The term “in situ processing” has evolved over the last decade to mean both a specific strategy for visualizing and analyzing data and an umbrella term for a processing paradigm. The resulting confusion makes it difficult for visualization and analysis scientists to communicate with each other and with their stakeholders. To address this problem, a group of over fifty experts convened with the goal of standardizing terminology. This paper summarizes their findings and proposes a new terminology for describing in situ systems. An important finding from this group was that in situ systems are best described via multiple, distinct axes: integration type, proximity, access, division of execution, operation controls, and output type. This paper discusses these axes, evaluates existing systems within the axes, and explores how currently used terms relate to the axes.
L. Cinquini, S. Petruzza, Jason J. Boutte, S. Ames, G. Abdulla, V. Balaji, R. Ferraro, A. Radhakrishnan, L. Carriere, T. Maxwell, G. Scorzelli, V. Pascucci. Distributed Resources for the Earth System Grid Advanced Management (DREAM), Final Report, 2020.
The DREAM project was funded more than 3 years ago to design and implement a next-generation ESGF (Earth System Grid Federation ) architecture which would be suitable for managing and accessing data and services resources on a distributed and scalable environment. In particular, the project intended to focus on the computing and visualization capabilities of the stack, which at the time were rather primitive. At the beginning, the team had the general notion that a better ESGF architecture could be built by modularizing each component, and redefining its interaction with other components by defining and exposing a well defined API. Although this was still the high level principle that guided the work, the DREAM project was able to accomplish its goals by leveraging new practices in IT that started just about 3 or 4 years ago: the advent of containerization technologies (specifically, Docker), the development of frameworks to manage containers at scale (Docker Swarm and Kubernetes), and their application to the commercial Cloud. Thanks to these new technologies, DREAM was able to improve the ESGF architecture (including its computing and visualization services) to a level of deployability and scalability beyond the original expectations.
Objective: Clinical outcomes from deep brain stimulation (DBS) can be highly variable, and two critical factors underlying this variability are the location and type of stimulation. In this study we quantified how robustly DBS activates a target region when taking into account a range of different lead designs and realistic variations in placement. The objective of the study is to assess the likelihood of achieving target activation.
Approach: We performed finite element computational modeling and established a metric of performance robustness to evaluate the ability of directional and multi-lead configurations to activate target fiber pathways while taking into account location variability. A more robust lead configuration produces less variability in activation across all stimulation locations around the target.
Main results: Directional leads demonstrated higher overall performance robustness compared to axisymmetric leads, primarily 1-2 mm outside of the target. Multi-lead configurations demonstrated higher levels of robustness compared to any single lead due to distribution of electrodes in a broader region around the target.
Significance: Robustness measures can be used to evaluate the performance of existing DBS lead designs and aid in the development of novel lead designs to better accommodate known variability in lead location and orientation. This type of analysis may also be useful to understand how DBS clinical outcome variability is influenced by lead location among groups of patients.
K. A. Johnson, G. Duffley, D. Nesterovich Anderson, J. L. Ostrem, M. Welter, J. C. Baldermann, J. Kuhn, D. Huys, V. Visser-Vandewalle, T. Foltynie, L. Zrinzo, M. Hariz, A. F. G. Leentjens, A. Y. Mogilner, M. H. Pourfar, L. Almeida, A. Gunduz, K. D. Foote, M. S. Okun, C. R. Butson.
Structural connectivity predicts clinical outcomes of deep brain stimulation for Tourette syndrome, In Brain, July, 2020.
