3T MRI Whole-Brain Microscopy Discrimination of Subcortical Anatomy, Part 2: Basal Forebrain.

BACKGROUND AND PURPOSE: The basal forebrain contains multiple structures of great interest to emerging functional neurosurgery applications, yet many neuroradiologists are unfamiliar with this neuroanatomy because it is not resolved with current clinical MR imaging. MATERIALS AND METHODS: We applied an optimized TSE T2 sequence to washed whole postmortem brain samples (n = 13) to demonstrate and characterize the detailed anatomy of the basal forebrain using a clinical 3T MR imaging scanner. We measured the size of selected internal myelinated pathways and measured subthalamic nucleus size, oblique orientation, and position relative to the intercommissural point. RESULTS: We identified most basal ganglia and diencephalon structures using serial axial, coronal, and sagittal planes relative to the intercommissural plane. Specific oblique image orientations demonstrated the positions and anatomic relationships for selected structures of interest to functional neurosurgery. We observed only 0.2- to 0.3-mm right-left differences in the anteroposterior and superoinferior length of the subthalamic nucleus (P = .084 and .047, respectively). Individual variability for the subthalamic nucleus was greatest for angulation within the sagittal plane (range, 15°-37°), transverse dimension (range, 2-6.7 mm), and most inferior border (range, 4-7 mm below the intercommissural plane). CONCLUSIONS: Direct identification of basal forebrain structures in multiple planes using the TSE T2 sequence makes this challenging neuroanatomy more accessible to practicing neuroradiologists. This protocol can be used to better define individual variations relevant to functional neurosurgical targeting and validate/complement advanced MR imaging methods being developed for direct visualization of these structures in living patients.

Palliative CT-Guided Cordotomy for Medically Intractable Pain in Patients with Cancer.

Palliative cervical cordotomy can be performed via percutaneous radiofrequency ablation of the lateral C1-2 spinothalamic tract. This rare procedure can be safe, effective, and advantageous in mitigating medically intractable unilateral extremity pain for selected patients with end-stage cancer. This report reviews the indications, techniques, risks, and potential benefits of cordotomy. We describe our recent experience treating 3 patients with CT-guided C1-2 cordotomy and provide the first characterization of spinal cord diffusion MR imaging changes associated with successful cordotomy.

Optimized, Minimal Specific Absorption Rate MRI for High-Resolution Imaging in Patients with Implanted Deep Brain Stimulation Electrodes.

BACKGROUND AND PURPOSE: Obtaining high-resolution brain MR imaging in patients with a previously implanted deep brain stimulator has been challenging and avoided by many centers due to safety concerns relating to implantable devices. We present our experience with a practical clinical protocol at 1.5T by using 2 magnet systems capable of achieving presurgical quality imaging in patients undergoing bilateral, staged deep brain stimulator insertion. MATERIALS AND METHODS: Protocol optimization was performed to minimize the specific absorption rate while providing image quality necessary for adequate surgical planning of the second electrode placement. We reviewed MR imaging studies performed with a minimal specific absorption rate protocol in patients with a deep brain stimulator in place at our institution between February 1, 2012, and August 1, 2015. Images were reviewed by a neuroradiologist and a functional neurosurgeon. Image quality was qualitatively graded, and the presence of artifacts was noted. RESULTS: Twenty-nine patients (22 with Parkinson disease, 6 with dystonia, 1 with essential tremor) were imaged with at least 1 neuromodulation implant in situ. All patients were imaged under general anesthesia. There were 25 subthalamic and 4 globus pallidus implants. Nineteen patients were preoperative for the second stage of bilateral deep brain stimulator placement; 10 patients had bilateral electrodes in situ and were being imaged for other neurologic indications, including lead positioning. No adverse events occurred during or after imaging. Mild device-related local susceptibility artifacts were present in all studies, but they were not judged to affect overall image quality. Minimal aliasing artifacts were seen in 7, and moderate motion, in 4 cases on T1WI only. All preoperative studies were adequate for guidance of a second deep brain stimulator placement. CONCLUSIONS: An optimized MR imaging protocol that minimizes the specific absorption rate can be used to safely obtain high-quality images in patients with previously implanted deep brain stimulators, and these images are adequate for surgical guidance.

