. Tensor-valued diffusion encoding schemes (b-tensor) have been developed to enrich the microstructural data that can be obtained through DW-MRI. These advanced methods have proven to be more specific to microstructural properties than conventional DW-MRI acquisitions. Additionally, machine learning methods are particularly useful for the study of multidimensional data sets. In this work, we have tested the reach of b-tensor encoding data analyses with machine learning in different histopathological scenarios. We achieved this in three steps: 1) We induced different levels of white matter damage in rodent optic nerves. 2) We obtained ex vivo DW-MRI data with b-tensor encoding schemes and calculated quantitative metrics using Q-space trajectory imaging. 3) We used a machine learning model to identify the main contributing features and built a voxel-wise probabilistic classification map of histological damage. Our results show that this model is sensitive to characteristics of microstructural damage. In conclusion, b-tensor encoded DW-MRI data analyzed with machine learning methods, have the potential to be further developed for the detection of histopathology and neurodegeneration.
... Diffusion tensor is an advanced MRI technique that is based on measurements of water diffusion in cellular compartments [3,17]. Water diffusion depends on orientation, spacing, and structural barriers, such as myelin and cellular membranes, in the brain tissue [18,19]. ...
Central nervous system (CNS) involvement in childhood-onset systemic lupus erythematosus (cSLE) occurs in more than 50% of patients. Structural magnetic resonance imaging (MRI) has identified global cerebral atrophy, as well as the involvement of the corpus callosum and hippocampus, which is associated with cognitive impairment. In this cross-sectional study we included 71 cSLE (mean age 24.7 years (SD 4.6) patients and a disease duration of 11.8 years (SD 4.8) and two control groups: (1) 49 adult-onset SLE (aSLE) patients (mean age of 33.2 (SD 3.7) with a similar disease duration and (2) 58 healthy control patients (mean age of 29.9 years (DP 4.1)) of a similar age. All of the individuals were evaluated on the day of the MRI scan (Phillips 3T scanner). We reviewed medical charts to obtain the clinical and immunological features and treatment history of the SLE patients. Segmentation of the corpus callosum was performed through an automated segmentation method. Patients with cSLE had a similar mid-sagittal area of the corpus callosum in comparison to the aSLE patients. When compared to the control groups, cSLE and aSLE had a significant reduction in the mid-sagittal area in the posterior region of the corpus callosum. We observed significantly lower FA values and significantly higher MD, RD, and AD values in the total area of the corpus callosum and in the parcels B, C, D, and E in cSLE patients when compared to the aSLE patients. Low complement, the presence of anticardiolipin antibodies, and cognitive impairment were associated with microstructural changes. In conclusion, we observed greater microstructural changes in the corpus callosum in adults with cSLE when compared to those with aSLE. Longitudinal studies are necessary to follow these changes, however they may explain the worse cognitive function and disability observed in adults with cSLE when compared to aSLE.
... In recent years, parameter estimation using supervised machine learning has received significant attention as a potential solution to some issues with conventional model fitting such as slow convergence, poor noise robustness, and terminating at local minima [14][15][16][17][18][19][20][21][22][23][24]. In the context of microstructural neuroimaging, a particularly promising development in the field of deep learning has been the invention of spherical convolutional neural networks (sCNNs) [25][26][27]. ...
... The sCNN could estimate apparent neurite density and diffusivity from spherical data more accurately than conventional non-linear least squares (NLLS) or a multilayer perceptron (MLP) applied to powder-averaged data. To demonstrate that our method is applicable to any Gaussian compartment model, the network was also trained to estimate the parameters of a constrained 3-compartment model by Gyori et al. [18] that enables the estimation of apparent neural soma density using tensor-valued diffusion encoding [33]. ...
... We trained our sCNN to estimate the parameters of two microstructural models and applied the trained network to imaging data acquired in a clinical setting to generate microstructural parameter maps. The sCNN was compared to NLLS using the software by Kaden et al. [11] and to an MLP similar to the ones used by Gyori et al. [18,23]. The MLP had three hidden layers with 256 nodes each and was trained to predict the model parameters from powder-averaged data. ...
Diffusion-weighted magnetic resonance imaging is sensitive to the microstructural properties of brain tissue. However, estimating clinically and scientifically relevant microstructural properties from the measured signals remains a highly challenging inverse problem. This paper presents a novel framework for estimating microstructural parameters using recently developed orientationally invariant spherical convolutional neural networks and efficiently simulated training data with a known ground truth. The network was trained to predict the ground-truth parameter values from simulated noisy data and applied to imaging data acquired in a clinical setting to generate microstructural parameter maps. Our model could estimate model parameters from spherical data more accurately than conventional non-linear least squares or a multi-layer perceptron applied on powder-averaged data (i.e., the spherical mean technique, a popular method for orientationally invariant microstructural parameter estimation). Importantly, our method is generalizable and can be used to estimate the parameters of any Gaussian compartment model.
... Recently, there has been a renewed interest in using deep neural network (DNN) for parameter estimation in studies such as intravoxel incoherent motion, [22][23][24] chemical exchange saturation transfer, [25][26][27] and tissue microstructure in the brain. [28][29][30] These successful implementations have inspired us to use this powerful tool to estimate the microstructural parameters of the IMPULSED model. ...