Deep brain stimulation may be an effective therapy for select cases of severe, treatment-refractory Tourette syndrome; however, patient responses are variable, and there are no reliable methods to predict clinical outcomes. The objectives of this retrospective study were to identify the stimulation-dependent structural networks associated with improvements in tics and comorbid obsessive-compulsive behaviour, compare the networks across surgical targets, and determine if connectivity could be used to predict clinical outcomes. Volumes of tissue activated for a large multisite cohort of patients (n = 66) implanted bilaterally in globus pallidus internus (n = 34) or centromedial thalamus (n = 32) were used to generate probabilistic tractography to form a normative structural connectome. The tractography maps were used to identify networks that were correlated with improvement in tics or comorbid obsessive-compulsive behaviour and to predict clinical outcomes across the cohort. The correlated networks were then used to generate ‘reverse’ tractography to parcellate the total volume of stimulation across all patients to identify local regions to target or avoid. The results showed that for globus pallidus internus, connectivity to limbic networks, associative networks, caudate, thalamus, and cerebellum was positively correlated with improvement in tics; the model predicted clinical improvement scores (P = 0.003) and was robust to cross-validation. Regions near the anteromedial pallidum exhibited higher connectivity to the positively correlated networks than posteroventral pallidum, and volume of tissue activated overlap with this map was significantly correlated with tic improvement (P < 0.017). For centromedial thalamus, connectivity to sensorimotor networks, parietal-temporal-occipital networks, putamen, and cerebellum was positively correlated with tic improvement; the model predicted clinical improvement scores (P = 0.012) and was robust to cross-validation. Regions in the anterior/lateral centromedial thalamus exhibited higher connectivity to the positively correlated networks, but volume of tissue activated overlap with this map did not predict improvement (P > 0.23). For obsessive-compulsive behaviour, both targets showed that connectivity to the prefrontal cortex, orbitofrontal cortex, and cingulate cortex was positively correlated with improvement; however, only the centromedial thalamus maps predicted clinical outcomes across the cohort (P = 0.034), but the model was not robust to cross-validation. Collectively, the results demonstrate that the structural connectivity of the site of stimulation are likely important for mediating symptom improvement, and the networks involved in tic improvement may differ across surgical targets. These networks provide important insight on potential mechanisms and could be used to guide lead placement and stimulation parameter selection, as well as refine targets for neuromodulation therapies for Tourette syndrome.
B. Kundu, T. S. Davis, B. Philip, E. H. Smith, A. Arain, A. Peters, B. Newman, C. R. Butson, J. D. Rolston. A systematic exploration of parameters affecting evoked intracranial potentials in patients with epilepsy, In Brain Stimulation, Vol. 13, No. 5, pp. 1232-1244. 2020.
Brain activity is constrained by and evolves over a network of structural and functional connections. Corticocortical evoked potentials (CCEPs) have been used to measure this connectivity and to discern brain areas involved in both brain function and disease. However, how varying stimulation parameters influences the measured CCEP across brain areas has not been well characterized.
To better understand the factors that influence the amplitude of the CCEPs as well as evoked gamma-band power (70–150 Hz) resulting from single-pulse stimulation via cortical surface and depth electrodes.
CCEPs from 4370 stimulation-response channel pairs were recorded across a range of stimulation parameters and brain regions in 11 patients undergoing long-term monitoring for epilepsy. A generalized mixed-effects model was used to model cortical response amplitudes from 5 to 100 ms post-stimulation.
Stimulation levels <5.5 mA generated variable CCEPs with low amplitude and reduced spatial spread. Stimulation at ≥5.5 mA yielded a reliable and maximal CCEP across stimulation-response pairs over all regions. These findings were similar when examining the evoked gamma-band power. The amplitude of both measures was inversely correlated with distance. CCEPs and evoked gamma power were largest when measured in the hippocampus compared with other areas. Larger CCEP size and evoked gamma power were measured within the seizure onset zone compared with outside this zone.
These results will help guide future stimulation protocols directed at quantifying network connectivity across cognitive and disease states.
Determining uranium ore concentrates and their calcination products via image classification of multiple magnifications, In Journal of Nuclear Materials, 2020.C. Ly, C. Vachet, I. Schwerdt, E. Abbott, A. Brenkmann, L.W. McDonald, T. Tasdizen.
Many tools, such as mass spectrometry, X-ray diffraction, X-ray fluorescence, ion chromatography, etc., are currently available to scientists investigating interdicted nuclear material. These tools provide an analysis of physical, chemical, or isotopic characteristics of the seized material to identify its origin. In this study, a novel technique that characterizes physical attributes is proposed to provide insight into the processing route of unknown uranium ore concentrates (UOCs) and their calcination products. In particular, this study focuses on the characteristics of the surface structure captured in scanning electron microscopy (SEM) images at different magnification levels. Twelve common commercial processing routes of UOCs and their calcination products are investigated. Multiple-input single-output (MISO) convolution neural networks (CNNs) are implemented to differentiate the processing routes. The proposed technique can determine the processing route of a given sample in under a second running on a graphics processing unit (GPU) with an accuracy of more than 95%. The accuracy and speed of this proposed technique enable nuclear scientists to provide the preliminary identification results of interdicted material in a short time period. Furthermore, this proposed technique uses a predetermined set of magnifications, which in turn eliminates the human bias in selecting the magnification during the image acquisition process.
