Abstract
Deep brain stimulation (DBS) is an established clinical therapy for a wide range of neurological disorders and constantly under investigation for increasing indications. Yet even after decades of clinical success, explicit understanding of the underlying brain response to DBS and subsequent scientific definition of the therapeutic mechanisms of action remain elusive. In addition, it is presently unclear which electrode designs and stimulation paradigms are optimal for maximum therapeutic benefit and minimal side effects with DBS. Detailed patient-specific computer modeling of DBS represents a powerful technique to enhance understanding of the effects and mechanisms of DBS, as well as enabling virtual testing grounds for new stimulation strategies. This chapter summarizes the fundamentals of neurostimulation modeling, presents some scientific contributions of computer models to the field of DBS, and demonstrates an application of DBS modeling tools to augment the clinical utility of DBS.
Keywords
Electrode, Neuromodulation, Neurostimulation
Acknowledgments
This work was supported by grants from the National Institutes of Health (R01 NS085188, R01 MH102238).
Conflict of Interest Statement
C.C.M. authored intellectual property related to the content of this chapter, is a paid consultant for Boston Scientific Neuromodulation, and is a shareholder in the following neuromodulation companies: Surgical Information Sciences, Inc.; Autonomic Technologies, Inc.; Cardionomics, Inc.; Neuros Medical, Inc.; and Enspire DBS, Inc.
Acknowledgments
This work was supported by grants from the National Institutes of Health (R01 NS085188, R01 MH102238).
Conflict of Interest Statement
C.C.M. authored intellectual property related to the content of this chapter, is a paid consultant for Boston Scientific Neuromodulation, and is a shareholder in the following neuromodulation companies: Surgical Information Sciences, Inc.; Autonomic Technologies, Inc.; Cardionomics, Inc.; Neuros Medical, Inc.; and Enspire DBS, Inc.
Deep Brain Stimulation
Deep brain stimulation (DBS) is a powerful clinical technology, positively affecting the lives of well over 100,000 patients worldwide. DBS currently has various forms of government regulatory approvals for the treatment of Parkinson disease (PD) ( ), essential tremor (ET) ( ), dystonia ( ), obsessive-compulsive disorder (OCD) ( ), and epilepsy ( ). However, for all of the clinical successes of DBS, numerous scientific questions remain on its therapeutic mechanisms and effects on the nervous system ( ).
It is commonly assumed that the fundamental purpose of DBS is to modulate pathological neural activity within targeted brain circuits ( ). However, quantitative details on which neurons are directly stimulated, the anatomical connections of those stimulated neurons, and the resulting synaptic effects of those stimulated neurons on the targeted brain circuits remain limited. In addition, DBS devices are capable of delivering thousands of different stimulation settings, where each parameter alteration can modify the neural response to the therapy. Fortunately, guidelines do exist for general stimulation parameter settings that are typically effective ( ), but it is infeasible to clinically evaluate the complete range of stimulation parameter combinations that may be useful to a given patient. As a result, the therapeutic benefit currently achievable with DBS is strongly dependent on the surgical placement accuracy of the DBS electrode and the intuitive skill of the clinician performing the stimulation parameter selection ( ).
An important and necessary step forward for more wide-scale use of DBS therapies is the development of assistive technologies that optimize and/or ease clinical implementation of the devices. Along that line, computational modeling is playing an important role in new developments to improve both electrode placement and stimulation parameter selection in DBS patients. Stereotactic neurosurgical navigation has a long history of relying on computational models to help identify target coordinates in the brain for electrode placement based on the patient’s medical imaging and intraoperative neurophysiological data (e.g., ). More recently, software technologies have been designed to assist clinicians in identifying therapeutic stimulation parameter settings customized to each patient (e.g., ). Such tools are leveraging the growing computational power available to DBS clinicians in the hospital, as well as the improved opportunities for data sharing across clinical divisions (e.g., radiology, neurosurgery, and neurology).
Patient-Specific DBS Models
Computational modeling of DBS has established utility for investigating theoretical mechanisms of the therapy, as well as a tool for designing techniques to optimize clinical application of the technology. Much of this field has focused on the creation and use of patient-specific DBS models, as well as the corresponding electric field generated by the standard human DBS electrode (cylindrical electrode contact, 1.5 mm in height and 1.27 mm in diameter). These models have evolved from point source electrodes in an infinite homogeneous medium ( ) to clinical electrodes in a human brain ( ) to detailed representations of the electrode–tissue interface ( ). The electric field predictions from modern DBS models have been validated against experimental measurements in the brains of nonhuman primates ( ) and electrophysiological measurements in human patients ( ). The general field of DBS electrode modeling has also expanded to include investigators from around the world addressing the biophysics of stimulation (e.g., ), as well as clinical investigations of stimulus spread (e.g., ).
