Rapid Quantification of White Matter Disconnection in the Human Brain
Abdelrahman Zayed, Yasser Iturria-Medina, Arno Villringer, Bernhard Sehm, Christopher J. Steele
RRapid Quantification of White Matter Disconnection in the HumanBrain
Abdelrahman Zayed , Yasser Iturria-Medina , Arno Villringer , Bernhard Sehm and Christopher J. Steele Abstract — With an estimated five million new stroke sur-vivors every year and a rapidly aging population sufferingfrom hyperintensities and diseases of presumed vascular originthat affect white matter and contribute to cognitive decline,it is critical that we understand the impact of white matterdamage on brain structure and behavior. Current techniques forassessing the impact of lesions consider only location, type, andextent, while ignoring how the affected region was connectedto the rest of the brain. Regional brain function is a product ofboth local structure and its connectivity. Therefore, obtaininga map of white matter disconnection is a crucial step thatcould help us predict the behavioral deficits that patientsexhibit. In the present work, we introduce a new practicalmethod for computing lesion-based white matter disconnectionmaps that require only moderate computational resources. Weachieve this by creating diffusion tractography models of thebrains of healthy adults and assessing the connectivity betweensmall regions. We then interrupt these connectivity models byprojecting patients’ lesions into them to compute predictedwhite matter disconnection. A quantified disconnection mapcan be computed for an individual patient in approximately35 seconds using a single core CPU-based computation. Incomparison, a similar quantification performed with other toolsprovided by MRtrix3 takes 5.47 minutes.
I. INTRODUCTIONThe problem of relating the location of a lesion to itsbehavioral effect has been studied by many researchers [1]–[5]. Bates et al. [6] developed a method called voxel-basedlesion-symptom mapping (VLSM) which relates overlap-ping lesion locations to common behavioural deficits. Thismethod does not require that a specific region of interestis identified, but does require overlap between the lesions.Depending on the type of clinical measure that is beingtargeted, different types of tests are performed to identifythe regions responsible for a specific impairment. Rorden *This research was funded by the Quebec Bio-imaging Network, Mon-treal, Quebec, Canada and Max Planck Institute for Human Cognitive andBrain Sciences, Leipzig, Germany. Abdelrahman Zayed is with Department of Electrical and Computer En-gineering and PERFORM Centre, Concordia University, Montreal, Quebec,Canada a [email protected] Yasser Iturria-Medina is with Department of Neurology andNeurosurgery, McGill University, Montreal, Quebec, Canada [email protected] Arno Villringer is the Director of the Department of Neurology,Max Planck Institute for Human Cognitive and Brain Sciences andClinic for Cognitive Neurology, University of Leipzig, Leipzig, Germany [email protected] Bernhard Sehm is with Department of Neurology, Max Planck Institutefor Human Cognitive and Brain Sciences and Clinic for Cognitive Neurol-ogy, University of Leipzig, Leipzig, Germany [email protected] Christopher J. Steele is with Department of Psy-chology, Concordia University, Montreal, Quebec, Canada [email protected] et al. [7] proposed further statistical enhancements thatcan provide more specific results than standard VLSM. Inaddition, Gleichgerrcht et al. [8] indicate that VLSM maybe supplanted by the concept of connectome-based lesion-symptom mapping. This work, and our own, assumes thatdamage does not exist only in the lesion location, but alsoextends to all other regions that are connected to the lesionthrough the underlying white matter architecture. Kuceyeski et al. [9] proposed the first method for generating lesion-based white matter disconnection maps with data fromdiffusion-weighted magnetic resonance imaging (DW-MRI):the network modification (NeMo) tool. Damage is computedfor the regions that are connected both directly (i.e. they lieinside the lesion volume) and indirectly (i.e. there is a whitematter connection between the lesion and a given region).Although all of the mentioned methods have acceptableperformance in identifying the regions that are responsiblefor behavioral deficits, they also have some drawbacks.Voxel-based methods such as [6] and [7] study the damagedue to brain injury in a voxel-by-voxel manner, requiringlesion overlap within the population for statistical signif-icance, and completely ignoring the fact that there arelesion effects that extend beyond the visible damage andthroughout the brain, according to underlying white matterarchitecture. The method used in [9] relies on a network ofpre-defined anatomical regions and takes up to several hoursto produce the disconnection map; thus restricting its generalapplicability and practical use.In this paper, we introduce a new method based onhuman DW-MRI estimates of white matter connectivity thatcan take as little as 35 seconds to produce a lesion-baseddisconnection map. Given a patient lesion and known modelof normative brain connectivity, we use the lesion’s spatiallocation to interrupt connections and quantify the degree ofdisconnection between all regions of the brain. This methodcould be applied in a clinical context to predict behavioraldeficits in individual patients and patient populations. Ourmethod has been tested on both simulated and real data froma stroke patient, and provides rapid results that are similarto those produced with MRtrix3 [10].II. METHODIn this section we describe our model and show howwe can modify it to further improve the resolution of thedisconnection map. a r X i v : . [ q - b i o . N C ] M a