T. A. J. Ouermi, R. M. Kirby, M. Berzins. Numerical Testing of a New Positivity-Preserving Interpolation Algorithm, Subtitled arXiv, 2020.
An important component of a number of computational modeling algorithms is an interpolation method that preserves the positivity of the function being interpolated. This report describes the numerical testing of a new positivity-preserving algorithm that is designed to be used when interpolating from a solution defined on one grid to different spatial grid. The motivating application is a numerical weather prediction (NWP) code that uses spectral elements as the discretization choice for its dynamics core and Cartesian product meshes for the evaluation of its physics routines. This combination of spectral elements, which use nonuniformly spaced quadrature/collocation points, and uniformly-spaced Cartesian meshes combined with the desire to maintain positivity when moving between these necessitates our work. This new approach is evaluated against several typical algorithms in use on a range of test problems in one or more space dimensions. The results obtained show that the new method is competitive in terms of observed accuracy while at the same time preserving the underlying positivity of the functions being interpolated.
V. Pascucci, I. Altintas, J. Fortes, I. Foster, H. Gu, S. Hariri, D. Stanzione, M. Taufer, X. Zhao. Report from the NSF Workshop on Smart Cyberinfrastructure 2020, NSF, 2020.
Machine learning and other Artifical Intelligenece technologies (all indicated in the following as AI) used within a modern, smart cyberinfrastructure have become critical new avenues for discovery and validation in data-driven science and engineering disciplines of all kinds. We can expect many landmark discoveries and new lines of productive research to be enabled through AI analysis of the rapidly growing treasure trove of scientific data. AI-based techniques have been applied in many fields of science and engineering, including remote sensing, cosmology, energy, cancer research, IT systems management, and machine design and control, but the lack of proper integration with the current NSF-supported cyberinfrastructure is limiting their potential. Recent events due to the COVID-19 pandemic have highlighted how cyberinfrastructure is a crucial enabler of modern research, with massive simulations and data management capabilities [8-10], but these events have also emphasized how the lack of proper integration with AI technology remains a major limiting factor for the advancement of science and engineering, especially when any kind of rapid response is needed.
S. P. Ponnapalli, M. W. Bradley, K. Devine, J. Bowen, S. E. Coppens, K. M. Leraas, B. A. Milash, F. Li, H. Luo, S. Qiu, K. Wu, H. Yang, C. T. Wittwer, C. A. Palmer, R. L. Jensen, J. M. Gastier-Foster, H. A. Hanson, J. S. Barnholtz-Sloan, O. Alter. Retrospective clinical trial experimentally validates glioblastoma genome-wide pattern of DNA copy-number alterations predictor of survival, In Applied Physics Letters (APL) Bioengineering, Vol. 4, No. 2, May, 2020.
Modeling of genomic profiles from the Cancer Genome Atlas (TCGA) by using recently developed mathematical frameworks has associated a genome-wide pattern of DNA copy-number alterations with a shorter, roughly one-year, median survival time in glioblastoma (GBM) patients. Here, to experimentally test this relationship, we whole-genome sequenced DNA from tumor samples of patients. We show that the patients represent the U.S. adult GBM population in terms of most normal and disease phenotypes. Intratumor heterogeneity affects ≈11% and profiling technology and reference human genome specifics affect <1% of the classifications of the tumors by the pattern, where experimental batch effects normally reduce the reproducibility, i.e., precision, of classifications based upon between one to a few hundred genomic loci by >30%. With a 2.25-year Kaplan–Meier median survival difference, a 3.5 univariate Cox hazard ratio, and a 0.78 concordance index, i.e., accuracy, the pattern predicts survival better than and independent of age at diagnosis, which has been the best indicator since 1950. The prognostic classification by the pattern may, therefore, help to manage GBM pseudoprogression. The diagnostic classification may help drugs progress to regulatory approval. The therapeutic predictions, of previously unrecognized targets that are correlated with survival, may lead to new drugs. Other methods missed this relationship in the roughly 3B-nucleotide genomes of the small, order of magnitude of 100, patient cohorts, e.g., from TCGA. Previous attempts to associate GBM genotypes with patient phenotypes were unsuccessful. This is a proof of principle that the frameworks are uniquely suitable for discovering clinically actionable genotype–phenotype relationships.
