Oscillator Model, DBS and non-linear oscillator systems
Erwin B.Montgomery Jr., Professor, University of Alabama at Birmingham, Birmingham Veteran Affairs Medical Centeremontgom@uab.edu
Submitted May 25, 2012
Tsang et al. [1] and editorialist Toyoda [2] noted frequencies of gamma oscillations recorded from the subthalamic nucleus (STN) and the clinically optimal Deep Brain Stimulation (DBS) frequencies, expecting them to be the same or harmonics. [1,2] This would be reasonable assuming a single harmonic oscillator for each frequency band and resonance between the oscillator and DBS. This is consistent for non-linear oscillators in loosely coupled networks as shown in mathematical models.[3] Such oscillators, including DBS, can interact when frequencies are commensurate (their ratio is a rational number) and not just harmonic. Such an oscillator can be driven at its fundamental frequency by another of a different frequency.
The basal ganglia-thalamic-cortical system can be considered a loosely coupled system of polysynaptic reentrant oscillators whose components are non-linear. [4] Recordings in non-human primates demonstrated that individual neurons entrain multiple frequencies simultaneously [5] and demonstrated multiple resonance frequencies to a single DBS frequency. [5] Furthermore, local field potentials represent summed activity in the dendritic trees across many neurons. The risk is attribution of the resultant oscillation to the single volume, thus single oscillator, when in fact the oscillations within the volume are many and different, including phase as well as frequency.
1. Tsang EW, Hamani C, Moro E, et al. Subthalamic deep brain stimulation at individualized frequencies for Parkinson disease. Neurology 2012;78:1930-1938.
2. Wagle Shukla A, Okun MS. Personalized medicine in deep brain stimulation through utilization of neural oscillations. Neurology 2012;78:1900-1901.
Tsang et al. [1] and editorialist Toyoda [2] noted frequencies of gamma oscillations recorded from the subthalamic nucleus (STN) and the clinically optimal Deep Brain Stimulation (DBS) frequencies, expecting them to be the same or harmonics. [1,2] This would be reasonable assuming a single harmonic oscillator for each frequency band and resonance between the oscillator and DBS. This is consistent for non-linear oscillators in loosely coupled networks as shown in mathematical models.[3] Such oscillators, including DBS, can interact when frequencies are commensurate (their ratio is a rational number) and not just harmonic. Such an oscillator can be driven at its fundamental frequency by another of a different frequency.
The basal ganglia-thalamic-cortical system can be considered a loosely coupled system of polysynaptic reentrant oscillators whose components are non-linear. [4] Recordings in non-human primates demonstrated that individual neurons entrain multiple frequencies simultaneously [5] and demonstrated multiple resonance frequencies to a single DBS frequency. [5] Furthermore, local field potentials represent summed activity in the dendritic trees across many neurons. The risk is attribution of the resultant oscillation to the single volume, thus single oscillator, when in fact the oscillations within the volume are many and different, including phase as well as frequency.
1. Tsang EW, Hamani C, Moro E, et al. Subthalamic deep brain stimulation at individualized frequencies for Parkinson disease. Neurology 2012;78:1930-1938.
2. Wagle Shukla A, Okun MS. Personalized medicine in deep brain stimulation through utilization of neural oscillations. Neurology 2012;78:1900-1901.
3. Hoppensteadt FC, Izhikevich EM. Weakly Connected Neural Networks: Springer Verlag, NY, 1997.
4. Montgomery EB Jr. Dynamically Coupled, High-Frequency Reentrant, Non-linear Oscillators Embedded in Scale-Free Basal Ganglia-Thalamic- Cortical Networks Mediating Function and Deep Brain Stimulation Effects. Nonlinear Studies 2004;11:385-421.
5. Montgomery EB Jr, Gale JT. Mechanisms of action of Deep Brain Stimulation (DBS). Neurosci Biobeh Rev 2008;32:388-407.
For disclosures, contact editorial office at journal@neurology.org.