Axonal Orientation Research Articles

Multi-scale and Multimodal Fusion of Tract-tracing, Myelin Stain and DTI-derived Fibers in Macaque Brains.

Assessment of structural connectivity patterns of brains can be an important avenue for better understanding mechanisms of structural and functional brain architectures. Therefore, many efforts have been made to estimate and validate axonal pathways via a number of techniques, such as myelin stain, tract-tracing and diffusion MRI (dMRI). The three modalities have their own advantages and are complimentary to each other. From myelin stain data, we can infer rich in-plane information of axonal orientation at micro-scale. Tract-tracing data is considered as 'gold standard' to estimate trustworthy meso-scale pathways. dMRI currently is the only way to estimate global macro-scale pathways given further validation. We propose a framework to take advantage of these three modalities. Information of the three modalities is integrated to determine the optimal tractography parameters for dMRI fibers and identify cross-validated fiber bundles that are finally used to construct atlas. We demonstrate the effectiveness of the framework by a collection of experimental results.

A THREE-PHASE INDUCTIVE SENSOR FOR IN VIVO MEASUREMENT OF ELECTRICAL ANISOTROPY OF BIOLOGICAL TISSUES

Biological tissue will have anisotropy in electrical conductivity, due to the orientation of muscular fibers or neural axons as well as the distribution of large size blood vessels. Thus, the in vivo measurement of electrical conductivity anisotropy can be used to detect deep-seated vessels in large organs such as the liver during surgeries. For diagnostic applications, decrease of anisotropy may indicate the existence of cancer in anisotropic tissues such as the white matter of the brain or the mammary gland in the breast. In this paper, we will introduce a new tri-phase induction method to drive rotating high-frequency electrical current in the tissue for the measurement of electrical conductivity anisotropy. In the measurement, three electromagnets are symmetrically placed on the tissue surface and driven by high-frequency alternative currents of 0 kHz, modulated with 1 kHz 3-phase signals. In the center area of three magnets, magnetic fields are superimposed to produce a rotating induction current. This current produces electrical potentials among circularly arranged electrodes to be used to find the conductivity in each direction determined by the electrode pairs. To find the horizontal and vertical signal components, the measured potentials are amplified by a 2ch lock-in amplifier phase-locked with the 1 kHz reference signal. The superimposed current in the tissue was typically 45 micro Amperes when we applied 150 micro Tesla of magnetic field. We showed the validity of our method by conducting in vitro measurements with respect to artificially formed anisotropic materials and preliminary in vivo measurements on the pig’s liver. Compared to diffusion tensor MRI method, our anisotropy sensor is compact and advantageous for use during surgical operations because our method does not require strong magnetic field that may disturb ongoing surgical operations.

Solving the Orientation Specific Constraints in Transcranial Magnetic Stimulation by Rotating Fields

Transcranial Magnetic Stimulation (TMS) is a promising technology for both neurology and psychiatry. Positive treatment outcome has been reported, for instance in double blind, multi-center studies on depression. Nonetheless, the application of TMS towards studying and treating brain disorders is still limited by inter-subject variability and lack of model systems accessible to TMS. The latter are required to obtain a deeper understanding of the biophysical foundations of TMS so that the stimulus protocol can be optimized for maximal brain response, while inter-subject variability hinders precise and reliable delivery of stimuli across subjects. Recent studies showed that both of these limitations are in part due to the angular sensitivity of TMS. Thus, a technique that would eradicate the need for precise angular orientation of the coil would improve both the inter-subject reliability of TMS and its effectiveness in model systems. We show here how rotation of the stimulating field relieves the angular sensitivity of TMS and provides improvements in both issues. Field rotation is attained by superposing the fields of two coils positioned orthogonal to each other and operated with a relative phase shift in time. Rotating field TMS (rfTMS) efficiently stimulates both cultured hippocampal networks and rat motor cortex, two neuronal systems that are notoriously difficult to excite magnetically. This opens the possibility of pharmacological and invasive TMS experiments in these model systems. Application of rfTMS to human subjects overcomes the orientation dependence of standard TMS. Thus, rfTMS yields optimal targeting of brain regions where correct orientation cannot be determined (e.g., via motor feedback) and will enable stimulation in brain regions where a preferred axonal orientation does not exist.

