Stereotactic Awake Basal Ganglia Electrophysiological Recording and Stimulation (SABERS): A Novel Staged Procedure for Personalized Targeting of Deep Brain Stimulation in Pediatric Movement and Neuropsychiatric Disorders.

Selection of targets for deep brain stimulation (DBS) has been based on clinical experience, but inconsistent and unpredictable outcomes have limited its use in patients with heterogeneous or rare disorders. In this large case series, a novel staged procedure for neurophysiological assessment from 8 to 12 temporary depth electrodes is used to select targets for neuromodulation that are tailored to each patient's functional needs. Thirty children and young adults underwent deep brain stimulation target evaluation with the new procedure: Stereotactic Awake Basal ganglia Electrophysiological Recording and Stimulation (SABERS). Testing is performed in an inpatient neuromodulation monitoring unit over 5-7 days, and results guide the decision to proceed and the choice of targets for permanent deep brain stimulation implantation. Results were evaluated 3-6 months postoperatively with the Burke-Fahn-Marsden Dystonia Rating Scale and the Barry-Albright Dystonia Scale. Stereotactic Awake Basal ganglia Electrophysiological Recording and Stimulation testing allowed modulation to be tailored to specific neurologic deficits in a heterogeneous population, including subjects with primary dystonia, secondary dystonia, and Tourette syndrome. All but one subject were implanted with 4 permanent deep brain stimulation leads. Results showed significant improvement on both scales at postoperative follow-up. No significant adverse events occurred. Use of the Stereotactic Awake Basal ganglia Electrophysiological Recording and Stimulation protocol with evaluation in the neuromodulation monitoring unit is feasible and results in significant patient benefit compared with previously published results in these populations. This new technique supports a significant expansion of functional neurosurgery to predict effective stimulation targets in a wide range of disorders of brain function, including those for which the optimal target is not yet known.

Novel utilization of deep brain stimulation in the pedunculopontine nucleus with globus pallidus internus for treatment of childhood-onset dystonia.

Introduction: Deep brain stimulation (DBS) is a well-documented therapy for dystonia utilized in many adult and pediatric movement disorders. Pedunculopontine nucleus (PPN) has been investigated as a DBS target primarily in adult patients with dystonia or dyskinesias from Parkinson's disease, showing improvement in postural instability and gait dysfunction. Due to the difficulty in targeting PPN using standard techniques, it is not commonly chosen as a target for adult or pediatric pathology. There is no current literature describing the targeting of PPN in DBS for childhood-onset dystonia. Methods: Two pediatric and one young adult patient with childhood-onset dystonia who underwent DBS implantation at our institution were identified. Patient 1 has Mitochondrial Enoyl CoA Reductase Protein-Associated Neurodegeneration (MEPAN) syndrome. Patient 2 has Glutaric Aciduria Type 1 (GA1). Patient 3 has atypical pantothenate kinase-associated neurodegeneration (PKAN). PPN was identified as a potential target for these patients due to axial or orofacial dystonia. Pre- and post-operative videos taken as part of routine clinical assessments were evaluated and scored on the Burke-Fahn-Marsden Dystonia Rating Scale (BFMDRS) and Barry-Albright Dystonia Scale (BADS). All patients had permanent electrodes placed bilaterally in PPN and globus pallidus internus (GPi). A Likert scale on quality of life was also obtained from the patient/parents as applicable. Results: Significant programming was necessary over the first 3-12 months to optimize patients' response to stimulation. All patients experienced at least a 34% improvement in the BFMDRS score. Patients 2 and 3 also experienced an over 30% improvement in BADS score. All patients/parents appreciated improvement in quality of life postoperatively. Discussion: Deep brain stimulation in PPN was safely and successfully used in two pediatric patients and one young adult patient with childhood-onset dystonia. These patients showed clinically significant improvements in BFMDRS scoring post operatively. This represents the first reported DBS targeting of PPN in pediatric patients, and suggests that PPN is a possible target for pediatric-onset dystonia with axial and orofacial symptoms that may be refractory to traditional pallidal stimulation alone.

Improvement of speed-accuracy tradeoff during practice of a point-to-point task in children with acquired dystonia.