Mechanical activation of cells induces chromatin remodeling preceding MKL nuclear transport.

For cells to adapt to different tissues and changes in tissue mechanics, they must be able to respond to mechanical cues by changing their gene expression patterns. Biochemical signaling pathways for these responses have been elucidated, and recent evidence points to the involvement of force-induced deformation of the nucleus. However, it is still unclear how physical cues received at the plasma membrane (PM) spatiotemporally integrate to the functional chromatin organization of the cell nucleus. To investigate this issue, we applied mechanical forces through magnetic particles adhered to the PM of single cells and mapped the accompanying changes in actin polymerization, nuclear morphology, chromatin remodeling, and nuclear transport of soluble signaling intermediates using high-resolution fluorescence anisotropy imaging. Using this approach, we show the timescales associated with force-induced polymerization of actin and changes in the F/G actin ratio resulting in nuclear translocation of the G-actin-associated transcriptional cofactor, megakaryoblastic acute leukemia factor-1 (MKL). Further, this method of measuring nuclear organization at high spatiotemporal resolution with simultaneous force application revealed the physical propagation of forces to the nucleus, resulting in changes to chromatin organization, followed by nuclear deformation. We also describe a quantitative model that incorporates active stresses and chemical kinetics to evaluate the observed timescales. Our work suggests that mechanical activation of cells is accompanied by distinct timescales involved in the reorganization of actin and chromatin assembly, followed by translocation of transcription cofactors from the cytoplasm to the nucleus.

The emergence of sarcomeric, graded-polarity and spindle-like patterns in bundles of short cytoskeletal polymers and two opposite molecular motors.

We use linear stability analysis and numerical solutions of partial differential equations to investigate pattern formation in the one-dimensional system of short dynamic polymers and one (plus-end directed) or two (one is plus-end, another minus-end directed) molecular motors. If polymer sliding and motor gliding rates are slow and/or the polymer turnover rate is fast, then the polymer-motor bundle has mixed polarity and homogeneous motor distribution. However, if motor gliding is fast, a sarcomeric pattern with periodic bands of alternating polymer polarity separated by motor aggregates evolves. On the other hand, if polymer sliding is fast, a graded-polarity bundle with motors at the center emerges. In the presence of the second, minus-end directed motor, the sarcomeric pattern is more ubiquitous, while the graded-polarity pattern is destabilized. However, if the minus-end motor is weaker than the plus-end directed one, and/or polymer nucleation is autocatalytic, and/or long polymers are present in the bundle, then a spindle-like architecture with a sorted-out polarity emerges with the plus-end motors at the center and minus-end motors at the edges. We discuss modeling implications for actin-myosin fibers and in vitro and meiotic spindles.

Actin disassembly 'clock' and membrane tension determine cell shape and turning: a mathematical model.

Motile cells regulate their shape and movements largely by remodeling the actin cytoskeleton. Principles of this regulation are becoming clear for simple-shaped steadily crawling cells, such as fish keratocytes. In particular, the shape of the leading edge and sides of the lamellipodium-cell motile appendage-is determined by graded actin distribution at the cell boundary, so that the denser actin network at the front grows, while sparser actin filaments at the sides are stalled by membrane tension. Shaping of the cell rear is less understood. Here we theoretically examine the hypothesis that the cell rear is shaped by the disassembly clock: the front-to-rear lamellipodial width is defined by the time needed for the actin-adhesion network to disassemble to the point at which the membrane tension can crush this network. We demonstrate that the theory predicts the observed cell shapes. Furthermore, turning of the cells can be explained by biases in the actin distribution. We discuss experimental implications of this hypothesis.

The elasticity of motor-microtubule bundles and shape of the mitotic spindle.