D. Sahasrabudhe, M. Berzins.
Improving Performance of the Hypre Iterative Solver for Uintah Combustion Codes on Manycore Architectures Using MPI Endpoints and Kernel Consolidation, In Computational Science -- ICCS 2020, 20th International Conference, Amsterdam, The Netherlands, June 3–5, 2020, Proceedings, Part I, Springer International Publishing, pp. 175--190. 2020.
The solution of large-scale combustion problems with codes such as the Arches component of Uintah on next generation computer architectures requires the use of a many and multi-core threaded approach and/or GPUs to achieve performance. Such codes often use a low-Mach number approximation, that require the iterative solution of a large system of linear equations at every time step. While the discretization routines in such a code can be improved by the use of, say, OpenMP or Cuda Approaches, it is important that the linear solver be able to perform well too. For Uintah the Hypre iterative solver has proved to solve such systems in a scalable way. The use of Hypre with OpenMP leads to at least 2x slowdowns due to OpenMP overheads, however. This behavior is analyzed and a solution proposed by using the MPI Endpoints approach is implemented within Hypre, where each team of threads acts as a different MPI rank. This approach minimized OpenMP synchronization overhead, avoided slowdowns, performed as fast or (up to 1.5x) faster than Hypre’s MPI only version, and allowed the rest of Uintah to be optimized using OpenMP. Profiling of the GPU version of Hypre showed the bottleneck to be the launch overhead of thousands of micro-kernels. The GPU performance was improved by fusing these micro kernels and was further optimized by using Cuda-aware MPI. The overall speedup of 1.26x to 1.44x was observed compared to the baseline GPU implementation.
The solution of large-scale combustion problems with codes such as Uintah on modern computer architectures requires the use of multithreading and GPUs to achieve performance. Uintah uses a low-Mach number approximation that requires iteratively solving a large system of linear equations. The Hypre iterative solver has solved such systems in a scalable way for Uintah, but the use of OpenMP with Hypre leads to at least 2x slowdown due to OpenMP overheads. The proposed solution uses the MPI Endpoints within Hypre, where each team of threads acts as a different MPI rank. This approach minimizes OpenMP synchronization overhead and performs as fast or (up to 1.44x) faster than Hypre’s MPI-only version, and allows the rest of Uintah to be optimized using OpenMP. The profiling of the GPU version of Hypre shows the bottleneck to be the launch overhead of thousands of micro-kernels. The GPU performance was improved by fusing these micro-kernels and was further optimized by using Cuda-aware MPI, resulting in an overall speedup of 1.16–1.44x compared to the baseline GPU implementation.
The above optimization strategies were published in the International Conference on Computational Science 2020. This work extends the previously published research by carrying out the second phase of communication-centered optimizations in Hypre to improve its scalability on large-scale supercomputers. This includes an efficient non-blocking inter-thread communication scheme, communication-reducing patch assignment, and expression of logical communication parallelism to a new version of the MPICH library that utilizes the underlying network parallelism. The above optimizations avoid communication bottlenecks previously observed during strong scaling and improve performance by up to 2x on 256 nodes of Intel Knight’s Landing processor.
F. Wang, N. Marshak, W. Usher, C. Burstedde, A. Knoll, T. Heister, C. R. Johnson. CPU Ray Tracing of Tree-Based Adaptive Mesh Refinement Data, In Eurographics Conference on Visualization (EuroVis) 2020, Vol. 39, No. 3, 2020.
Adaptive mesh refinement (AMR) techniques allow for representing a simulation’s computation domain in an adaptive fashion. Although these techniques have found widespread adoption in high-performance computing simulations, visualizing their data output interactively and without cracks or artifacts remains challenging. In this paper, we present an efficient solution for direct volume rendering and hybrid implicit isosurface ray tracing of tree-based AMR (TB-AMR) data. We propose a novel reconstruction strategy, Generalized Trilinear Interpolation (GTI), to interpolate across AMR level boundaries without cracks or discontinuities in the surface normal. We employ a general sparse octree structure supporting a wide range of AMR data, and use it to accelerate volume rendering, hybrid implicit isosurface rendering and value queries. We demonstrate that our approach achieves artifact-free isosurface and volume rendering and provides higher quality output images compared to existing methods at interactive rendering rates.
L. Zhou, M. Rivinius, C. R. Johnson,, D. Weiskopf. Photographic High-Dynamic-Range Scalar Visualization, In IEEE Transactions on Visualization and Computer Graphics, Vol. 26, No. 6, IEEE, pp. 2156-2167. 2020.
