Morphogenesis as Bayesian inference: A variational approach to pattern formation and control in complex biological systems

Recent advances in molecular biology such as gene editing [1], bioelectric recording and manipulation [2] and live cell microscopy using fluorescent reporters [3], [4] – especially with the advent of light-controlled protein activation through optogenetics [5] – have provided the tools to measure and manipulate molecular signaling pathways with unprecedented spatiotemporal precision. This has produced ever increasing detail about the molecular mechanisms underlying development and regeneration in biological organisms. However, an overarching concept – that can predict the emergence of form and the robust maintenance of complex anatomy – is largely missing in the field. Classic (i.e., dynamic systems and analytical mechanics) approaches such as least action principles are difficult to use when characterizing open, far-from equilibrium systems that predominate in Biology. Similar issues arise in neuroscience when trying to understand neuronal dynamics from first principles. In this (neurobiology) setting, a variational free energy principle has emerged based upon a formulation of self-organization in terms of (active) Bayesian inference. The free energy principle has recently been applied to biological self-organization beyond the neurosciences [6], [7]. For biological processes that underwrite development or regeneration, the Bayesian inference framework treats cells as information processing agents, where the driving force behind morphogenesis is the maximization of a cell's model evidence. This is realized by the appropriate expression of receptors and other signals that correspond to the cell's internal (i.e., generative) model of what type of receptors and other signals it should express. The emerging field of the free energy principle in pattern formation provides an essential quantitative formalism for understanding cellular decision-making in the context of embryogenesis, regeneration, and cancer suppression. In this paper, we derive the mathematics behind Bayesian inference – as understood in this framework – and use simulations to show that the formalism can reproduce experimental, top-down manipulations of complex morphogenesis. First, we illustrate this ‘first principle’ approach to morphogenesis through simulated alterations of anterior-posterior axial polarity (i.e., the induction of two heads or two tails) as in planarian regeneration. Then, we consider aberrant signaling and functional behavior of a single cell within a cellular ensemble – as a first step in carcinogenesis as false ‘beliefs’ about what a cell should ‘sense’ and ‘do’. We further show that simple modifications of the inference process can cause – and rescue – mis-patterning of developmental and regenerative events without changing the implicit generative model of a cell as specified, for example, by its DNA. This formalism offers a new road map for understanding developmental change in evolution and for designing new interventions in regenerative medicine settings

Ultrahigh field MRI in clinical neuroimmunology: a potential contribution to improved diagnostics and personalised disease management

Conventional magnetic resonance imaging (MRI) at 1.5 Tesla (T) is limited by modest spatial resolution and signal-to-noise ratio (SNR), impeding the identification and classification of inflammatory central nervous system changes in current clinical practice. Gaining from enhanced susceptibility effects and improved SNR, ultrahigh field MRI at 7 T depicts inflammatory brain lesions in great detail. This review summarises recent reports on 7 T MRI in neuroinflammatory diseases and addresses the question as to whether ultrahigh field MRI may eventually improve clinical decision-making and personalised disease management

Scaling properties of granular materials

Given an assembly of viscoelastic spheres with certain material properties, we raise the question how the macroscopic properties of the assembly will change if all lengths of the system, i.e. radii, container size etc., are scaled by a constant. The result leads to a method to scale down experiments to lab-size.Comment: 4 pages, 2 figure

Normal volumes and microstructural integrity of deep gray matter structures in AQP4+ NMOSD

OBJECTIVE: To assess volumes and microstructural integrity of deep gray matter structures in a homogeneous cohort of patients with neuromyelitis optica spectrum disorder (NMOSD). METHODS: This was a cross-sectional study including 36 aquaporin-4 antibody-positive (AQP4 Ab-positive) Caucasian patients with NMOSD and healthy controls matched for age, sex, and education. Volumetry of deep gray matter structures (DGM; thalamus, caudate, putamen, globus pallidus, hippocampus, amygdala, nucleus accumbens) was performed using 2 independent automated methods. Microstructural integrity was assessed based on diffusion tensor imaging. RESULTS: Both volumetric analysis methods consistently revealed similar volumes of DGM structures in patients and controls without significant group differences. Moreover, no differences in DGM microstructural integrity were observed between groups. CONCLUSIONS: Deep gray matter structures are not affected in AQP4 Ab-positive Caucasian patients with NMOSD. NMOSD imaging studies should be interpreted with respect to Ab status, educational background, and ethnicity of included patients