In the process of cell division, chromosomes are segregated by mitotic spindles -- bipolar microtubule arrays that have a characteristic fusiform shape. Mitotic spindle function is based on motor-generated forces of hundreds of piconewtons. These forces have to deform the spindle, yet the role of microtubule elastic deformations in the spindle remains unclear. Here we solve equations of elasticity theory for spindle microtubules, compare the solutions with shapes of early Drosophila embryo spindles and discuss the biophysical and cell biological implications of this analysis. The model suggests that microtubule bundles in the spindle behave like effective compressed springs with stiffness of the order of tens of piconewtons per micron, that microtubule elasticity limits the motors' power, and that clamping and cross-linking of microtubules are needed to transduce the motors' forces in the spindle. Some data are hard to reconcile with the model predictions, suggesting that cytoskeletal structures laterally reinforce the spindle and/or that rapid microtubule turnover relieves the elastic stresses.

Nonlocal mechanism of self-organization and centering of microtubule asters.

Fragments of fish melanophore cells can form and center aggregates of pigment granules by dynein-motor-driven transport along a self-organized radial array of microtubules (MTs). We present a quantitative model that describes pigment aggregation and MT-aster self-organization and the subsequent centering of both structures. The model is based on the observations that MTs are immobile and treadmill, while dynein-motor-covered granules have the ability to nucleate MTs. From assumptions based on experimental observations, we derive partial integro-differential equations describing the coupled granule-MT interaction. We use scaling arguments and perturbation theory to study the model in two limiting cases. The model analysis explains the mechanism of aster self-organization as a positive feedback loop between motor aggregation at the MT minus ends and MT nucleation by motors. Furthermore, the centering mechanism is explained by the spontaneous nucleation of MTs throughout the cytosol which acts as a volume sensing tool. Numerical simulations lend additional support to the analysis. The model sheds light on role of polymer dynamics and polymer-motor interactions in cytoskeletal organization.

Model of chromosome motility in Drosophila embryos: adaptation of a general mechanism for rapid mitosis.

During mitosis, ensembles of dynamic MTs and motors exert forces that coordinate chromosome segregation. Typically, chromosomes align at the metaphase spindle equator where they oscillate along the pole-pole axis before disjoining and moving poleward during anaphase A, but spindles in different cell types display differences in MT dynamicity, in the amplitude of chromosome oscillations and in rates of chromatid-to-pole motion. Drosophila embryonic mitotic spindles, for example, display remarkably dynamic MTs, barely detectable metaphase chromosome oscillations, and a rapid rate of "flux-pacman-dependent" anaphase chromatid-to-pole motility. Here we develop a force-balance model that describes Drosophila embryo chromosome motility in terms of a balance of forces acting on kinetochores and kMTs that is generated by multiple polymer ratchets and mitotic motors coupled to tension-dependent kMT dynamics. The model shows that i), multiple MTs displaying high dynamic instability can drive steady and rapid chromosome motion; ii), chromosome motility during metaphase and anaphase A can be described by a single mechanism; iii), high kinetochore dynein activity is deployed to dampen metaphase oscillations, to augment the basic flux-pacman mechanism, and to drive rapid anaphase A; iv), modulation of the MT rescue frequency by the kinetochore-associated kinesin-13 depolymerase promotes metaphase chromosome oscillations; and v), this basic mechanism can be adapted to a broad range of spindles.

Early spindle assembly in Drosophila embryos: role of a force balance involving cytoskeletal dynamics and nuclear mechanics.

Mitotic spindle morphogenesis depends upon the action of microtubules (MTs), motors and the cell cortex. Previously, we proposed that cortical- and MT-based motors acting alone can coordinate early spindle assembly in Drosophila embryos. Here, we tested this model using microscopy of living embryos to analyze spindle pole separation, cortical reorganization, and nuclear dynamics in interphase-prophase of cycles 11-13. We observe that actin caps remain flat as they expand and that furrows do not ingress. As centrosomes separate, they follow a linear trajectory, maintaining a constant pole-to-furrow distance while the nucleus progressively deforms along the elongating pole-pole axis. These observations are incorporated into a model in which outward forces generated by zones of active cortical dynein are balanced by inward forces produced by nuclear elasticity and during cycle 13, by Ncd, which localizes to interpolar MTs. Thus, the force-balance driving early spindle morphogenesis depends upon MT-based motors acting in concert with the cortex and nucleus.