Purpose
This work introduces and validates a deep‐learning‐based fitting method, which can rapidly provide accurate and robust estimation of cytological features of brain tumor based on the IMPULSED (imaging microstructural parameters using limited spectrally edited diffusion) model fitting with diffusion‐weighted MRI data.
Methods
The U‐Net was applied to rapidly quantify extracellular diffusion coefficient (Dex), cell size (d), and intracellular volume fraction (vin) of brain tumor. At the training stage, the image‐based training data, synthesized by randomizing quantifiable microstructural parameters within specific ranges, was used to train U‐Net. At the test stage, the pre‐trained U‐Net was applied to estimate the microstructural parameters from simulated data and the in vivo data acquired on patients at 3T. The U‐Net was compared with conventional non‐linear least‐squares (NLLS) fitting in simulations in terms of estimation accuracy and precision.
Results
Our results confirm that the proposed method yields better fidelity in simulations and is more robust to noise than the NLLS fitting. For in vivo data, the U‐Net yields obvious quality improvement in parameter maps, and the estimations of all parameters are in good agreement with the NLLS fitting. Moreover, our method is several orders of magnitude faster than the NLLS fitting (from about 5 min to <1 s).
Conclusion
The image‐based training scheme proposed herein helps to improve the quality of the estimated parameters. Our deep‐learning‐based fitting method can estimate the cell microstructural parameters fast and accurately.
... Informed by findings in Chapter 4, in this chapter we formulate a biophysical model that approximates spherical and cylindrical cellular entities as di↵erently shaped microscopic Gaussian di↵usion tensors, and we fit this model to B-tensor data using supervised ML. The results in this chapter were published in Gyori et al. (2019a) and Gyori et al. (2021a). In this thesis, we refer to the developed technique as apparent neural soma imaging (ANSI). ...
... To probe this further and determine whether the contrast observed in apparent spherical compartment densities is an artefact of CSF contamination, in this chapter we combine ANSI with FLAIR, which suppresses the signal from CSF. The results in this chapter were presented in Gyori et al. (2020b) and partially in Gyori et al. (2021a). ...
... Our findings inform the modelling approach we take in the subsequent chapters of this thesis. We presented our results in this chapter inGyori et al. (2020a) and part of the results were also published inGyori et al. (2021a). ...
Today, a plethora of model-based diffusion MRI (dMRI) techniques exist that aim to provide quantitative metrics of cellular-scale tissue properties. In the brain, many of these techniques focus on cylindrical projections such as axons and dendrites. Capturing additional tissue features is challenging, as conventional dMRI measurements have limited sensitivity to different cellular components, and modelling cellular architecture is not trivial in heterogeneous tissues such as grey matter. Additionally, fitting complex non-linear models with traditional techniques can be time-consuming and prone to local minima, which hampers their widespread use. In this thesis, we harness recent advances in measurement technology and modelling efforts to tackle these challenges. We probe the utility of B-tensor encoding, a technique that offers additional sensitivity to tissue microstructure compared to conventional measurements, and observe that B-tensor encoding provides unique contrast in grey matter. Motivated by this and recent work showing that the diffusion signature of soma in grey matter may be captured with spherical compartments, we use B-tensor encoding measurements and a biophysical model to disentangle spherical and cylindrical cellular structures. We map apparent markers of these geometries in healthy human subjects and evaluate the extent to which they may be interpreted as correlates of soma and projections. To ensure fast and robust model fitting, we use supervised machine learning (ML) to estimate parameters. We explore limitations in ML fitting in several microstructure models, including the model developed here, and demonstrate that the choice of training data significantly impacts estimation performance. We highlight that high precision obtained using ML may mask strong biases and that visual assessment of the parameter maps is not sufficient for evaluating the quality of the estimates. We believe that the methods developed in this work provide new insight into the reliability and potential utility of advanced dMRI and ML in microstructure imaging.
... Taken together, our results suggest that inter-compartment exchange is not negligible in gray matter at typical PGSE or clinical diffusion times ( t > 20 ms) and should therefore be accounted for in biophysical models of gray matter and potentially even in thinner white matter tracts such as the cingulum (in rodents), and by extension to demyelinating WM as a result of disease. Our findings also highlight an additional challenge for approaches that use b -tensor encoding techniques to disentangle various tissue geometries or solve model degeneracy ( Afzali et al., 2021 ;Coelho et al., 2019 ;Gyori et al., 2021a ;Reisert et al., 2019 ). Since free gradient waveforms introduce by design a whole spectrum of relatively long diffusion times ( > 20 ms), the ill-definition of the diffusion time may become problematic in a regime where exchange cannot be neglected. ...