The influence of anisotropy on brain injury prediction

Traumatic Brain Injury (TBI) occurs when a mechanical insult produces damage to the brain and disrupts its normal function. Numerical head models are often used as tools to analyze TBIs and to measure injury based on mechanical parameters. However, the reliability of such models depends on the incorporation of an appropriate level of structural detail and accurate representation of the material behavior. Since recent studies have shown that several brain regions are characterized by a marked anisotropy, constitutive equations should account for the orientation-dependence within the brain. Nevertheless, in most of the current models brain tissue is considered as completely isotropic. To study the influence of the anisotropy on the mechanical response of the brain, a head model that incorporates the orientation of neural fibers is used and compared with a fully isotropic model. A simulation of a concussive impact based on a sport accident illustrates that significantly lowered strains in the axonal direction as well as increased maximum principal strains are detected for anisotropic regions of the brain. Thus, the orientation-dependence strongly affects the response of the brain tissue. When anisotropy of the whole brain is taken into account, deformation spreads out and white matter is particularly affected. The introduction of local axonal orientations and fiber distribution into the material model is crucial to reliably address the strains occurring during an impact and should be considered in numerical head models for potentially more accurate predictions of brain injury.

A THREE-PHASE INDUCTIVE SENSOR FOR IN VIVO MEASUREMENT OF ELECTRICAL ANISOTROPY OF BIOLOGICAL TISSUES

Biological tissue will have anisotropy in electrical conductivity, due to the orientation of muscular fibers or neural axons as well as the distribution of large size blood vessels. Thus, the in vivo measurement of electrical conductivity anisotropy can be used to detect deep-seated vessels in large organs such as the liver during surgeries. For diagnostic applications, decrease of anisotropy may indicate the existence of cancer in anisotropic tissues such as the white matter of the brain or the mammary gland in the breast. In this paper, we will introduce a new tri-phase induction method to drive rotating high-frequency electrical current in the tissue for the measurement of electrical conductivity anisotropy. In the measurement, three electromagnets are symmetrically placed on the tissue surface and driven by high-frequency alternative currents of 0 kHz, modulated with 1 kHz 3-phase signals. In the center area of three magnets, magnetic fields are superimposed to produce a rotating induction current. This current produces electrical potentials among circularly arranged electrodes to be used to find the conductivity in each direction determined by the electrode pairs. To find the horizontal and vertical signal components, the measured potentials are amplified by a 2ch lock-in amplifier phase-locked with the 1 kHz reference signal. The superimposed current in the tissue was typically 45 micro Amperes when we applied 150 micro Tesla of magnetic field. We showed the validity of our method by conducting in vitro measurements with respect to artificially formed anisotropic materials and preliminary in vivo measurements on the pig’s liver. Compared to diffusion tensor MRI method, our anisotropy sensor is compact and advantageous for use during surgical operations because our method does not require strong magnetic field that may disturb ongoing surgical operations.

A Machine Learning Approach for Specification of Spinal Cord Injuries Using Fractional Anisotropy Values Obtained from Diffusion Tensor Images

Diffusion Tensor Imaging (DTI) uses in vivo images that describe extracellular structures by measuring the diffusion of water molecules. These images capture axonal movement and orientation using echo-planar imaging and provide critical information for evaluating lesions and structural damage in the central nervous system. This information can be used for prediction of Spinal Cord Injuries (SCIs) and for assessment of patients who are recovering from such injuries. In this paper, we propose a classification scheme for identifying healthy individuals and patients. In the proposed scheme, a dataset is first constructed from DTI images, after which the constructed dataset undergoes feature selection and classification. The experiment results show that the proposed scheme aids in the diagnosis of SCIs.

Microanisotropy imaging: quantification of microscopic diffusion anisotropy and orientational order parameter by diffusion MRI with magic-angle spinning of the q-vector

Diffusion tensor imaging (DTI) is the method of choice for non-invasive investigations of the structure of human brain white matter. The results are conventionally reported as maps of the fractional anisotropy (FA), which is a parameter related to microstructural features such as axon density, diameter, and myelination. The interpretation of FA in terms of microstructure becomes ambiguous when there is a distribution of axon orientations within the image voxel. In this paper, we propose a procedure for resolving this ambiguity by determining a new parameter, the microscopic fractional anisotropy (µFA), which corresponds to the FA without the confounding influence of orientation dispersion. In addition, we suggest a method for measuring the orientational order parameter (OP) for the anisotropic objects. The experimental protocol is capitalizing on a recently developed diffusion NMR pulse sequence based on magic-angle spinning of the q-vector. Proof-of-principle experiments are carried out on microimaging and clinical MRI equipment using lyotropic liquid crystals and plant tissues as model materials with high µFA and low FA on account of orientation dispersion. We expect the presented method to be especially fruitful in combination with DTI and high angular resolution acquisition protocols for neuroimaging studies of grey and white matter.