y . Model description In order to be able to accurately compute the damage inevery region in the brain as a result of having a lesion, wepartition the brain volume into nodes, where each node isa cube of side length l , such that l is a hyperparameterchosen by the user. Every node is further partitioned intoeven smaller units called voxels, such that a voxel is a tinycube of dimensions 1 mm × mm × mm . Hence, the nodecontains l voxels.For any model of the brain, we use MRtrix3 (a set of toolsfor analyzing DW-MRI images) to generate probabilisticwhite matter connectivity between every pair of nodes. Wethen compute the two matrices that are used to calculatequantified disconnection maps. The first matrix is referredto as the connectivity matrix, which has the number ofconnections (probabilistic streamline counts) between anytwo nodes in the brain. The second matrix is the weightsmatrix, which describes the density of connections at eachvoxel. It is important to note that these two matrices needto be computed only once offline using MRtrix3, subsequentcalculations use them to compute the disconnection map.Given a lesion in any spatial location within the brain, weclassify the affected nodes into two types: directly affected(nodes that lie inside the lesion volume) and indirectlyaffected (located outside the lesion volume but connected todirectly affected nodes). In every node, we define a metriccalled damage, which is a number that goes from 0, when noconnections are affected, to 1 when all connections from/tothis node are affected. To compute the overall damage due tothe lesion, we take the union of both the direct and indirectdamage, as described in detail below.
1) Computing the direct damage:
To compute the directdamage in a certain node that lies partially or completelyinside the lesion volume, we calculate the ratio between thevolume of the node inside the lesion to the total volume ofthe node. In other words, we calculate the ratio between thenumber of node voxels inside the lesion to the total numberof node voxels as shown in Eq.1: d direct [ i ] = N [ i ] l (1)such that: • d direct [ i ] is the direct damage at node i . • N [ i ] is the number of voxels in node i that lie inside thelesion volume. • l is the total number of voxels in the node.The direct damage is 1 for nodes that lie completely insidethe lesion volume. Fig.1 shows an example of how the directdamage is computed for different nodes.
2) Computing the indirect damage:
To illustrate the con-cept of indirect damage, consider having two nodes A and Bthat are connected. Assume that node A has direct damagebecause it lies within the lesion volume. Node B, on the otherhand, does not lie inside the lesion volume and thereforedoes not have direct damage. However, node B has indirectdamage as a result of its connection to node A. To calculate the damage that occurs to the nodes thatdo not lie inside the lesion volume (i.e. indirectly affectednodes), we need to know the number of connections theyhave with the directly affected nodes and with the rest of thenodes in the brain. This is computed using the connectivitymatrix, where we infer indirect damage at node i as follows: d indirect [ i ] = ∑ Qj = W i j d direct [ j ] ∑ Mj = W i j (2)where: • d indirect [ i ] refers to the indirect damage at node i . • Q is the total number of directly affected nodes. • W i j is the number of connections between nodes i and j . • M is the total number of nodes that we have in the brain.Fig. 2 shows an example with three different nodes A, Band C. Assuming that nodes A and C are directly affectedby a lesion, it is required to compute the indirect effect atnode B. By applying Eq. 2, we can deduce that the indirectdamage at node B is 60%. B. Increasing the resolution of the disconnection map
The damage computed from Eq. 1 and 2 is for the wholenode. Since our nodes are of size l mm × l mm × l mm ,which is equivalent to l voxels, this means that all of the l voxels inside the node share the same damage. This isan acceptable approximation given the theoretical accuracyof probabilistic tractography for relatively small values of l ,but as l increases the resolution will degrade. The effectiveresolution of our approach can, however, be improved withminimal computational time. This is achieved by allowingdifferent voxels inside a given node to have different damage.This yields an approximate l times increase in the resolutionand leads to a substantial improvement in the spatial accuracyof damage distribution within the node.The idea depends on using the weights matrix that waspreviously generated by MRtrix3. Intuitively, voxels withhigh connectome density would have more damage comparedto those with less connectome density inside the same node.Assuming we have node i with a damage d [ i ] (the unionof d direct [ i ] and d indirect [ i ] ), instead of having this value ineach of the l voxels inside the node, d [ i ] will change fromone voxel to another by a modulation factor that is the ratiobetween the connectome density in a voxel to the averageconnectome density of its parent node. Therefore, if a voxellying inside a certain node has twice the average connectomedensity of its parent node, its modulated damage will betwice its original damage.III. EXPERIMENTS AND RESULTSIn this section, we compare the performance of our methodon lesions from both simulated and real masks. We set l to 5, rendering nodes of volume 125 mm , for a total of31,262 nodes inside the brain volume. We also show theeffect of increasing the resolution of the disconnection map.After that, we will discuss the running time of our method,which is considered to be one of its main advantages. % damage 70 % damage 100 % damage Fig. 1: Computing the direct damage for different nodes.