Cortical topological network changes following optic neuritis

OBJECTIVE: To differentiate between visual cortical network topology changes following optic neuritis (ON) stemming from different inflammatory disease types, we used mathematical graph theory-based tools to analyze functional imaging data. METHODS: Sixty-two patients were recruited into this cross-sectional study, 23 of whom had neuromyelitis optica spectrum disorder (NMOSD) with ON, 18 with clinically isolated syndrome (CIS)-ON, and 21 with other CIS episodes. Twenty-six healthy controls (HCs) were also recruited. All participants underwent resting-state functional MRI. Visual networks were defined using 50 visual regions of interest. Analysis included graph theory metrics, including degree, density, modularity, and local and global efficiency. RESULTS: Visual network density shows decreased connectivity in all patient groups compared with controls. A higher degree of connections is seen in both ON groups (CIS and NMOSD) compared with the the non-ON group. This pattern is most pronounced in dorsal-lateral regions. Information transfer efficiency and modularity were reduced in both CIS groups, but not in the NMOSD group, compared with the HC group. CONCLUSIONS: Visual network density appears affected by the neurologic deficit sustained (ON), and connectivity changes are more evident in dorsal-lateral regions. Efficiency and modularity appear to be associated with the specific disease type (CIS vs NMOSD). Thus, topological cortical changes in the visual system are associated with the type of neurologic deficit within the limits set on them by the underlying pathophysiology. We suggest that cortical patterns of activity should be considered in the outcome of the patients despite the localized nature of ON

Uncovering convolutional neural network decisions for diagnosing multiple sclerosis on conventional MRI using layer-wise relevance propagation

Machine learning-based imaging diagnostics has recently reached or even surpassed the level of clinical experts in several clinical domains. However, classification decisions of a trained machine learning system are typically non-transparent, a major hindrance for clinical integration, error tracking or knowledge discovery. In this study, we present a transparent deep learning framework relying on 3D convolutional neural networks (CNNs) and layer-wise relevance propagation (LRP) for diagnosing multiple sclerosis (MS), the most widespread autoimmune neuroinflammatory disease. MS is commonly diagnosed utilizing a combination of clinical presentation and conventional magnetic resonance imaging (MRI), specifically the occurrence and presentation of white matter lesions in T2-weighted images. We hypothesized that using LRP in a naive predictive model would enable us to uncover relevant image features that a trained CNN uses for decision-making. Since imaging markers in MS are well-established this would enable us to validate the respective CNN model. First, we pre-trained a CNN on MRI data from the Alzheimer's Disease Neuroimaging Initiative (n = 921), afterwards specializing the CNN to discriminate between MS patients (n = 76) and healthy controls (n = 71). Using LRP, we then produced a heatmap for each subject in the holdout set depicting the voxel-wise relevance for a particular classification decision. The resulting CNN model resulted in a balanced accuracy of 87.04% and an area under the curve of 96.08% in a receiver operating characteristic curve. The subsequent LRP visualization revealed that the CNN model focuses indeed on individual lesions, but also incorporates additional information such as lesion location, non-lesional white matter or gray matter areas such as the thalamus, which are established conventional and advanced MRI markers in MS. We conclude that LRP and the proposed framework have the capability to make diagnostic decisions of CNN models transparent, which could serve to justify classification decisions for clinical review, verify diagnosis-relevant features and potentially gather new disease knowledge

Accelerated simultaneous T2 and T2* mapping of multiple sclerosis lesions using compressed sensing reconstruction of radial RARE-EPI MRI

(1) BACKGROUND: Radial RARE-EPI MRI facilitates simultaneous T2 and T2* mapping (2in1-RARE-EPI). With modest undersampling (R = 2), the speed gain of 2in1-RARE-EPI relative to Multi-Spin-Echo and Multi-Gradient-Recalled-Echo references is limited. Further reduction in scan time is crucial for clinical studies investigating T2 and T2* as imaging biomarkers. We demonstrate the feasibility of further acceleration, utilizing compressed sensing (CS) reconstruction of highly undersampled 2in1-RARE-EPI. (2) METHODS: Two-fold radially-undersampled 2in1-RARE-EPI data from phantoms, healthy volunteers (n = 3), and multiple sclerosis patients (n = 4) were used as references, and undersampled (Rextra = 1–12, effective undersampling Reff = 2–24). For each echo time, images were reconstructed using CS-reconstruction. For T2 (RARE module) and T2* mapping (EPI module), a linear least-square fit was applied to the images. T2 and T2* from CS-reconstruction of undersampled data were benchmarked against values from CS-reconstruction of the reference data. (3) RESULTS: We demonstrate accelerated simultaneous T2 and T2* mapping using undersampled 2in1-RARE-EPI with CS-reconstruction is feasible. For Rextra = 6 (TA = 01:39 min), the overall MAPE was ≤8% (T2*) and ≤4% (T2); for Rextra = 12 (TA = 01:06 min), the overall MAPE was <13% (T2*) and <5% (T2). (4) CONCLUSION: Substantial reductions in scan time are achievable for simultaneous T2 and T2* mapping of the brain using highly undersampled 2in1-RARE-EPI with CS-reconstruction