Efficient chromosome capture requires a bias in the 'search-and-capture' process during mitotic-spindle assembly.

The mitotic spindle assembles into a bipolar, microtubule-based protein machine during prometaphase. One proposed mechanism for this process is "search-and-capture," in which dynamically unstable microtubules (MTs) search space to capture chromosomes. Although existing theoretical estimates suggest that dynamic instability is efficient enough to allow capture within characteristic mitotic timescales, they are limited in scope and do not address the capture times for realistic numbers of chromosomes. Here we used mathematical modeling to explore this issue. We show that without any bias toward the chromosomes, search-and-capture is not efficient enough to explain the typical observed duration of prometaphase. We further analyze search-and-capture in the presence of a spatial gradient of a stabilizing factor that biases MT dynamics toward the chromosomes. We show theoretically that such biased search-and-capture is efficient enough to account for chromosome capture. We also show that additional factors must contribute to accelerate the spindle assembly for cells with large nuclear volumes. We discuss the possibility that a RanGTP gradient introduces a spatial bias into microtubule dynamics and thus improves the efficiency of search-and-capture as a mechanism for spindle assembly.

The physics of filopodial protrusion.

Filopodium, a spike-like actin protrusion at the leading edge of migrating cells, functions as a sensor of the local environment and has a mechanical role in protrusion. We use modeling to examine mechanics and spatial-temporal dynamics of filopodia. We find that >10 actin filaments have to be bundled to overcome the membrane resistance and that the filopodial length is limited by buckling for 10-30 filaments and by G-actin diffusion for >30 filaments. There is an optimal number of bundled filaments, approximately 30, at which the filopodial length can reach a few microns. The model explains characteristic interfilopodial distance of a few microns as a balance of initiation, lateral drift, and merging of the filopodia. The theory suggests that F-actin barbed ends have to be focused and protected from capping (the capping rate has to decrease one order of magnitude) once every hundred seconds per micron of the leading edge to initiate the observed number of filopodia. The model generates testable predictions about how filopodial length, rate of growth, and interfilopodial distance should depend on the number of bundled filaments, membrane resistance, lamellipodial protrusion rate, and G-actin diffusion coefficient.

MULTISCALE TWO-DIMENSIONAL MODELING OF A MOTILE SIMPLE-SHAPED CELL.

Cell crawling is an important biological phenomenon underlying coordinated cell movement in morphogenesis, cancer, and wound healing. In recent decades the process of cell crawling has been experimentally and theoretically dissected into further subprocesses: protrusion of the cell at its leading edge, retraction of the cell body, and graded adhesion. A number of one-dimensional (1-D) models explain successfully a proximal-distal organization and movement of the motile cell. However, more adequate two-dimensional (2-D) models are lacking. We propose a multiscale 2-D computational model of the lamellipodium (motile appendage) of a simply shaped, rapidly crawling fish keratocyte cell. We couple submodels of (i) protrusion and adhesion at the leading edge, (ii) the elastic 2-D lamellipodial actin network, (iii) the actin-myosin contractile bundle at the rear edge, and (iv) the convection-reaction-diffusion actin transport on the free boundary lamellipodial domain. We simulate the combined model numerically using a finite element approach. The simulations reproduce observed cell shapes, forces, and movements and explain some experimental results on perturbations of the actin machinery. This novel 2-D model of the crawling cell makes testable predictions and posits questions to be answered by future modeling.

Model of coupled transient changes of Rac, Rho, adhesions and stress fibers alignment in endothelial cells responding to shear stress.

