The effect of responsive neurostimulation (RNS) on neuropsychiatric and psychosocial outcomes in drug-resistant epilepsy.

OBJECTIVE: The impact of responsive neurostimulation (RNS) on neuropsychiatric and psychosocial outcomes has not been extensively evaluated outside of the original clinical trials and post-approval studies. The goal of this study was to ascertain the potential real-world effects of RNS on cognitive, psychiatric, and quality of life (QOL) outcomes in relation to seizure outcomes by examining 50 patients undergoing RNS implantation for drug-resistant epilepsy (DRE). METHODS: We performed a retrospective review of all patients treated at our institution with RNS for DRE with at least 12 months of follow-up. In addition to baseline demographic and disease-related characteristics, we collected cognitive (Full-Scale Intelligence Quotient, Verbal Comprehension, and Perceptual Reasoning Index), psychiatric (Beck Depression and Anxiety Inventory Scores), and QOL (QOLIE-31) outcomes at 6 and 12 months after RNS implantation and correlated them with seizure outcomes. RESULTS: Fifty patients (median age 39.5 years, 64% female) were treated with RNS for DRE in our institution from 2005 to 2020. Of the 37 of them who had well-documented pre and post-implantation seizure diaries, the 6-month median seizure frequency reduction was 88%, the response rate (50% or greater seizure frequency reduction) was 78%, and 32% of patients were free of disabling seizures in this timeframe. There was no statistically significant difference at a group level in any of the evaluated cognitive, psychiatric, and QOL outcomes at 6 and 12 months post-implantation compared to the pre-implantation baseline, irrespective of seizure outcomes, although a subset of patients experienced a decline in mood or cognitive variables. SIGNIFICANCE: Responsive neurostimulation does not appear to have a statistically significant negative or positive impact on neuropsychiatric and psychosocial status at the group level. We observed significant variability in outcome, with a minority of patients experiencing worse behavioral outcomes, which seemed related to RNS implantation. Careful outcome monitoring is required to identify the subset of patients experiencing a poor response and to make appropriate adjustments in care.

Anterior nucleus of the thalamus deep brain stimulation vs temporal lobe responsive neurostimulation for temporal lobe epilepsy.

OBJECTIVE: Based on the promising results of randomized controlled trials, deep brain stimulation (DBS) and responsive neurostimulation (RNS) are used increasingly in the treatment of patients with drug-resistant epilepsy. Drug-resistant temporal lobe epilepsy (TLE) is an indication for either DBS of the anterior nucleus of the thalamus (ANT) or temporal lobe (TL) RNS, but there are no studies that directly compare the seizure benefits and adverse effects associated with these therapies in this patient population. We, therefore, examined all patients who underwent ANT-DBS or TL-RNS for drug-resistant TLE at our center. METHODS: We performed a retrospective review of patients who were treated with either ANT-DBS or TL-RNS for drug-resistant TLE with at least 12 months of follow-up. Along with the clinical characteristics of each patient's epilepsy, seizure frequency was recorded throughout each patient's postoperative clinical course. RESULTS: Twenty-six patients underwent ANT-DBS implantation and 32 patients underwent TL-RNS for drug-resistant TLE. The epilepsy characteristics of both groups were similar. Patients who underwent ANT-DBS demonstrated a median seizure reduction of 58% at 12-15 months, compared to a median seizure reduction of 70% at 12-15 months in patients treated with TL-RNS (p > .05). The responder rate (percentage of patients with a 50% decrease or more in seizure frequency) was 54% for ANT-DBS and 56% for TL-RNS (p > .05). The incidence of complications and stimulation-related side effects did not significantly differ between therapies. SIGNIFICANCE: We demonstrate in our single-center experience that patients with drug-resistant TLE benefit similarly from either ANT-DBS or TL-RNS. Selection of either ANT-DBS or TL-RNS may, therefore, depend more heavily on patient and provider preference, as each has unique capabilities and configurations. Future studies will consider subgroup analyses to determine if specific patients have greater seizure frequency reduction from one form of neuromodulation strategy over another.

Microscale Physiological Events on the Human Cortical Surface.