Biophysical models of diffusion in white matter have been center-stage over the past two decades and are essentially based on what is now commonly referred to as the “Standard Model” (SM) of non-exchanging anisotropic compartments with Gaussian diffusion. In this work, we focus on diffusion MRI in gray matter, which requires rethinking basic microstructure modeling blocks. In particular, at least three contributions beyond the SM need to be considered for gray matter: water exchange across the cell membrane – between neurites and the extracellular space; non-Gaussian diffusion along neuronal and glial processes – resulting from structural disorder; and signal contribution from soma. For the first contribution, we propose Neurite Exchange Imaging (NEXI) as an extension of the SM of diffusion, which builds on the anisotropic Kärger model of two exchanging compartments. Using datasets acquired at multiple diffusion weightings (b) and diffusion times (t) in the rat brain in vivo, we investigate the suitability of NEXI to describe the diffusion signal in the gray matter, compared to the other two possible contributions. Our results for the diffusion time window 20-45 ms show minimal diffusivity time-dependence and more pronounced kurtosis decay with time, which is well fit by the exchange model. Moreover, we observe lower signal for longer diffusion times at high b. In light of these observations, we identify exchange as the mechanism that best explains these signal signatures in both low-b and high-b regime, and thereby propose NEXI as the minimal model for gray matter microstructure mapping. We finally highlight multi-b multi-t acquisitions protocols as being best suited to estimate NEXI model parameters reliably. Using this approach, we estimate the inter-compartment water exchange time to be 15 – 60 ms in the rat cortex and hippocampus in vivo, which is of the same order or shorter than the diffusion time in typical diffusion MRI acquisitions. This suggests water exchange as an essential component for interpreting diffusion MRI measurements in gray matter.
... Recent works that leverage supervised ML for model parameter estimation in qMRI typically employ one of two training data distributions: (1) parameter combinations obtained from traditional model fitting and the corresponding measured qMRI signals, 4,6,9,11,[14][15][16][17] or (2) parameters sampled uniformly from the entire plausible parameter space with simulated qMRI signals. 5,[18][19][20][21][22][23][24] While (1) uses parameter combinations directly estimated from the data so likely quantifies the model parameters with higher accuracy and precision for a given specific dataset, (2) supports choice of training data distribution, which may help improve generalizability and avoid problems arising from imbalance. ...
Purpose
Supervised machine learning (ML) provides a compelling alternative to traditional model fitting for parameter mapping in quantitative MRI. The aim of this work is to demonstrate and quantify the effect of different training data distributions on the accuracy and precision of parameter estimates when supervised ML is used for fitting.
Methods
We fit a two‐ and three‐compartment biophysical model to diffusion measurements from in‐vivo human brain, as well as simulated diffusion data, using both traditional model fitting and supervised ML. For supervised ML, we train several artificial neural networks, as well as random forest regressors, on different distributions of ground truth parameters. We compare the accuracy and precision of parameter estimates obtained from the different estimation approaches using synthetic test data.
Results
When the distribution of parameter combinations in the training set matches those observed in healthy human data sets, we observe high precision, but inaccurate estimates for atypical parameter combinations. In contrast, when training data is sampled uniformly from the entire plausible parameter space, estimates tend to be more accurate for atypical parameter combinations but may have lower precision for typical parameter combinations.
Conclusion
This work highlights that estimation of model parameters using supervised ML depends strongly on the training‐set distribution. We show that high precision obtained using ML may mask strong bias, and visual assessment of the parameter maps is not sufficient for evaluating the quality of the estimates.
... It is plausible that this degeneracy can be lifted with dedicated experiments employing for instance double wave vector (Cory et al., 1990;Shemesh et al., 2016) or b-tensor encoding Lampinen et al., 2020), as has been the case for the reminiscent branch issue in WM modelling (Coelho et al., 2019;Reisert et al., 2019;Olesen et al., 2021). This has recently been explored in the context of SANDI (Afzali et al., 2021;Gyori et al., 2021) but without incorporating exchange. ...
Diffusion MRI (dMRI) provides contrast that reflect diffusing spins' interactions with microstructural features of biological systems, but its specificity remains limited due to the ambiguity of its relation to the underlying microstructure. To improve specificity, biophysical models of white matter (WM) typically express dMRI signals according to the Standard Model (SM) and have more recently in gray matter (GM) attempted to incorporate cell soma (the SANDI model). The validity of the assumptions underlying these models, however, remains largely undetermined, especially in GM. Observing the models' unique, functional properties, such as the $b^{-1/2}$ power-law associated with 1d diffusion, has emerged as a fruitful strategy for experimental validation. The absence of this signature in GM has been explained by neurite water exchange, non-linear morphology, and/or obscuring soma signal contributions. Here, we present simulations in realistic neurons demonstrating that curvature and branching does not destroy the stick power-law in impermeable neurites, but that their signal is drowned by the soma under typical experimental conditions: Nevertheless, we identify an attainable experimental regime in which the neurite signal dominates. Furthermore, we find that exchange-driven time dependence produces a behavior opposite to that expected from restricted diffusion, thereby providing a functional signature disambiguating the two effects. We present data from dMRI experiments in ex vivo rat brain at ultrahigh field and observe a time dependence consistent with substantial exchange and a GM stick power-law. The first finding suggests significant water exchange while the second suggests a small sub-population of impermeable neurites. To quantify our observations, we harness the K\"arger exchange model and incorporate the corresponding signal time dependence in SM and SANDI.