We propose a photographic method to show scalar values of high dynamic range (HDR) by color mapping for 2D visualization. We combine (1) tone-mapping operators that transform the data to the display range of the monitor while preserving perceptually important features based on a systematic evaluation and (2) simulated glares that highlight high-value regions. Simulated glares are effective for highlighting small areas (of a few pixels) that may not be visible with conventional visualizations; through a controlled perception study, we confirm that glare is preattentive. The usefulness of our overall photographic HDR visualization is validated through the feedback of expert users.
Objective. During deep brain stimulation (DBS), it is well understood that extracellular cathodic stimulation can cause activation of passing axons. Activation can be predicted from the second derivative of the electric potential along an axon, which depends on axonal orientation with respect to the stimulation source. We hypothesize that fiber orientation influences activation thresholds and that fiber orientations can be selectively targeted with DBS waveforms. Approach. We used bioelectric field and multicompartment NEURON models to explore preferential activation based on fiber orientation during monopolar or bipolar stimulation. Preferential fiber orientation was extracted from the principal eigenvectors and eigenvalues of the Hessian matrix of the electric potential. We tested cathodic, anodic, and charge-balanced pulses to target neurons based on fiber orientation in general and clinical scenarios. Main results. Axons passing the DBS lead have positive second derivatives around a cathode, whereas orthogonal axons have positive second derivatives around an anode, as indicated by the Hessian. Multicompartment NEURON models confirm that passing fibers are activated by cathodic stimulation, and orthogonal fibers are activated by anodic stimulation. Additionally, orthogonal axons have lower thresholds compared to passing axons. In a clinical scenario, fiber pathways associated with therapeutic benefit can be targeted with anodic stimulation at 50% lower stimulation amplitudes. Significance. Fiber orientations can be selectively targeted with simple changes to the stimulus waveform. Anodic stimulation preferentially activates orthogonal fibers, approaching or leaving the electrode, at lower thresholds for similar therapeutic benefit in DBS with decreased power consumption.
C.J. Anderson, D.N. Anderson, S.M. Pulst, C.R. Butson, A.D. Dorval.
Neural Selectivity, Efficiency, and Dose Equivalence in Deep Brain Stimulation through Pulse Width Tuning and Segmented Electrodes, In bioRxiv, Cold Spring Harbor Laboratory, April, 2019.
Achieving deep brain stimulation (DBS) dose equivalence is challenging, especially with pulse width tuning and directional contacts. Further, the precise effects of pulse width tuning are unknown.
We created multicompartment neuron models for two axon diameters and used finite element modeling to determine extracellular influence from standard and segmented electrodes. We analyzed axon activation profiles and calculated volumes of tissue activated.
Long pulse widths focus the stimulation effect on small, nearby fibers, suppressing white matter tract activation (responsible for some DBS side effects) and improving battery utilization. Directional leads enable similar benefits to a greater degree. We derive equations for equivalent activation with pulse width tuning and segmented contacts.
We find agreement with classic studies and reinterpret recent articles concluding that short pulse widths focus the stimulation effect on small, nearby fibers, decrease side effects, and improve power consumption. Our field should reconsider shortened pulse widths.
Directional deep brain stimulation (DBS) leads have recently been approved and used in patients, and growing evidence suggests that directional contacts can increase the therapeutic window by redirecting stimulation to the target region while avoiding side-effect-inducing regions. We outline the design, fabrication, and testing of a novel directional DBS lead, theμDBS, which utilizes microscale contacts to increase the spatial resolution of stimulation steering and improve the selectivity in targeting small diameter fibers. We outline the steps of fabrication of theμDBS, from an integrated circuit design to post-processing and validation testing. We tested the onboard digital circuitry for programming fidelity, characterized impedance for a variety of electrode sizes, and demonstrated functionality in a saline bath. In a computational experiment,we determined that reduced electrode sizes focus the stimulation effect on small, nearby fibers. Smaller electrode sizes allow for a relative decrease in small-diameter axon thresholds compared to thresholds of large-diameter fibers, demonstrating a focusing of the stimulation effect within small, and possibly therapeutic, fibers. This principle of selectivity could be useful in further widening the window of therapy. TheμDBS offers a unique, multi resolution design in which any combination of microscale contacts can be used together to function as electrodes of various shapes and sizes. Multiscale electrodes could be useful in selective neural targeting for established neurological targets and in exploring novel treatment targets for new neurological indications.
C. C. Aquino, G. Duffley, D. M. Hedges, J. Vorwerk, P. A. House, H. B. Ferraz, J. D. Rolston, C. R. Butson, L. E. Schrock.