Despite ongoing advances in our understanding of local single-cellular and network-level activity of neuronal populations in the human brain, extraordinarily little is known about their "intermediate" microscale local circuit dynamics. Here, we utilized ultra-high-density microelectrode arrays and a rare opportunity to perform intracranial recordings across multiple cortical areas in human participants to discover three distinct classes of cortical activity that are not locked to ongoing natural brain rhythmic activity. The first included fast waveforms similar to extracellular single-unit activity. The other two types were discrete events with slower waveform dynamics and were found preferentially in upper cortical layers. These second and third types were also observed in rodents, nonhuman primates, and semi-chronic recordings from humans via laminar and Utah array microelectrodes. The rates of all three events were selectively modulated by auditory and electrical stimuli, pharmacological manipulation, and cold saline application and had small causal co-occurrences. These results suggest that the proper combination of high-resolution microelectrodes and analytic techniques can capture neuronal dynamics that lay between somatic action potentials and aggregate population activity. Understanding intermediate microscale dynamics in relation to single-cell and network dynamics may reveal important details about activity in the full cortical circuit.

Selective Formation of Porous Pt Nanorods for Highly Electrochemically Efficient Neural Electrode Interfaces.

The enhanced electrochemical activity of nanostructured materials is readily exploited in energy devices, but their utility in scalable and human-compatible implantable neural interfaces can significantly advance the performance of clinical and research electrodes. We utilize low-temperature selective dealloying to develop scalable and biocompatible one-dimensional platinum nanorod (PtNR) arrays that exhibit superb electrochemical properties at various length scales, stability, and biocompatibility for high performance neurotechnologies. PtNR arrays record brain activity with cellular resolution from the cortical surfaces in birds and nonhuman primates. Significantly, strong modulation of surface recorded single unit activity by auditory stimuli is demonstrated in European Starling birds as well as the modulation of local field potentials in the visual cortex by light stimuli in a nonhuman primate and responses to electrical stimulation in mice. PtNRs record behaviorally and physiologically relevant neuronal dynamics from the surface of the brain with high spatiotemporal resolution, which paves the way for less invasive brain-machine interfaces.

Experimental Malaria in Pregnancy Induces Neurocognitive Injury in Uninfected Offspring via a C5a-C5a Receptor Dependent Pathway.

The in utero environment profoundly impacts childhood neurodevelopment and behaviour. A substantial proportion of pregnancies in Africa are at risk of malaria in pregnancy (MIP) however the impact of in utero exposure to MIP on fetal neurodevelopment is unknown. Complement activation, in particular C5a, may contribute to neuropathology and adverse outcomes during MIP. We used an experimental model of MIP and standardized neurocognitive testing, MRI, micro-CT and HPLC analysis of neurotransmitter levels, to test the hypothesis that in utero exposure to malaria alters neurodevelopment through a C5a-C5aR dependent pathway. We show that malaria-exposed offspring have persistent neurocognitive deficits in memory and affective-like behaviour compared to unexposed controls. These deficits were associated with reduced regional brain levels of major biogenic amines and BDNF that were rescued by disruption of C5a-C5aR signaling using genetic and functional approaches. Our results demonstrate that experimental MIP induces neurocognitive deficits in offspring and suggest novel targets for intervention.

Genomic approaches to deconstruct pluripotency.

Embryonic stem cells (ESCs) first derived from the inner cell mass of blastocyst-stage embryos have the unique capacity of indefinite self-renewal and potential to differentiate into all somatic cell types. Similar developmental potency can be achieved by reprogramming differentiated somatic cells into induced pluripotent stem cells (iPSCs). Both types of pluripotent stem cells provide great potential for fundamental studies of tissue differentiation, and hold promise for disease modeling, drug development, and regenerative medicine. Although much has been learned about the molecular mechanisms that underlie pluripotency in such cells, our understanding remains incomplete. A comprehensive understanding of ESCs and iPSCs requires the deconstruction of complex transcription regulatory networks, epigenetic mechanisms, and biochemical interactions critical for the maintenance of self-renewal and pluripotency. In this review, we will discuss recent advances gleaned from application of global "omics" techniques to dissect the molecular mechanisms that define the pluripotent state.

Anterior thalamic nucleus local field potentials during focal temporal lobe epileptic seizures.