20 % damage
Node A Node B × 100 % + × 20 % = 60 % damage Node C
Fig. 2: An example for computing the indirect damage for a certain node. Nodes A and C are directly affected as they liepartially or completely inside the lesion volume, whereas node B is indirectly affected as it is connected to them.
A. Results on simulated data
Fig.3 (A-C) shows a comparison between the disconnec-tion map produced by both our method, before and aftermodulation to increase resolution, and MRtrix3 when testedon a lesion from a simulated mask in the corpus callosum.We can observe that the modification we introduced for thedisconnection map substantially increased the resolution andbrings our results closer to those of MRtrix3.
B. Results on real data
Fig.3 (D-F) shows a comparison between the disconnec-tion map produced by both our method, before and afterincreasing the resolution, and MRtrix3 when tested on alesion from a real mask obtained from a stroke patient. Asobserved before with the simulated data, our method gives avery close approximation to the actual disconnection map.
C. Running time
Our method takes an average of 35 seconds on an 8thgeneration 2.7 GHz Intel core i7 computer with a lesion thatimparts direct damage to 33 nodes. All of our code is writtenin Python (v3.6). Computation time will scale with lesionvolume. It is important to mention that the modification weintroduced to increase the resolution of the disconnectionmap will only add an extra 1 second to the running time.MRtrix3, on the other hand, takes 5.47 minutes to producea slightly higher resolution disconnection map. IV. DISCUSSION AND FUTURE WORKIn this paper, we present a rapid and practical methodfor quantifying the impact of white matter disconnectionin individual patients that requires little computational andstorage resources. Our method is more than 9 times fasterthan MRtrix3, which is currently one of the most widelyused tools for the analyses of DW-MRI. We also showedhow to increase the spatial resolution of our disconnectionmap by approximately 125 times, without adding significantoverhead to the running time. The resulting maps of dis-connection are patient-specific, quantitative, and thereforeenable direct comparison between patients suffering froma variety of lesions in different locations and with differ-ent behavioral deficits. Our method leverages pre-computedconnectivity and weights matrices to reduce storage spaceand decrease computation time. Each model is reduced fromapproximately 6 GB (raw probabilistic streamlines file usedin the MRtrix3 comparison computations) to less than 300MB (connectivity and weights matrices when l = 5).Our future work will focus on extending the currentmethod to calculate the disconnection map from brain modelscomputed from a variety of different brains, which wouldyield multiple disconnection maps. This would enable usto calculate an approximate population distribution for thedamage in every node across different brain models. Themedian disconnection map should be a more accurate discon-nection map, taking into consideration individual variability.Our method will also be embedded into a user-friendly toolig. 3: Disconnection maps obtained using different methods. The first row shows the disconnection maps due to a simulatedlesion in the corpus callosum, where A and B refer to the result of our method before and after modulation respectively,while C refers to the result of MRtrix3. The second row shows the results due to a real lesion from a stroke patient, whereD and E refer to our method before and after modulation respectively, while F refers to MRtrix3.that will be made publicly available. Further extension to ourwork would include relating the disconnection maps obtainedto the behavioral effects on patients.ACKNOWLEDGMENTPatient lesion data was collected at the Max PlanckInstitute for Human Cognitive and Brain Sciences NeurologyClinic and provided by Dr. Bernhard Sehm with the help ofLeila Gajiyeva. The simulated mask in the corpus callosumwas provided by Dr. Christopher Steele. The model brainused to generate the probabilistic streamlines and connectiv-ity matrices was obtained from the publicly available HumanConnectome Project [11].R EFERENCES[1] A. Charil, A. P. Zijdenbos, J. Taylor, C. Boelman, K. J. Worsley, A. C.Evans, and A. Dagher, “Statistical mapping analysis of lesion locationand neurological disability in multiple sclerosis: application to 452patient data sets,”
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