The tradeoff between speed and accuracy is a well-known constraint for human movement, but previous work has shown that this tradeoff can be modified by practice, and the quantitative relationship between speed and accuracy may be an indicator of skill in some tasks. We have previously shown that children with dystonia are able to adapt their movement strategy in a ballistic throwing game to compensate for increased variability of movement. Here, we test whether children with dystonia can adapt and improve skills learned on a trajectory task. We use a novel task in which children move a spoon with a marble between two targets. Difficulty is modified by changing the depth of the spoon. Our results show that both healthy children and children with acquired dystonia move more slowly with the more difficult spoons, and both groups improve the relationship between speed and spoon difficulty following 1 wk of practice. By tracking the marble position in the spoon, we show that children with dystonia use a larger fraction of the available variability, whereas healthy children adopt a much safer strategy and remain farther from the margins, as well as learning to adapt and have more control over the marble's utilized area by practice. Together, our results show that both healthy children and children with dystonia choose trajectories that compensate for risk and inherent variability, and that the increased variability in dystonia can be modified with continued practice.NEW & NOTEWORTHY This study provides insights into the adaptability of children with dystonia in learning a point-to-point task. We show that these children adjust their strategies to account for increased difficulty in the task. Our findings underscore the potential of task-specific practice in improving motor skills and show higher level of signal-dependent noise can be controlled through repetition and learned strategies, which provides an avenue for the quantitative evaluation of rehabilitation strategies in this challenging group.

What is the effect of benzodiazepines on deep brain activity? A study in pediatric patients with dystonia.

Introduction: Benzodiazepines (BDZs) are commonly used to treat the symptoms of movement disorders; however, deep brain stimulation (DBS) has become a popular treatment for these disorders. Previous studies have investigated the effects of BDZ on cortical activity, no data are currently available on their effects on deep brain regions, nor on these regions' responses to DBS. How the BDZ affects the thalamus and basal ganglia in dystonia patients remains unknown. Methods: DBS recordings were performed in ventral oralis anterior/posterior (VoaVop), ventral intermediate (VIM) and ventral anterior (VA) thalamic subnuclei, as well as globus pallidus interna (GPi) and subthalamic nucleus (STN). Evoked potentials (EP) and frequency domain analysis were performed to determine the BDZ effect on neural activities compared to the control condition (off-BDZ). Three male pediatric patients with dystonia treated with BDZ and undergoing depth electrode evaluation for clinical targeting were recruited for the study. Stimulation was administered at 25 and 55 Hz frequencies and recordings were simultaneously gathered through pairs of externalized stereoelectroencephalography (sEEG) electrodes. EP amplitude and the effect of stimulation on the frequency spectrum of activity were compared at baseline and following clinical administration of BDZ. Results: Frequency analysis showed consistent reductions in activity during BDZ treatment in all studied brain regions for all patients. Evoked potential (EP) analysis showed increased subthalamic nucleus (STN) EP amplitude and decreased ventral intermediate (VIM) and STN EP amplitude during BDZ treatment. Interpretation: BDZs reduce thalamic and basal ganglia activity in multiple regions and alter the efficacy of transmission between these regions. While the mechanism is unknown our results confirm the known widespread effects of this class of medications and identify specific areas within the motor system that are directly affected.

Deep brain stimulation in an adolescent with hypomyelination with atrophy of the basal ganglia and cerebellum due to a TUBB4A mutation: illustrative case.

BACKGROUND: Hypomyelination with atrophy of the basal ganglia and cerebellum (H-ABC) is a rare genetic disease due to a TUBB4A mutation, with motor features including dystonia. Deep brain stimulation (DBS) can be used to treat dystonia in pediatric populations, although the response is highly variable and preferential toward specific etiologies. OBSERVATIONS: A single pediatric subject with H-ABC received DBS using a staged procedure involving temporary depth electrode placement, identification of optimal stimulation targets, and permanent electrode implantation. After surgery, the patient significantly improved on both the Burke-Fahn-Marsden Dystonia Rating Scale and the Barry-Albright Dystonia Scale. The patient's response suggests that DBS can have potential benefit in H-ABC. LESSONS: TUBB4A mutations are associated with a variety of clinical phenotypes, and there is a lack of clearly identified targets for DBS, with this case being the second reported instance of DBS in this condition. The staged procedure with temporary depth electrode testing is recommended to identify optimal stimulation targets. The response seen in this patient implies that such a staged procedure may provide benefit in other conditions where DBS targets are currently unknown, including rare genetic or metabolic conditions associated with movement disorders.