Characterizing Brain Structures and Remodeling after TBI Based on Information Content, Diffusion Entropy

BackgroundTo overcome the limitations of conventional diffusion tensor magnetic resonance imaging resulting from the assumption of a Gaussian diffusion model for characterizing voxels containing multiple axonal orientations, Shannon's entropy was employed to evaluate white matter structure in human brain and in brain remodeling after traumatic brain injury (TBI) in a rat.MethodsThirteen healthy subjects were investigated using a Q-ball based DTI data sampling scheme. FA and entropy values were measured in white matter bundles, white matter fiber crossing areas, different gray matter (GM) regions and cerebrospinal fluid (CSF). Axonal densities' from the same regions of interest (ROIs) were evaluated in Bielschowsky and Luxol fast blue stained autopsy (n = 30) brain sections by light microscopy. As a case demonstration, a Wistar rat subjected to TBI and treated with bone marrow stromal cells (MSC) 1 week after TBI was employed to illustrate the superior ability of entropy over FA in detecting reorganized crossing axonal bundles as confirmed by histological analysis with Bielschowsky and Luxol fast blue staining.ResultsUnlike FA, entropy was less affected by axonal orientation and more affected by axonal density. A significant agreement (r = 0.91) was detected between entropy values from in vivo human brain and histologically measured axonal density from post mortum from the same brain structures. The MSC treated TBI rat demonstrated that the entropy approach is superior to FA in detecting axonal remodeling after injury. Compared with FA, entropy detected new axonal remodeling regions with crossing axons, confirmed with immunohistological staining.ConclusionsEntropy measurement is more effective in distinguishing axonal remodeling after injury, when compared with FA. Entropy is also more sensitive to axonal density than axonal orientation, and thus may provide a more accurate reflection of axonal changes that occur in neurological injury and disease.

Development and validation of an advanced anisotropic visco-hyperelastic human brain FE model

This paper proposes the implementation of fractional anisotropy and axonal fiber orientation from diffusion tensor imaging (DTI) of 12 healthy patients into an existing human FE head model to develop a more realistic brain model with advanced constitutive laws. Further, the brain behavior was validated in terms of brain strain against experimental data published by Hardy et al. (2001, 2007) and for brain pressure against Nahum et al. (1977) experimental impacts. A reasonable agreement was observed between the simulation and experimental data. Results showed the feasibility of integrating axonal direction information into FE analysis and established the context of computation of axonal elongation in case of head trauma.

Neuron Glia-Related Cell Adhesion Molecule (NrCAM) Promotes Topographic Retinocollicular Mapping

NrCAM (Neuron-glial related cell adhesion molecule), a member of the L1 family of cell adhesion molecules, reversibly binds ankyrin and regulates axon growth, but it has not been studied for a role in retinotopic mapping. During development of retino-collicular topography, NrCAM was expressed uniformly in retinal ganglion cells (RGCs) along both mediolateral and anteroposterior retinal axes, and was localized on RGC axons within the optic tract and superior colliculus (SC). Anterograde tracing of RGC axons in NrCAM null mutant mice at P10, when the map resembles its mature form, revealed laterally displaced ectopic termination zones (eTZs) of axons from the temporal retina, indicating defective mediolateral topography, which is governed by ephrinB/EphBs. Axon tracing at P2 revealed that interstitial branch orientation of ventral-temporal RGC axons in NrCAM null mice was compromised in the medial direction, likely accounting for displacement of eTZs. A similar retinocollicular targeting defect in EphB mutant mice suggested that NrCAM and EphB interact to regulate mediolateral retino-collicular targeting. We found that EphB2 tyrosine kinase but not an EphB2 kinase dead mutant, phosphorylated NrCAM at a conserved tyrosine residue in the FIGQY ankyrin binding motif, perturbing ankyrin recruitment in NrCAM transfected HEK293 cells. Furthermore, the phosphorylation of NrCAM at FIGQY in SC was decreased in EphB1/3 and EphB1/2/3 null mice compared to WT, while phospho-FIGQY of NrCAM in SC was increased in EphB2 constitutively active (F620D/F620D) mice. These results demonstrate that NrCAM contributes to mediolateral retinocollicular axon targeting by regulating RGC branch orientation through a likely mechanism in which ephrinB/EphB phosphorylates NrCAM to modulate linkage to the actin cytoskeleton.