Interactions of cell adhesions, Rho GTPases and actin in the endothelial cells' response to external forces are complex and not fully understood, but a qualitative understanding of the mechanosensory response begins to emerge. Here, we formulate a mathematical model of the coupled dynamics of cell adhesions, small GTPases Rac and Rho and actin stress fibers guiding a directional reorganization of the actin cytoskeleton. The model is based on the assumptions that the interconnected cytoskeleton transfers the shear force to the adhesion sites, which in turn transduce the force into a chemical signal that activates integrins at the basal surface of the cell. Subsequently, activated and ligated integrins signal and transiently de-activate Rho, causing the disassembly of actin stress fibers and inhibiting the maturation of focal complexes into focal contacts. Focal complexes and ligated integrins activate Rac, which in turn enhances focal complex assembly. When Rho activity recovers, stress fibers re-assemble and promote the maturation of focal complexes into focal contacts. Merging stress fibers self-align, while the elevated level of Rac activity at the downstream edge of the cell is translated into an alignment of the cells and the newly forming stress fibers in the flow direction. Numerical solutions of the model equations predict transient changes in Rac and Rho that compare well with published experimental results. We report quantitative data on early alignment of the stress fibers and its dependence on cell shape that agrees with the model.

Model for anaphase B: role of three mitotic motors in a switch from poleward flux to spindle elongation.

It has been proposed that the suppression of poleward flux within interpolar microtubule (ipMT) bundles of Drosophila embryonic spindles couples outward forces generated by a sliding filament mechanism to anaphase spindle elongation. Here, we (i) propose a molecular mechanism in which the bipolar kinesin KLP61F persistently slides dynamically unstable ipMTs outward, the MT depolymerase KLP10A acts at the poles to convert ipMT sliding to flux, and the chromokinesin KLP3A inhibits the depolymerase to suppress flux, thereby coupling ipMT sliding to spindle elongation; (ii) used KLP3A inhibitors to interfere with the coupling process, which revealed an inverse linear relation between the rates of flux and elongation, supporting the proposed mechanism and demonstrating that the suppression of flux controls both the rate and onset of spindle elongation; and (iii) developed a mathematical model using force balance and rate equations to describe how motors sliding the highly dynamic ipMTs apart can drive spindle elongation at a steady rate determined by the extent of suppression of flux.

Computational model of dynein-dependent self-organization of microtubule asters.

Polar arrays of microtubules play many important roles in the cell. Normally, such arrays are organized by a centrosome anchoring the minus ends of the microtubules, while the plus ends extend to the cell periphery. However, ensembles of molecular motors and microtubules also demonstrate the ability to self-organize into polar arrays. We use quantitative modeling to analyze the self-organization of microtubule asters and the aggregation of motor-driven pigment granules in fragments of fish melanophore cells. The model is based on the observation that microtubules are immobile and treadmilling, and on the experimental evidence that cytoplasmic dynein motors associated with granules have the ability to nucleate MTs and attenuate their minus-end dynamics. The model explains the observed sequence of events as follows. Initially, pigment granules driven by cytoplasmic dynein motors aggregate to local clusters of microtubule minus ends. The pigment aggregates then nucleate microtubules with plus ends growing toward the fragment boundary, while the minus ends stay transiently in the aggregates. Microtubules emerging from one aggregate compete with any aggregates they encounter leading to the gradual formation of a single aggregate. Simultaneously, a positive feedback mechanism drives the formation of a single MT aster--a single loose aggregate leads to focused MT nucleation and hence a tighter aggregate which stabilizes MT minus ends more effectively leading to aster formation. We translate the model assumptions based on experimental measurements into mathematical equations. The model analysis and computer simulations successfully reproduce the observed pathways of pigment aggregation and microtubule aster self-organization. We test the model predictions by observing the self-organization in fragments of various sizes and in bi-lobed fragments. The model provides stringent constraints on rates and concentrations describing microtubule and motor dynamics, and sheds light on the role of polymer dynamics and polymer-motor interactions in cytoskeletal organization.

Model of bacterial band formation in aerotaxis.