Improvement of speed-accuracy tradeoff during practice of a point to point task in children with secondary dystonia.

The tradeoff between speed and accuracy is a well-known constraint for human movement, but previous work has shown that this tradeoff can be modified by practice, and the quantitative relationship between speed and accuracy may be an indicator of skill in some tasks. We have previously shown that children with dystonia are able to adapt their movement strategy in a ballistic throwing game to compensate for increased variability of movement. Here we test whether children with dystonia can adapt and improve skill learnt on a trajectory task. We use a novel task in which children move a spoon with a marble between two targets. Difficulty is modified by changing the depth of the spoon. Our results show that both healthy children and children with secondary dystonia move more slowly with the more difficult spoons, and both groups improve the relationship between speed and spoon difficulty following one week of practice. By tracking the marble position in the spoon, we show that children with dystonia use a larger fraction of the available variability, whereas healthy children adopt a much safer strategy and remain farther from the margins, as well as learning to adopt and have more control over the marble's utilized area by practice. Together, our results show that both healthy children and children with dystonia choose trajectories that compensate for risk and inherent variability, and that the increased variability in dystonia can be modified with continued practice.

Globus pallidus internus activity increases during voluntary movement in children with dystonia.

The rate model of basal ganglia function predicts that muscle activity in dystonia is due to disinhibition of thalamus resulting from decreased inhibitory input from pallidum. We seek to test this hypothesis in children with dyskinetic cerebral palsy undergoing evaluation for deep brain stimulation (DBS) to analyze movement-related activity in different brain regions. The results revealed prominent beta-band frequency peaks in the globus pallidus interna (GPi), ventral oralis anterior/posterior (VoaVop) subnuclei of the thalamus, and subthalamic nucleus (STN) during movement but not at rest. Connectivity analysis indicated stronger coupling between STN-VoaVop and STN-GPi compared to GPi-STN. These findings contradict the hypothesis of decreased thalamic inhibition in dystonia, suggesting that abnormal patterns of inhibition and disinhibition, rather than reduced GPi activity, contribute to the disorder. Additionally, the study implies that correcting abnormalities in GPi function may explain the effectiveness of DBS targeting the STN and GPi in treating dystonia.

The Effects of Prolonged Vibrotactile EMG-Based Biofeedback on Ankle Joint Range of Motion During Gait in Children with Spastic Cerebral Palsy: A Case Series.

AIMS: The objective of this case series was to examine the feasibility of vibrotactile EMG-based biofeedback (BF) as a home-based intervention tool to enhance sensory information during everyday motor activities and to explore its effectiveness to induce changes in active ankle range of motion during gait in children with spastic cerebral palsy (CP). METHODS: Ten children ages 6 to 13 years with spastic CP were recruited. Participants wore two EMG-based vibro-tactile BF devices for at least 4 hours per day for 1-month on the ankle and knee joints muscles. The device computed the amplitude of the EMG signal of the target muscle and actuated a silent vibration motor proportional to the magnitude of the EMG. RESULTS: Our results demonstrated the feasibility of the augmented sensory information of muscle activity to induce changes of the active ankle range of motion during gait for 6 children with an increase ranging from 8.9 to 51.6% compared to a one-month period without treatment. CONCLUSIONS: Preliminary findings of this case series demonstrate the feasibility of vibrotactile EMG-based BF and suggest potential effectiveness to increase active ankle range of motion, therefore serving as a promising therapeutic tool to improve gait in children with spastic CP.

Application of deep brain stimulation for the treatment of childhood-onset dystonia in patients with MEPAN syndrome.