Microstructural organization of axons in the human corpus callosum quantified by diffusion-weighted magnetic resonance spectroscopy of N-acetylaspartate and post-mortem histology

Diffusion-weighted magnetic resonance spectroscopy of brain metabolites offers unique access to compartment-specific microstructural information on neural tissue. Here, we investigated in detail the diffusion characteristics of the neuronal/axonal markers N-acetylaspartate+N-acetyl aspartyl glutamate (tNAA) in a small region of the human corpus callosum at 7T. The diffusion-weighted spectroscopy data were analyzed by fitting to a model in which information about cross-callosal tract orientation within the spectroscopy volume, obtained from diffusion tensor imaging data, was incorporated. We estimated the microscopic misalignment of axons (σ φ =18.6°±3.0°) in excellent agreement with independent histological results (σ φ =18.1°±4.6°) obtained from microscopic analysis of axonal orientations in the body of the corpus callosum from post-mortem human brain slices. We also robustly quantified the diffusion coefficient of tNAA (0.51±0.06×10(-3)mm(2)/s) in axonal cytoplasm, unbiased by the tract curvature. This work supports the notion that microscopic axonal misalignment is a dominant microstructural property in white matter tracts and has a strong impact on the evaluation of tissue microstructure using diffusion information, and should therefore be taken into consideration in the evaluation of white matter microstructure. Additionally, this study enabled robust and unbiased assessment of the cytosolic diffusion coefficient of tNAA, a potential biomarker for axonopathy and neuronal degeneration.

Anatomical validation of diffusion tensor imaging (DTI)

The Magnetic Resonance Image (MRI) based Diffusion Tensor Imaging (DTI) technique reveals brain white matter architecture in vivo by measuring the direction of the diffusion of water molecules along the anisotropic fiber bundles. Validation of DTI at present is limited to qualitative comparisons of previously known connections in the common normal human brain. Anatomical validation of DTI through histological analysis ensures that each image is representative of the inherent white matter architecture, and improves algorithms that create a tractographic image from the tensor signals in each voxel of the image. Human brain samples were imaged at 3 Tesla (T) (2.5 mm voxels) followed by sectioning and histologic processing of the tissue. Results comparing the histologic data to the imaging show good correspondence in white matter areas between both fiber integrity and axonal orientation. Vector coordinates drawn from the tissue image match the principal fiber direction derived from the probability density function of the corresponding image voxel. We anticipate that this will provide a valuable resource for the validation of DTI methods.Grant Funding Source: NIH/NIA 1 R21 AG037843‐02, NIH/NCRR P41 RR013642‐12S1, Translational Research Fund (UCLA), and the McGinty Family Foundation

Tissue engineering the retinal ganglion cell nerve fiber layer

Retinal degenerative diseases, such as glaucoma and macular degeneration, affect millions of people worldwide and ultimately lead to retinal cell death and blindness. Cell transplantation therapies for photoreceptors demonstrate integration and restoration of function, but transplantation into the ganglion cell layer is more complex, requiring guidance of axons from transplanted cells to the optic nerve head in order to reach targets in the brain. Here we create a biodegradable electrospun (ES) scaffold designed to direct the growth of retinal ganglion cell (RGC) axons radially, mimicking axon orientation in the retina. Using this scaffold we observed an increase in RGC survival and no significant change in their electrophysiological properties. When analyzed for alignment, 81% of RGCs were observed to project axons radially along the scaffold fibers, with no difference in alignment compared to the nerve fiber layer of retinal explants. When transplanted onto retinal explants, RGCs on ES scaffolds followed the radial pattern of the host retinal nerve fibers, whereas RGCs transplanted directly grew axons in a random pattern. Thus, the use of this scaffold as a cell delivery device represents a significant step towards the use of cell transplant therapies for the treatment of glaucoma and other retinal degenerative diseases.