Patient-specific DBS models have had their greatest impact in analysis of the combined anatomical and electrical target of the stimulation. DBS surgical targeting traditionally focused on electrode placement within the confines of subcortical gray matter nuclei, following the early assumption that stimulation of the cell bodies of the neurons in the given nucleus was responsible for therapeutic benefit. However, numerous theoretical and experimental studies have demonstrated that a primary effect of DBS is to stimulate axons that surround the electrode (e.g., ). These axons may be associated with the implanted nucleus (i.e., axonal projections originating from the nucleus) or any other axon projecting to or passing by the nucleus. In the case of subthalamic DBS for PD, patient-specific models have suggested that activation of the white matter dorsal to the subthalamic nucleus (STN) is most associated with therapeutic benefit ( ). Further, when this region is explicitly targeted via surgical electrode placement ( ), or stimulation parameter selection ( ), outcomes improve relative to stimulation concentrated on the STN itself ( ). These results support the concept that detailed computational models can provide clinically relevant input on surgical targeting and stimulation parameter selection.
Modeling Neural Stimulation
The electric field generated by an implanted DBS electrode is a three-dimensionally complex phenomenon that is distributed throughout the brain ( ). This field is applied to the complex three-dimensional geometry of the surrounding neural processes (i.e., axons and dendrites). The response of an individual neuron to the applied field is related to the second derivative of the extracellular potential distribution along each neural process ( ). In turn, each neuron (or neural process) surrounding the electrode will be subject to both depolarizing and hyperpolarizing effects from the stimulation ( ). For example, during a monopolar cathodic stimulus pulse, the compartments of a neural process closest to the active electrode contact will experience a high-magnitude depolarization, while flanking compartments will be experience a low-magnitude hyperpolarization. The absolute magnitude of those polarizations depends on the electrode-to-neuron distance.
In general, three classes of neurons can be affected by the stimulation: local cells, afferent inputs, and fibers of passage. Local cells represent neurons that have their cell body in close proximity to the electrode and an axon that may project locally and/or distally to a different brain region. Afferent inputs represent neurons that project to the region near the electrode and whose axon terminals make synaptic connections with local cells. Fibers of passage represent neurons where both the cell body and axon terminals are far from the electrode but the axonal process of the neuron traces a path that comes in close proximity to the electrode. Experimental measurements indicate that local cells, afferent inputs, and fibers of passage have similar thresholds for activation ( ). In addition, local cells can be directly excited by the stimulus and/or have their excitability indirectly altered via activation of afferent inputs that make synaptic connections on their dendritic arbor ( ).
Neural modeling allows for simultaneous study of the effects of stimulation on all the different types of neurons around the electrode. In addition, models provide a highly controlled environment to study the effects of stimulation on neural activity, which is something that is difficult to achieve experimentally. However, the strengths of modeling are tempered by the necessary simplifications made in any reasonable model. In turn, modeling should be coupled as closely as possible to experimental work, allowing for a synergistic analysis of results.
The modeling techniques currently used to predict the neural response to extracellular stimulation date back to , who was the first to integrate an electric field model and multicompartment cable model to predict action potential generation from electrical stimulation ( Fig. 12.1 ). In general, modeling extracellular stimulation of neurons in the brain relies on two fundamental components: (1) a model of the voltage distribution generated by the stimulating electrode(s) and (2) a model of the neuron(s) being stimulated. Voltage distribution models range from simple (i.e., theoretical point source electrode in an infinite homogeneous isotropic medium) to complex (i.e., finite element volume conductor with explicit representation of electrode geometry, time dependence, and tissue inhomogeneity/anisotropy). Irrespective of the voltage distribution model selected, the simulated extracellular potentials (V e [ n ]) at the location of individual compartments of neurons in the surrounding tissue medium can be predicted.
The neural response to the stimulation is simulated with electrical circuits of conductances (G m [ n ]) and capacitors (C m [ n ]) in parallel, which are connected in series by intracellular conductances (G i [ n ]), to create a multicompartment cable model ( ). The transmembrane conductances associated with a given compartment are typically modeled using nonlinear differential equations based on the formalism. Such membrane conductance models enable explicit representation of the various ion channels (e.g., Na + , K + , Ca 2+ , etc.) present in a given compartment.
When extracellular stimulation is applied to the neuron model, the membrane current at compartment n is equal to the sum of the incoming axial currents and the sum of the capacitive and ionic currents through the membrane:
C m [ n ] ( dV m [ n ] / dt ) + I i [ n ] = G i [ n − 1 ] ( V i [ n − 1 ] − V i [ n ] + V e [ n − 1 ] − V e [ n ] ) + G i [ n ] ( V i [ n + 1 ] − V i [ n ] + V e [ n + 1 ] − V e [ n ] )
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