Introduction: Mitochondrial Enoyl CoA Reductase Protein-Associated Neurodegeneration (MEPAN) syndrome is a rare inherited metabolic condition caused by MECR gene mutations. This gene encodes a protein essential for fatty acid synthesis, and defects cause progressively worsening childhood-onset dystonia, optic atrophy, and basal ganglia abnormalities. Deep brain stimulation (DBS) has shown mixed improvement in other childhood-onset dystonia conditions. To the best of our knowledge, DBS has not been investigated as a treatment for dystonia in patients with MEPAN syndrome. Methods: Two children with MEPAN were identified as possible DBS candidates due to severe generalized dystonia unresponsive to pharmacotherapy. Temporary depth electrodes were placed in six locations bilaterally and tested during a 6-day hospitalization to determine the best locations for permanent electrode placement. The Burke-Fahn-Marsden Dystonia Rating Scale (BFMDRS) and Barry-Albright Dystonia Scale (BADS) were used for preoperative and postoperative testing to quantitatively assess dystonia severity changes. Patient 1 had permanent electrodes placed at the globus pallidus internus (GPi) and pedunculopontine nucleus (PPN). Patient 2 had permanent electrodes placed at the GPi and ventralis intermedius nucleus of the thalamus (VIM). Results: Both patients successfully underwent DBS placement with no perioperative complications and significant improvement in their BFMDRS score. Patient 2 also demonstrated improvement in the BADS. Discussion: We demonstrated a novel application of DBS in MEPAN syndrome patients with childhood-onset dystonia. These patients showed clinically significant improvements in dystonia following DBS, indicating that DBS can be considered for dystonia in patients with rare metabolic disorders that currently have no other proven treatment options.

Increased movement-related signals in both basal ganglia and cerebellar output pathways in two children with dystonia.

The contribution of different brain regions to movement abnormalities in children with dystonia is unknown. Three awake subjects undergoing depth electrode implantation for assessments of potential deep brain recording targets performed a rhythmic figure-8 drawing task. Two subjects had dystonia, one was undergoing testing for treatment of Tourette Syndrome and had neither dystonia nor abnormal movements during testing. Movement-related signals were evaluated by determining the magnitude of task-related frequency components. Brain signals were recorded in globus pallidus internus (GPi), the ventral oralis anterior/posterior (VoaVop) and the ventral intermediate (Vim) nuclei of the thalamus. In comparison to the subject without dystonia, both children with dystonia showed increased task-related activity in GPi and Vim. This finding is consistent with a role of both basal ganglia and cerebellar outputs in the pathogenesis of dystonia. Our results further suggest that frequency analysis of brain recordings during cyclic movements may be a useful tool for analysis of the presence of movement-related signals in various brain regions.

Assisting Forearm Function in Children With Movement Disorders via A Soft Wearable Robot With Equilibrium-Point Control.

Wearable robots are envisioned to amplify the independence of people with movement impairments by providing daily physical assistance. For portable, comfortable, and safe devices, soft pneumatic-based robots are emerging as a potential solution. However, due to the inherent complexities, including compliance and nonlinear mechanical behavior, feedback control for facilitating human-robot interaction remains a challenge. Herein, we present the design, fabrication, and control architecture of a soft wearable robot that assists in supination and pronation of the forearm. The soft wearable robot integrates an antagonistic pair of pneumatic-based helical actuators to provide active pronation and supination torques. Our main contribution is a bio-inspired equilibrium-point control scheme for integrating proprioceptive feedback and exteroceptive input (e.g., the user's muscle activation signals) directly with the on/off valve behavior of the soft pneumatic actuators. The proposed human-robot controller is directly inspired by the equilibrium-point hypothesis of motor control, which suggests that voluntary movements arise through shifts in the equilibrium state of the antagonistic muscle pair spanning a joint. We hypothesized that the proposed method would reduce the required effort during dynamic manipulation without affecting the error. In order to evaluate our proposed method, we recruited seven pediatric participants with movement disorders to perform two dynamic interaction tasks with a haptic manipulandum. Each task required the participant to track a sinusoidal trajectory while the haptic manipulandum behaved as a Spring-Dominate system or Inertia-Dominate system. Our results reveal that the soft wearable robot, when active, reduced user effort on average by 14%. This work demonstrates the practical implementation of an equilibrium-point volitional controller for wearable robots and provides a foundational path toward versatile, low-cost, and soft wearable robots.

Transient Complete Resolution of Tourette Syndrome Symptoms Following Personalized Depth Electrode Placement.

Treatment refractory Tourette syndrome has been shown to be improved with deep brain stimulation, but with multiple possible stimulation locations and variable and incomplete benefit. This study presents a single case of complete amelioration of motor and verbal tics in a patient with Tourette syndrome during placement of 12 stereo-EEG electrodes to identify optimal targets for permanent stimulating electrodes. Subsequently, substantial improvement in motor and verbal tic frequency occurred with placement and programming of permanent electrodes in bilateral globus pallidus internus and nucleus accumbens, but without the complete resolution seen during depth electrode placement. We suggest that simultaneous stimulation at multiple patient-specific targets could provide effective control of Tourette symptomatology, but further study will be needed.