Microstructural visual system changes in AQP4-antibody-seropositive NMOSD

OBJECTIVE: To trace microstructural changes in patients with aquaporin-4 antibody (AQP4-ab)-seropositive neuromyelitis optica spectrum disorders (NMOSDs) by investigating the afferent visual system in patients without clinically overt visual symptoms or visual pathway lesions. METHODS: Of 51 screened patients with NMOSD from a longitudinal observational cohort study, we compared 6 AQP4-ab-seropositive NMOSD patients with longitudinally extensive transverse myelitis (LETM) but no history of optic neuritis (ON) or other bout (NMOSD-LETM) to 19 AQP4-ab-seropositive NMOSD patients with previous ON (NMOSD-ON) and 26 healthy controls (HCs). Foveal thickness (FT), peripapillary retinal nerve fiber layer (pRNFL) thickness, and ganglion cell and inner plexiform layer (GCIPL) thickness were measured with optical coherence tomography (OCT). Microstructural changes in the optic radiation (OR) were investigated using diffusion tensor imaging (DTI). Visual function was determined by high-contrast visual acuity (VA). OCT results were confirmed in a second independent cohort. RESULTS: FT was reduced in both patients with NMOSD-LETM (p = 3.52e(-14)) and NMOSD-ON (p = 1.24e(-16)) in comparison with HC. Probabilistic tractography showed fractional anisotropy reduction in the OR in patients with NMOSD-LETM (p = 0.046) and NMOSD-ON (p = 1.50e(-5)) compared with HC. Only patients with NMOSD-ON but not NMOSD-LETM showed neuroaxonal damage in the form of pRNFL and GCIPL thinning. VA was normal in patients with NMOSD-LETM and was not associated with OCT or DTI parameters. CONCLUSIONS: Patients with AQP4-ab-seropositive NMOSD without a history of ON have microstructural changes in the afferent visual system. The localization of retinal changes around the Mueller-cell rich fovea supports a retinal astrocytopathy

Optic chiasm measurements may be useful markers of anterior optic pathway degeneration in neuromyelitis optica spectrum disorders

OBJECTIVES: We aimed to evaluate optic chiasm (OC) measures as potential imaging marker for anterior optic pathway damage assessment in the context of neuromyelitis optica spectrum disorders (NMOSD). MATERIALS AND METHOD: This cross-sectional study included 39 patients exclusively with aquaporin 4-IgG seropositive NMOSD of which 25 patients had a history of optic neuritis (NMOSD-ON) and 37 age- and sex-matched healthy controls (HC). OC heights, width, and area were measured using standard 3D T1-weighted MRI. Sensitivity of these measures to detect neurodegeneration in the anterior optic pathway was assessed in receiver operating characteristics analyses. Correlation coefficients were used to assess associations with structural measures of the anterior optic pathway (optic nerve dimensions, retinal ganglion cell loss) and clinical measures (visual function and disease duration). RESULTS: OC heights and area were significantly smaller in NMOSD-ON compared to HC (NMOSD-ON vs. HC p < 0.0001). An OC area smaller than 22.5 mm(2) yielded a sensitivity of 0.92 and a specificity of 0.92 in separating chiasms of NMOSD-ON from HC. OC area correlated well with structural and clinical measures in NMOSD-ON: optic nerve diameter (r = 0.4, p = 0.047), peripapillary retinal nerve fiber layer thickness (r = 0.59, p = 0.003), global visual acuity (r = − 0.57, p = 0.013), and diseases duration (r = − 0.5, p = 0.012). CONCLUSION: Our results suggest that OC measures are promising and easily accessible imaging markers for the assessment of anterior optic pathway damage. KEY POINTS: (1) Optic chiasm dimensions were smaller in neuromyelitis optica spectrum disorder patients compared to healthy controls. (2) Optic chiasm dimensions are associated with retinal measures and visual dysfunction. (3) The optic chiasm might be used as an easily accessible imaging marker of neurodegeneration in the anterior optic pathway with potential functional relevance

Functional connectome fingerprinting and stability in multiple sclerosis

BACKGROUND: Functional connectome fingerprinting can identify individuals based on their functional connectome. Previous studies relied mostly on short intervals between fMRI acquisitions. OBJECTIVE: This cohort study aimed to determine the stability of connectome-based identification and their underlying signatures in patients with multiple sclerosis and healthy individuals with long follow-up intervals. METHODS: We acquired resting-state fMRI in 70 patients with multiple sclerosis and 273 healthy individuals with long follow-up times (up to 4 and 9 years, respectively). Using functional connectome fingerprinting, we examined the stability of the connectome and additionally investigated which regions, connections and networks supported individual identification. Finally, we predicted cognitive and behavioural outcome based on functional connectivity. RESULTS: Multiple sclerosis patients showed connectome stability and identification accuracies similar to healthy individuals, with longer time delays between imaging sessions being associated with accuracies dropping from 89% to 76%. Lesion load, brain atrophy or cognitive impairment did not affect identification accuracies within the range of disease severity studied. Connections from the fronto-parietal and default mode network were consistently most distinctive, i.e., informative of identity. The functional connectivity also allowed the prediction of individual cognitive performances. CONCLUSION: Our results demonstrate that discriminatory signatures in the functional connectome are stable over extended periods of time in multiple sclerosis, resulting in similar identification accuracies and distinctive long-lasting functional connectome fingerprinting signatures in patients and healthy individuals