Interleaved deep brain stimulation for dyskinesia management in Parkinson's disease, In Movement Disorders, 2019.
In patients with Parkinson's disease, stimulation above the subthalamic nucleus (STN) may engage the pallidofugal fibers and directly suppress dyskinesia.
The objective of this study was to evaluate the effect of interleaving stimulation through a dorsal deep brain stimulation contact above the STN in a cohort of PD patients and to define the volume of tissue activated with antidyskinesia effects.
We analyzed the Core Assessment Program for Surgical Interventional Therapies dyskinesia scale, Unified Parkinson's Disease Rating Scale parts III and IV, and other endpoints in 20 patients with interleaving stimulation for management of dyskinesia. Individual models of volume of tissue activated and heat maps were used to identify stimulation sites with antidyskinesia effects.
The Core Assessment Program for Surgical Interventional Therapies dyskinesia score in the on medication phase improved 70.9 ± 20.6% from baseline with noninterleaved settings (P < 0.003). With interleaved settings, dyskinesia improved 82.0 ± 27.3% from baseline (P < 0.001) and 61.6 ± 39.3% from the noninterleaved phase (P = 0.006). The heat map showed a concentration of volume of tissue activated dorsally to the STN during the interleaved setting with an antidyskinesia effect.
Interleaved deep brain stimulation using the dorsal contacts can directly suppress dyskinesia, probably because of the involvement of the pallidofugal tract, allowing more conservative medication reduction. © 2019 International Parkinson and Movement Disorder Society
We present a framework for the analysis of uncertainty in isocontour extraction. The marching squares (MS) algorithm for isocontour reconstruction generates a linear topology that is consistent with hyperbolic curves of a piecewise bilinear interpolation. The saddle points of the bilinear interpolant cause topological ambiguity in isocontour extraction. The midpoint decider and the asymptotic decider are well-known mathematical techniques for resolving topological ambiguities. The latter technique investigates the data values at the cell saddle points for ambiguity resolution. The uncertainty in data, however, leads to uncertainty in underlying bilinear interpolation functions for the MS algorithm, and hence, their saddle points. In our work, we study the behavior of the asymptotic decider when data at grid vertices is uncertain. First, we derive closed-form distributions characterizing variations in the saddle point values for uncertain bilinear interpolants. The derivation assumes uniform and nonparametric noise models, and it exploits the concept of ratio distribution for analytic formulations. Next, the probabilistic asymptotic decider is devised for ambiguity resolution in uncertain data using distributions of the saddle point values derived in the first step. Finally, the confidence in probabilistic topological decisions is visualized using a colormapping technique. We demonstrate the higher accuracy and stability of the probabilistic asymptotic decider in uncertain data with regard to existing decision frameworks, such as deciders in the mean field and the probabilistic midpoint decider, through the isocontour visualization of synthetic and real datasets.
A statistical framework for quantification and visualisation of positional uncertainty in deep brain stimulation electrodes, In Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, Vol. 7, No. 4, Taylor & Francis, pp. 438-449. 2019.
Deep brain stimulation (DBS) is an established therapy for treating patients with movement disorders such as Parkinson’s disease. Patient-specific computational modelling and visualisation have been shown to play a key role in surgical and therapeutic decisions for DBS. The computational models use brain imaging, such as magnetic resonance (MR) and computed tomography (CT), to determine the DBS electrode positions within the patient’s head. The finite resolution of brain imaging, however, introduces uncertainty in electrode positions. The DBS stimulation settings for optimal patient response are sensitive to the relative positioning of DBS electrodes to a specific neural substrate (white/grey matter). In our contribution, we study positional uncertainty in the DBS electrodes for imaging with finite resolution. In a three-step approach, we first derive a closed-form mathematical model characterising the geometry of the DBS electrodes. Second, we devise a statistical framework for quantifying the uncertainty in the positional attributes of the DBS electrodes, namely the direction of longitudinal axis and the contact-centre positions at subvoxel levels. The statistical framework leverages the analytical model derived in step one and a Bayesian probabilistic model for uncertainty quantification. Finally, the uncertainty in contact-centre positions is interactively visualised through volume rendering and isosurfacing techniques. We demonstrate the efficacy of our contribution through experiments on synthetic and real datasets. We show that the spatial variations in true electrode positions are significant for finite resolution imaging, and interactive visualisation can be instrumental in exploring probabilistic positional variations in the DBS lead.