The role of tissue microstructure and water exchange in biophysical modelling of diffusion in white matter

Biophysical models that describe the outcome of white matter diffusion MRI experiments have various degrees of complexity. While the simplest models assume equal-sized and parallel axons, more elaborate ones may include distributions of axon diameters and axonal orientation dispersions. These microstructural features can be inferred from diffusion-weighted signal attenuation curves by solving an inverse problem, validated in several Monte Carlo simulation studies. Model development has been paralleled by microscopy studies of the microstructure of excised and fixed nerves, confirming that axon diameter estimates from diffusion measurements agree with those from microscopy. However, results obtained in vivo are less conclusive. For example, the amount of slowly diffusing water is lower than expected, and the diffusion-encoded signal is apparently insensitive to diffusion time variations, contrary to what may be expected. Recent understandings of the resolution limit in diffusion MRI, the rate of water exchange, and the presence of microscopic axonal undulation and axonal orientation dispersions may, however, explain such apparent contradictions. Knowledge of the effects of biophysical mechanisms on water diffusion in tissue can be used to predict the outcome of diffusion tensor imaging (DTI) and of diffusion kurtosis imaging (DKI) studies. Alterations of DTI or DKI parameters found in studies of pathologies such as ischemic stroke can thus be compared with those predicted by modelling. Observations in agreement with the predictions strengthen the credibility of biophysical models; those in disagreement could provide clues of how to improve them. DKI is particularly suited for this purpose; it is performed using higher b-values than DTI, and thus carries more information about the tissue microstructure. The purpose of this review is to provide an update on the current understanding of how various properties of the tissue microstructure and the rate of water exchange between microenvironments are reflected in diffusion MRI measurements. We focus on the use of biophysical models for extracting tissue-specific parameters from data obtained with single PGSE sequences on clinical MRI scanners, but results obtained with animal MRI scanners are also considered. While modelling of white matter is the central theme, experiments on model systems that highlight important aspects of the biophysical models are also reviewed.

Steerable-filter based quantification of axonal populations at the developing optic chiasm reveal significant defects in Slit2 −/− as well as Slit1 −/− Slit2 −/− embryos

BackgroundPrevious studies have suggested that the axon guidance proteins Slit1 and Slit2 co-operate to establish the optic chiasm in its correct position at the ventral diencephalic midline. This is based on the observation that, although both Slit1 and Slit2 are expressed around the ventral midline, mice defective in either gene alone exhibit few or no axon guidance defects at the optic chiasm whereas embryos lacking both Slit1 and Slit2 develop a large additional chiasm anterior to the chiasm’s normal position. Here we used steerable-filters to quantify key properties of the population of axons at the chiasm in wild-type, Slit1−/−, Slit2−/− and Slit1−/−Slit2−/− embryos.ResultsWe applied the steerable-filter algorithm successfully to images of embryonic retinal axons labelled from a single eye shortly after they have crossed the midline. We combined data from multiple embryos of the same genotype and made statistical comparisons of axonal distributions, orientations and curvatures between genotype groups. We compared data from the analysis of axons with data on the expression of Slit1 and Slit2. The results showed a misorientation and a corresponding anterior shift in the position of many axons at the chiasm of both Slit2−/− and Slit1−/−Slit2−/− mutants. There were very few axon defects at the chiasm of Slit1−/− mutants.ConclusionsWe found defects of the chiasms of Slit1−/−Slit2−/− and Slit1−/− mutants similar to those reported previously. In addition, we discovered previously unreported defects resulting from loss of Slit2 alone. This indicates the value of a quantitative approach to complex pathway analysis and shows that Slit2 can act alone to control aspects of retinal axon routing across the ventral diencephalic midline.

Electric axon guidance in embryonic retina: Galvanotropism revisited

In addition to well-known mechanisms of chemical guidance, growing axons in the nervous system are directed by an extracellular electric field in a process known as galvanotropism. The galvanotropic behavior of nerve cells in vitro was first demonstrated as long ago as 1920. However, it remains unknown whether embryonic nerve tissues generate a similar electric field in order to guide growing axons. The present study reveals that an extracellular voltage gradient exists in the embryonic retina and that this gradient guides the axons of newborn retinal ganglion cells towards their targets. These findings indicate an important role for galvanotropism in the initial orientation of axons that extend over long distances, and provide insight into the mechanisms underlying the proper extension of developing axons in the embryonic brain.