High-fidelity transmission of high-frequency burst stimuli from peripheral nerve to thalamic nuclei in children with dystonia.

High-frequency peripheral nerve stimulation has emerged as a noninvasive alternative to thalamic deep brain stimulation for some patients with essential tremor. It is not known whether such techniques might be effective for movement disorders in children, nor is the mechanism and transmission of the peripheral stimuli to central brain structures understood. This study was designed to investigate the fidelity of transmission from peripheral nerves to thalamic nuclei in children with dystonia undergoing deep brain stimulation surgery. The ventralis intermediate (VIM) thalamus nuclei showed a robust evoked response to peripheral high-frequency burst stimulation, with a greatest response magnitude to intra-burst frequencies between 50 and 100 Hz, and reliable but smaller responses up to 170 Hz. The earliest response occurred at 12-15 ms following stimulation onset, suggesting rapid high-fidelity transmission between peripheral nerve and thalamic nuclei. A high-bandwidth, low-latency transmission path from peripheral nerve to VIM thalamus is consistent with the importance of rapid and accurate sensory information for the control of coordination and movement via the cerebello-thalamo-cortical pathway. Our results suggest the possibility of non-invasive modulation of thalamic activity in children with dystonia, and therefore the possibility that a subset of children could have beneficial clinical response without the need for invasive deep brain stimulation.

Can spatial filtering separate voluntary and involuntary components in children with dyskinetic cerebral palsy?

The design of myocontrolled devices faces particular challenges in children with dyskinetic cerebral palsy because the electromyographic signal for control contains both voluntary and involuntary components. We hypothesized that voluntary and involuntary components of movements would be uncorrelated and thus detectable as different synergistic patterns of muscle activity, and that removal of the involuntary components would improve online EMG-based control. Therefore, we performed a synergy-based decomposition of EMG-guided movements, and evaluated which components were most controllable using a Fitts' Law task. Similarly, we also tested which muscles were most controllable. We then tested whether removing the uncontrollable components or muscles improved overall function in terms of movement time, success rate, and throughput. We found that removal of less controllable components or muscles did not improve EMG control performance, and in many cases worsened performance. These results suggest that abnormal movement in dyskinetic CP is consistent with a pervasive distortion of voluntary movement rather than a superposition of separable voluntary and involuntary components of movement.

Constraint-induced intervention as an emergent phenomenon from synaptic competition in biological systems.

The principle of constraint-induced therapy is widely practiced in rehabilitation. In hemiplegic cerebral palsy (CP) with impaired contralateral corticospinal projection due to unilateral injury, function improves after imposing a temporary constraint on limbs from the less affected hemisphere. This type of partially-reversible impairment in motor control by early brain injury bears a resemblance to the experience-dependent plastic acquisition and modification of neuronal response selectivity in the visual cortex. Previously, such mechanism was modeled within the framework of BCM (Bienenstock-Cooper-Munro) theory, a rate-based synaptic modification theory. Here, we demonstrate a minimally complex yet sufficient neural network model which provides a fundamental explanation for inter-hemispheric competition using a simplified spike-based model of information transmission and plasticity. We emulate the restoration of function in hemiplegic CP by simulating the competition between cells of the ipsilateral and contralateral corticospinal tracts. We use a high-speed hardware neural simulation to provide realistic numbers of spikes and realistic magnitudes of synaptic modification. We demonstrate that the phenomenon of constraint-induced partial reversal of hemiplegia can be modeled by simplified neural descending tracts with 2 layers of spiking neurons and synapses with spike-timing-dependent plasticity (STDP). We further demonstrate that persistent hemiplegia following unilateral cortical inactivation or deprivation is predicted by the STDP-based model but is inconsistent with BCM model. Although our model is a highly simplified and limited representation of the corticospinal system, it offers an explanation of how constraint as an intervention can help the system to escape from a suboptimal solution. This is a display of an emergent phenomenon from the synaptic competition.

A Cerebellar Computational Mechanism for Delay Conditioning at Precise Time Intervals.