Objective: To analyze the local field potentials (LFPs) in patients with focal drug-resistant epilepsy (DRE) from the anterior nucleus of the thalamus (ANT) during inter-ictal state and seizure state. Method: ANT stereotactic EEG (SEEG) recordings were studied in four patients with focal temporal lobe epilepsy. SEEG data was classified as inter-ictal and ictal state and sub-categorized into electrographic (ESz), focal aware seizure (FAS), focal with impaired awareness (FIA), or focal to bilateral tonic-clonic seizure (FBTC). LFP was analyzed at 4 Hz, 8 Hz, 16 Hz, 32 Hz, high gamma (100 Hz), and ripples (200 Hz) using spectrogram analysis and a statistical comparison of normalized power spectral density (PSD) averaged during seizures versus pre-ictal baseline segments. Result: The LFP recordings were analyzed for 162 seizures (127 ESz, 23 FAS, 6 FIA, and 6 FBTC). Based on time-frequency data (spectrogram), a broad band of activity, occurring between 2 and 6 Hz and centered at 4 Hz, and thin-band activity occurring specifically at 8 Hz on the frequency spectrogram were observed during the inter-ictal state. Statistically significant changes in LFP-PSD were seen for FAS, FIA, and FBTC. We observed a significant gain in LFP at the lower frequency band during FAS at 4 Hz, FIA, and FBTC at 4, 8, and 16 Hz while also observing increases at higher frequencies during FBTC at 100 and 200 Hz and a decrease during FAS seizures at 32 Hz. In contrast, no significant change in LFP power was seen for electrographic seizures. Interpretation: Our observations from a limited dataset indicate that all clinical seizure types, but not electrographic seizures, caused a change in ANT-LFP based on the magnitude of the associated power spectral density (PSD). Future work will be needed to validate the use of ANT-LFP at these frequencies as accurate measurements of seizure occurrence and severity. This work represents a first step toward understanding ANT thalamic LFP patterns during focal seizures and developing adaptive DBS strategies.

An electroencephalogram microdisplay to visualize neuronal activity on the brain surface.

Functional mapping during brain surgery is applied to define brain areas that control critical functions and cannot be removed. Currently, these procedures rely on verbal interactions between the neurosurgeon and electrophysiologist, which can be time-consuming. In addition, the electrode grids that are used to measure brain activity and to identify the boundaries of pathological versus functional brain regions have low resolution and limited conformity to the brain surface. Here, we present the development of an intracranial electroencephalogram (iEEG)-microdisplay that consists of freestanding arrays of 2048 GaN light-emitting diodes laminated on the back of micro-electrocorticography electrode grids. With a series of proof-of-concept experiments in rats and pigs, we demonstrate that these iEEG-microdisplays allowed us to perform real-time iEEG recordings and display cortical activities by spatially corresponding light patterns on the surface of the brain in the surgical field. Furthermore, iEEG-microdisplays allowed us to identify and display cortical landmarks and pathological activities from rat and pig models. Using a dual-color iEEG-microdisplay, we demonstrated coregistration of the functional cortical boundaries with one color and displayed the evolution of electrical potentials associated with epileptiform activity with another color. The iEEG-microdisplay holds promise to facilitate monitoring of pathological brain activity in clinical settings.

Responsive neurostimulation as a treatment for super-refractory focal status epilepticus: a systematic review and case series.

OBJECTIVE: Super-refractory status epilepticus (SRSE) has high rates of morbidity and mortality. Few published studies have investigated neurostimulation treatment options in the setting of SRSE. This systematic literature review and series of 10 cases investigated the safety and efficacy of implanting and activating the responsive neurostimulation (RNS) system acutely during SRSE and discusses the rationale for lead placement and selection of stimulation parameters. METHODS: Through a literature search (of databases and American Epilepsy Society abstracts that were last searched on March 1, 2023) and direct contact with the manufacturer of the RNS system, 10 total cases were identified that utilized RNS acutely during SE (9 SRSE cases and 1 case of refractory SE [RSE]). Nine centers obtained IRB approval for retrospective chart review and completed data collection forms. A tenth case had published data from a case report that were referenced in this study. Data from the collection forms and the published case report were compiled in Excel. RESULTS: All 10 cases presented with focal SE: 9 with SRSE and 1 with RSE. Etiology varied from known lesion (focal cortical dysplasia in 7 cases and recurrent meningioma in 1) to unknown (2 cases, with 1 presenting with new-onset refractory focal SE [NORSE]). Seven of 10 cases exited SRSE after RNS placement and activation, with a time frame ranging from 1 to 27 days. Two patients died of complications due to ongoing SRSE. Another patient's SE never resolved but was subclinical. One of 10 cases had a device-related significant adverse event (trace hemorrhage), which did not require intervention. There was 1 reported recurrence of SE after discharge among the cases in which SRSE resolved up to the defined endpoint. CONCLUSIONS: This case series offers preliminary evidence that RNS is a safe and potentially effective treatment option for SRSE in patients with 1-2 well-defined seizure-onset zone(s) who meet the eligibility criteria for RNS. The unique features of RNS offer multiple benefits in the SRSE setting, including real-time electrocorticography to supplement scalp EEG for monitoring SRSE progress and response to treatment, as well as numerous stimulation options. Further research is indicated to investigate the optimal stimulation settings in this unique clinical scenario.