Finite Element Modeling of CNS White Matter Kinematics: Use of a 3D RVE to Determine Material Properties.

Axonal injury represents a critical target area for the prevention and treatment of traumatic brain and spinal cord injuries. Finite element (FE) models of the head and/or brain are often used to predict brain injury caused by external mechanical loadings, such as explosive waves and direct impact. The accuracy of these numerical models depends on correctly determining the material properties and on the precise depiction of the tissues’ microstructure (microscopic level). Moreover, since the axonal microstructure for specific regions of the brain white matter is locally oriented, the stress, and strain fields are highly anisotropic and axon orientation dependent. Additionally, mechanical strain has been identified as the proximal cause of axonal injury, which further demonstrates the importance of this multi-scale relationship. In this study, our previously developed FE and kinematic axonal models are coupled and applied to a pseudo 3-dimensional representative volume element of central nervous system white matter to investigate the multi-scale mechanical behavior. An inverse FE procedure was developed to identify material parameters of spinal cord white matter by combining the results of uniaxial testing with FE modeling. A satisfactory balance between simulation and experiment was achieved via optimization by minimizing the squared error between the simulated and experimental force-stretch curve. The combination of experimental testing and FE analysis provides a useful analysis tool for soft biological tissues in general, and specifically enables evaluations of the axonal response to tissue-level loading and subsequent predictions of axonal damage.

Axon orientation by gradient of cytochalasin D inside microfluidic device

This paper describes the development of a microfluidic device for axon orientation. The device was fabricated with poly (dimethylsiloxane) by soft lithography and replica molding. There were two separated rooms in the device, and a control system and stable concentration gradient system were maintained in each room for at least 24 h. Finally, to demonstrate a practical application of the device, neuronal cells were cultured in both cell rooms, and the growth of cells and formation of axons were monitored under a concentration gradient of cytochalasin D for 8 h. Quantitative analysis of the orientation of axons was analyzed, and the data were plotted in a polar graph as a function of the direction. A figure of 33.8% of positive responding neurons were found in the cytochalasin D gradient room, while that figure was 23.3% of cells in control room. The extent of axon orientation shows a considerable difference between the two rooms, and the device developed here is capable of investigating axon orientation and can be used for other biological applications.

Automated determination of axonal orientation in the deep white matter of the human brain.

The wide-spread utilization of diffusion-weighted imaging in the clinical neurosciences to assess white-matter (WM) integrity and architecture calls for robust validation strategies applied to the data that are acquired with noninvasive imaging. However, the pathology and detailed fiber architecture of WM tissue can only be observed postmortem. With these considerations in mind, we designed an automated method for the determination of axonal orientation in high-resolution microscope images. The algorithm was tested on tissue that was stained using a silver impregnation technique that was optimized to resolve axonal fibers against very low levels of background. The orientation of individual nerve fibers was detected using spatial filtering and a template-matching algorithm, and the results are displayed as color-coded overlays. Quantitative models of WM fiber architecture at the microscopic level can lead to improved interpretation of low-resolution neuroimaging data and to more accurate mapping of fiber pathways in the human brain.

Serial section registration of axonal confocal microscopy datasets for long-range neural circuit reconstruction

In the context of long-range digital neural circuit reconstruction, this paper investigates an approach for registering axons across histological serial sections. Tracing distinctly labeled axons over large distances allows neuroscientists to study very explicit relationships between the brain's complex interconnects and, for example, diseases or aberrant development. Large scale histological analysis requires, however, that the tissue be cut into sections. In immunohistochemical studies thin sections are easily distorted due to the cutting, preparation, and slide mounting processes. In this work we target the registration of thin serial sections containing axons. Sections are first traced to extract axon centerlines, and these traces are used to define registration landmarks where they intersect section boundaries. The trace data also provides distinguishing information regarding an axon's size and orientation within a section. We propose the use of these features when pairing axons across sections in addition to utilizing the spatial relationships among the landmarks. The global rotation and translation of an unregistered section are accounted for using a random sample consensus (RANSAC) based technique. An iterative nonrigid refinement process using B-spline warping is then used to reconnect axons and produce the sought after connectivity information.