The cerebellum is known to have an important role in sensing and execution of precise time intervals, but the mechanism by which arbitrary time intervals can be recognized and replicated with high precision is unknown. We propose a computational model in which precise time intervals can be identified from the pattern of individual spike activity in a population of parallel fibers in the cerebellar cortex. The model depends on the presence of repeatable sequences of spikes in response to conditioned stimulus input. We emulate granule cells using a population of Izhikevich neuron approximations driven by random but repeatable mossy fiber input. We emulate long-term depression (LTD) and long-term potentiation (LTP) synaptic plasticity at the parallel fiber to Purkinje cell synapse. We simulate a delay conditioning paradigm with a conditioned stimulus (CS) presented to the mossy fibers and an unconditioned stimulus (US) some time later issued to the Purkinje cells as a teaching signal. We show that Purkinje cells rapidly adapt to decrease firing probability following onset of the CS only at the interval for which the US had occurred. We suggest that detection of replicable spike patterns provides an accurate and easily learned timing structure that could be an important mechanism for behaviors that require identification and production of precise time intervals.

Evoked Potentials During Peripheral Stimulation Confirm Electrode Location in Thalamic Subnuclei in Children With Secondary Dystonia.

Deep brain stimulation is an elective surgical intervention that improves the function and quality of life in children with dystonia and other movement disorders. Both basal ganglia and thalamic nuclei have been found to be relevant targets for treatment of dystonia in children, including the ventral intermediate nucleus of the thalamus, in which stimulation can control dystonic spasms. Electrophysiological confirmation of correct electrode location within the ventralis intermediate nucleus is thus important for the success of the surgical outcome. The present work shows the evoked potentials response during contralateral median-nerve stimulation at the wrist at low frequency (9 Hz) provides physiological evidence of the electrode's localization within the thalamus. We show the correlation between evoked potentials and magnetic resonance imaging (MRI) and computed tomography (CT) in 14 children undergoing implantation of deep brain stimulation electrodes for secondary dystonia. High fidelity and reproducibility of our results provides a new approach to ensure the electrode localization in the thalamic subnuclei.

Proceedings of the Seventh Annual Deep Brain Stimulation Think Tank: Advances in Neurophysiology, Adaptive DBS, Virtual Reality, Neuroethics and Technology.

The Seventh Annual Deep Brain Stimulation (DBS) Think Tank held on September 8th of 2019 addressed the most current: (1) use and utility of complex neurophysiological signals for development of adaptive neurostimulation to improve clinical outcomes; (2) Advancements in recent neuromodulation techniques to treat neuropsychiatric disorders; (3) New developments in optogenetics and DBS; (4) The use of augmented Virtual reality (VR) and neuromodulation; (5) commercially available technologies; and (6) ethical issues arising in and from research and use of DBS. These advances serve as both "markers of progress" and challenges and opportunities for ongoing address, engagement, and deliberation as we move to improve the functional capabilities and translational value of DBS. It is in this light that these proceedings are presented to inform the field and initiate ongoing discourse. As consistent with the intent, and spirit of this, and prior DBS Think Tanks, the overarching goal is to continue to develop multidisciplinary collaborations to rapidly advance the field and ultimately improve patient outcomes.

Tuning of Standing Postural Responses to Instability and Cost Function.

Whole-body movements are performed daily, and humans must constantly take into account the inherent instability of a standing posture. At times these movements may be performed in risky environments and when facing different costs of failure. The aim of the study was to test the hypothesis that in upright stance participants continuously estimate both probability of failure and cost of failure such that their postural responses will be based on these estimates. We designed a snowboard riding simulation experiment where participants were asked to control the position of a moving snowboard within a snow track in a risky environment. Cost functions were provided by modifying the penalty of riding in the area adjacent to the snow track. Uncertainty was modified by changing the gain of postural responses while participants were standing on a rocker board. We demonstrated that participants continually evaluated the environmental cost function and compensated for additional risk with feedback-based postural changes, even when probability of failure was negligible. Results showed also that the participants' estimates of the probability of failure accounted for their own inherent instability. Moreover, participants showed a tendency to overweight large probabilities of failure with more biomechanically constrained standing postures that results in suboptimal estimates of risky environments. Overall, our results suggest that participants tune their standing postural responses by empirically estimating the cost of failure and the uncertainty level in order to minimize the risk of falling when cost is high.