Intraoperative application and early experience with novel high-resolution, high-channel-count thin-film electrodes for human microelectrocorticography.

OBJECTIVE: The study objective was to evaluate intraoperative experience with newly developed high-spatial-resolution microelectrode grids composed of poly(3,4-ethylenedioxythiophene) with polystyrene sulfonate (PEDOT:PSS), and those composed of platinum nanorods (PtNRs). METHODS: A cohort of patients who underwent craniotomy for pathological tissue resection and who had high-spatial-resolution microelectrode grids placed intraoperatively were evaluated. Patient demographic and baseline clinical variables as well as relevant microelectrode grid characteristic data were collected. The primary and secondary outcome measures of interest were successful microelectrode grid utilization with usable resting-state or task-related data, and grid-related adverse intraoperative events and/or grid dysfunction. RESULTS: Included in the analysis were 89 cases of patients who underwent a craniotomy for resection of neoplasms (n = 58) or epileptogenic tissue (n = 31). These cases accounted for 94 grids: 58 PEDOT:PSS and 36 PtNR grids. Of these 94 grids, 86 were functional and used successfully to obtain cortical recordings from 82 patients. The mean cortical grid recording duration was 15.3 ± 1.15 minutes. Most recordings in patients were obtained during experimental tasks (n = 52, 58.4%), involving language and sensorimotor testing paradigms, or were obtained passively during resting state (n = 32, 36.0%). There were no intraoperative adverse events related to grid placement. However, there were instances of PtNR grid dysfunction (n = 8) related to damage incurred by suboptimal preoperative sterilization (n = 7) and improper handling (n = 1); intraoperative recordings were not performed. Vaporized peroxide sterilization was the most optimal sterilization method for PtNR grids, providing a significantly greater number of usable channels poststerilization than did steam-based sterilization techniques (median 905.0 [IQR 650.8-935.5] vs 356.0 [IQR 18.0-597.8], p = 0.0031). CONCLUSIONS: High-spatial-resolution microelectrode grids can be readily incorporated into appropriately selected craniotomy cases for clinical and research purposes. Grids are reliable when preoperative handling and sterilization considerations are accounted for. Future investigations should compare the diagnostic utility of these high-resolution grids to commercially available counterparts and assess whether diagnostic discrepancies relate to clinical outcomes.

Modular Phoneme Processing in Human Superior Temporal Gyrus.

Modular organization is fundamental to cortical processing, but its presence is human association cortex is unknown. We characterized phoneme processing with 128-1024 channel micro-arrays at 50-200µm pitch on superior temporal gyrus of 7 patients. High gamma responses were highly correlated within ~1.7mm diameter modules, sharply delineated from adjacent modules with distinct time-courses and phoneme-selectivity. We suggest that receptive language cortex may be organized in discrete processing modules.

Flexible, scalable, high channel count stereo-electrode for recording in the human brain.

Over the past decade, stereotactically placed electrodes have become the gold standard for deep brain recording and stimulation for a wide variety of neurological and psychiatric diseases. Current electrodes, however, are limited in their spatial resolution and ability to record from small populations of neurons, let alone individual neurons. Here, we report on an innovative, customizable, monolithically integrated human-grade flexible depth electrode capable of recording from up to 128 channels and able to record at a depth of 10 cm in brain tissue. This thin, stylet-guided depth electrode is capable of recording local field potentials and single unit neuronal activity (action potentials), validated across species. This device represents an advance in manufacturing and design approaches which extends the capabilities of a mainstay technology in clinical neurology.