Aerotaxis is a particular form of "energy taxis". It is based on a largely elusive signal transduction machinery. In aerotaxis, oxygen dissolved in water plays the role of both attractant (at moderate concentrations) and repellent (at high and low concentrations). Cells swimming from favorable oxygen concentrations into regions with unfavorable concentrations increase the frequency of reversals, turn back into the favorable domain, and become effectively trapped there. At the same time, bacteria consume oxygen, creating an oxygen gradient. This behavior leads to a pattern formation phenomenon: bacteria self-organize into a dense band at a certain distance from the air-water interface. We incorporate experimental observations of the aerotactic bacterium, Azospirillum brasilense, into a mathematical model. The model consists of a system of differential equations describing swimming bacterial cells and diffusing oxygen. The cells' frequency of reversals depends on the concentration of oxygen and its time derivative while oxygen is depleted by the bacteria. We suggest a hypothetical model of energy sensing mediated by aerotactic receptors Aer and Tsr. Computer simulations and analysis of the model equations allow comparisons of theoretical and experimental results and provide insight into the mechanisms of bacterial pattern formation and underlying signal transduction machinery. We make testable predictions about position and density of the bacterial band.

Mutual interactions, potentials, and individual distance in a social aggregation.

We formulate a Lagrangian (individual-based) model to investigate the spacing of individuals in a social aggregate (e.g., swarm, flock, school, or herd). Mutual interactions of swarm members have been expressed as the gradient of a potential function in previous theoretical studies. In this specific case, one can construct a Lyapunov function, whose minima correspond to stable stationary states of the system. The range of repulsion (r) and attraction (a) must satisfy r < a for cohesive groups (i.e., short range repulsion and long range attraction). We show quantitatively how repulsion must dominate attraction ( Rr(d+1) > cAa(d+1) where R, A are magnitudes, c is a constant of order 1, and d is the space dimension) to avoid collapse of the group to a tight cluster. We also verify the existence of a well-spaced locally stable state, having a characteristic individual distance. When the number of individuals in a group increases, a dichotomy occurs between swarms in which individual distance is preserved versus those in which the physical size of the group is maintained at the expense of greater crowding.

Brain stimulation: history, current clinical application, and future prospects.

The dramatic effects of chronic brain stimulation in the treatment of movement disorders have spurred a renewed interest in this technique for treating a variety of other conditions. This technique has only recently begun to reach its vast clinical potential, due to a number of significant advances in basic and clinical neurosciences. Current image-guided navigation systems and intraoperative physiological mapping techniques offer more efficient, consistent, and precise targeting. Advances in neurophysiology have helped elucidate the pathophysiology of a number of disease states and thus provided for rational target selection for therapy. The latest generation of stimulation equipment allows for precise tailoring of stimulation parameters to maximize clinical benefit. These techniques are now being applied to a variety of other conditions including chronic pain, epilepsy, and psychiatric disorders.

Analysis of actin dynamics at the leading edge of crawling cells: implications for the shape of keratocyte lamellipodia.

Leading edge protrusion is one of the critical events in the cell motility cycle and it is believed to be driven by the assembly of the actin network. The concept of dendritic nucleation of actin filaments provides a basis for understanding the organization and dynamics of the actin network at the molecular level. At a larger scale, the dynamic geometry of the cell edge has been described in terms of the graded radial extension model, but this level of description has not yet been linked to the molecular dynamics. Here, we measure the graded distribution of actin filament density along the leading edge of fish epidermal keratocytes. We develop a mathematical model relating dendritic nucleation to the long-range actin distribution and the shape of the leading edge. In this model, a steady-state graded actin distribution evolves as a result of branching, growth and capping of actin filaments in a finite area of the leading edge. We model the shape of the leading edge as a product of the extension of the actin network, which depends on actin filament density. The feedback between the actin density and edge shape in the model results in a cell shape and an actin distribution similar to those experimentally observed. Thus, we explain the stability of the keratocyte shape in terms of the self-organization of the branching actin network.