Transient changes during microwave ablation simulation : a comparative shape analysis.

Microwave ablation therapy is a hyperthermic treatment for killing cancerous tumours whereby microwave energy is dispersed into a target tissue region. Modelling can provide a prediction for the outcome of ablation, this paper explores changes in size and shape of temperature and Specific absorption rate fields throughout the course of simulated treatment with different probe concepts. Here, an axisymmetric geometry of a probe embedded within a tissue material is created, solving coupled electromagnetic and bioheat equations using the finite element method, utilizing hp discretisation with the NGSolve library. Results show dynamic changes across all metrics, with different responses from different probe concepts. The sleeve probe yielded the most circular specific absorption rate pattern with circularity of 0.81 initially but suffered the largest reduction throughout ablation. Similarly, reflection coefficients differ drastically from their initial values, with the sleeve probe again experiencing the largest change, suggesting that it is the most sensitive the changes in the tissue dielectric properties in these select probe designs. These collective characteristic observations highlight the need to consider dielectric property changes and probe specific responses during the design cycle.

The Brain Electroencephalogram Microdisplay for Precision Neurosurgery.

Brain surgeries are among the most delicate clinical procedures and must be performed with the most technologically robust and advanced tools. When such surgical procedures are performed in functionally critical regions of the brain, functional mapping is applied as a standard practice that involves direct coordinated interactions between the neurosurgeon and the clinical neurology electrophysiology team. However, information flow during these interactions is commonly verbal as well as time consuming which in turn increases the duration and cost of the surgery, possibly compromising the patient outcomes. Additionally, the grids that measure brain activity and identify the boundaries of pathological versus functional brain regions suffer from low resolution (3-10 mm contact to contact spacing) with limited conformity to the brain surface. Here, we introduce a brain intracranial electroencephalogram microdisplay (Brain-iEEG-microdisplay) which conforms to the brain to measure the brain activity and display changes in near real-time (40 Hz refresh rate) on the surface of the brain in the surgical field. We used scalable engineered gallium nitride (GaN) substrates with 6" diameter to fabricate, encapsulate, and release free-standing arrays of up to 2048 GaN light emitting diodes (µLEDs) in polyimide substrates. We then laminated the µLED arrays on the back of micro-electrocorticography (µECoG) platinum nanorod grids (PtNRGrids) and developed hardware and software to perform near real-time intracranial EEG analysis and activation of light patterns that correspond to specific cortical activities. Using the Brain-iEEG-microdisplay, we precisely ideFSntified and displayed important cortical landmarks and pharmacologically induced pathological activities. In the rat model, we identified and displayed individual cortical columns corresponding to individual whiskers and the near real-time evolution of epileptic discharges. In the pig animal model, we demonstrated near real-time mapping and display of cortical functional boundaries using somatosensory evoked potentials (SSEP) and display of responses to direct electrical stimulation (DES) from the surface or within the brain tissue. Using a dual-color Brain-iEEG-microdisplay, we demonstrated co-registration of the functional cortical boundaries with one color and displayed the evolution of electrical potentials associated with epileptiform activity with another color. The Brain-iEEG-microdisplay holds the promise of increasing the efficiency of diagnosis and possibly surgical treatment, thereby reducing the cost and improving patient outcomes which would mark a major advancement in neurosurgery. These advances can also be translated to broader applications in neuro-oncology and neurophysiology.

Phasic stimulation in the nucleus accumbens enhances learning after traumatic brain injury.

Traumatic brain injury (TBI) is a significant cause of morbidity and mortality worldwide. Despite improvements in survival, treatments that improve functional outcome remain lacking. There is, therefore, a pressing need to develop novel treatments to improve functional recovery. Here, we investigated task-matched deep-brain stimulation of the nucleus accumbens (NAc) to augment reinforcement learning in a rodent model of TBI. We demonstrate that task-matched deep brain stimulation (DBS) of the NAc can enhance learning following TBI. We further demonstrate that animals receiving DBS exhibited greater behavioral improvement and enhanced neural proliferation. Treated animals recovered to an uninjured behavioral baseline and showed retention of improved performance even after stimulation was stopped. These results provide encouraging early evidence for the potential of NAc DBS to improve functional outcomes following TBI and that its effects may be broad, with alterations in neurogenesis and synaptogenesis.

Centromedian thalamic deep brain stimulation for drug-resistant epilepsy: single-center experience.

OBJECTIVE: Neuromodulation of the centromedian nucleus of the thalamus (CM) has unclear effectiveness in the treatment of drug-resistant epilepsy. Prior reports suggest that it may be more effective in the generalized epilepsies such as Lennox-Gastaut syndrome (LGS). The objective of this study was to determine the outcome of CM deep brain stimulation (DBS) at the authors' institution. METHODS: Retrospective chart review was performed for all patients who underwent CM DBS at Emory University, which occurred between December 2018 and May 2021. CM DBS electrodes were implanted using three different surgical methods, including frame-based, robot-assisted, and direct MRI-guided. Seizure frequency, stimulation parameters, and adverse events were recorded from subsequent clinical follow-up visits. RESULTS: Fourteen patients underwent CM DBS: 9 had symptomatic generalized epilepsy (including 5 with LGS), 3 had primary or idiopathic generalized epilepsy, and 2 had bifrontal focal epilepsy. At last follow-up (mean [± SEM] 19 ± 5 months, range 4.1-33 months, ≥ 6 months in 11 patients), the median seizure frequency reduction was 91%. Twelve patients (86%) were considered responders (≥ 50% decrease in seizure frequency), including 10 of 12 with generalized epilepsy and both patients with bifrontal epilepsy. Surgical adverse events were rare and included 1 patient with hardware breakage, 1 with a postoperative aspiration event, and 1 with a nonclinically significant intracranial hemorrhage. CONCLUSIONS: CM DBS was an effective treatment for drug-resistant generalized and bifrontal epilepsies. Additional studies and analyses may investigate whether CM DBS is best suited for specific epilepsy types, and the relationship of lead location to outcome in different epilepsies.

Human brain mapping with multithousand-channel PtNRGrids resolves spatiotemporal dynamics.

Electrophysiological devices are critical for mapping eloquent and diseased brain regions and for therapeutic neuromodulation in clinical settings and are extensively used for research in brain-machine interfaces. However, the existing clinical and experimental devices are often limited in either spatial resolution or cortical coverage. Here, we developed scalable manufacturing processes with a dense electrical connection scheme to achieve reconfigurable thin-film, multithousand-channel neurophysiological recording grids using platinum nanorods (PtNRGrids). With PtNRGrids, we have achieved a multithousand-channel array of small (30 µm) contacts with low impedance, providing high spatial and temporal resolution over a large cortical area. We demonstrated that PtNRGrids can resolve submillimeter functional organization of the barrel cortex in anesthetized rats that captured the tissue structure. In the clinical setting, PtNRGrids resolved fine, complex temporal dynamics from the cortical surface in an awake human patient performing grasping tasks. In addition, the PtNRGrids identified the spatial spread and dynamics of epileptic discharges in a patient undergoing epilepsy surgery at 1-mm spatial resolution, including activity induced by direct electrical stimulation. Collectively, these findings demonstrated the power of the PtNRGrids to transform clinical mapping and research with brain-machine interfaces.

Fast and accurate methods for phylogenomic analyses.

BACKGROUND: Species phylogenies are not estimated directly, but rather through phylogenetic analyses of different gene datasets. However, true gene trees can differ from the true species tree (and hence from one another) due to biological processes such as horizontal gene transfer, incomplete lineage sorting, and gene duplication and loss, so that no single gene tree is a reliable estimate of the species tree. Several methods have been developed to estimate species trees from estimated gene trees, differing according to the specific algorithmic technique used and the biological model used to explain differences between species and gene trees. Relatively little is known about the relative performance of these methods. RESULTS: We report on a study evaluating several different methods for estimating species trees from sequence datasets, simulating sequence evolution under a complex model including indels (insertions and deletions), substitutions, and incomplete lineage sorting. The most important finding of our study is that some fast and simple methods are nearly as accurate as the most accurate methods, which employ sophisticated statistical methods and are computationally quite intensive. We also observe that methods that explicitly consider errors in the estimated gene trees produce more accurate trees than methods that assume the estimated gene trees are correct. CONCLUSIONS: Our study shows that highly accurate estimations of species trees are achievable, even when gene trees differ from each other and from the species tree, and that these estimations can be obtained using fairly simple and computationally tractable methods.