Electroceutical Modeling with Advanced COMSOL Techniques
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1 Electroceutical Modeling with Advanced COMSOL Techniques Kris Carlson 1, Jason Begnaud 2, Socrates Dokos 3, Jay L. Shils 4, Longzhi Mei 1, and Jeffrey E. Arle 1 1. Beth Israel Deaconess Medical Center, Boston, MA USA. 2. Livanova Neuromodulation, Houston, TX USA. 3. University of New South Wales, Sydney, Australia. 4. Rush Medical Center, Chicago, IL, USA.
2 Neuromodulation and Electroceutical Goals Neuromodulation: Applying an electromagnetic field to the central or peripheral nervous system Spinal cord for chronic back pain Deep brain for Parkinson s disease Vagus nerve for epilepsy, depression Transcranial (thru the scalp and skull) for cognitive decline and many others Electroceuticals $2.5B and 10+ years to get a drug through the FDA BUT medical device regulatory process ~1/10 of that Electroceuticals (GlaxoSmithKline, DARPA): modify any part of the nervous system
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4 Vagus nerve with helical electrodes
5 Table 1. COMSOL techniques used in model. Rectangular and piecewise stimulation waveforms Managing parameters and variables using external files Anisotropic material properties COMSOL s units consistency check COMSOL CAD functions (e.g. helix, Boolean operations, thin layers) Contact impedance to save solve time Infinite element domains to avoid edge effects Mapping an operator onto data with the General Extrusion Component Coupling to calculate running 2 nd differences along an edge General Form Edge PDE to calculate transmembrane potential over time Edge ODEs and DAEs interface to calculate probabilities that ion channel gates are open or closed Formulas in local Variables to calculate, e.g., ion channel open and closing rates Solving Laplace s equation with a Stationary solver, then using that solution in a Time-Dependent solver Separating the physics solved by each solver so that each can be run independently of the other to save solve time Study Extensions as alternative to Parameter Sweep to sweep parameters of each study individually Multiplying the electric potential along the axon by the waveform amplitude over time to drastically reduce solve time
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![D8 8[um] "axon diameter 8 um" D5 5[um] "axon diameter 5 um" D3 3[um] "axon diameter 3 um" stim 0.6 "Stimulation factor (see stim_wf in Variables)" VNRadius 1.5[mm] "Helmers 2mm diam 6.](/docs-images/94/119420865/images/7-0.jpg "05mm 270degree electrode model\" VNLength 50[mm] \"Helmers nerve length\" VNAxialPitch 1.15[mm] \"Drives Electrode Length\" ElectrodeMinorRadius (0.")
7 D8 8[um] "axon diameter 8 um" D5 5[um] "axon diameter 5 um" D3 3[um] "axon diameter 3 um" stim 0.6 "Stimulation factor (see stim_wf in Variables)" VNRadius 1.5[mm] "Helmers 2mm diam 6.05mm 270degree electrode model" VNLength 50[mm] "Helmers nerve length" VNAxialPitch 1.15[mm] "Drives Electrode Length" ElectrodeMinorRadius (0.775/2)[mm] "Half of electrode width-livanova" FascicleNerveRatio 0.9 "Ratio of Inner Fascicle to Nerve Diameter" NumberOfTurns 0.75 "Encirclement of electrode around nerve" ScarConductivity 0.03[S/m] "Scar conductivity" ScarThickness 0.11[mm] "Scar thickness" PerineuriumThickness.03[mm] "Perineurium thickness" PerineuriumConductivity 0.11[S/m] "Perineurium conductivity" EpineuriumConductivity 0.053[S/m] "Epineurium conductivity" C_m "0.033 [F/m^2]" "membrane capacitance" p_na " [dm^3/(m^2*s)]" "Sodium permeability" rho_i "0.33 [ohm*m]" "membrane resistance" C_d 0.76 "" dl "1.5 [um]" "nodal width" D_d "1.81 [um]" "" D_L "3.44 [um]" "" r8 (C_d*D8-D_d)/2 "axon radius-8um" r5 (C_d*D5-D_d)/2 "axon radius-5um" dx8 C_L*log(D8/D_L) "internodal length 8um-Wesselink" dx5 C_L*log(D5/D_L) "internodal length 5um-Wesselink" gamma8 dl/dx8 "internodal / nodal length-8um axon" gamma5 dl/dx5 "internodal / nodal length-5um axon" L 50[mm] "axon length" V_K "-132 [mv]" "Potassium reversal potential" Na_o "154 [mm]" "extracellular sodium concentration" Na_i 30[nM] "intracellular sodium concentration" g_k 300[S/m^2] "potassium conductance" T 310.5[K] temperature g_l 600[S/m^2] "Leak conductance" C_L 7.86[um] "" V_L [mV] "leakage reversal potential" I_output 300[A/m^2] "Output current to electrode" i_current 1.5[mA] "Current to electrode" OutputCurrent0.3 64[A/m^2] "Threshold of VN A fiber" OutputCurrent [A/m^2] "" OutputCurrent [A/m^2] "" OutputCurrent [A/m^2] "" electrode_area 2*ElectrodeMinorRadius*NumberOfTurns*pi*2*VNRadius "Area of electrode" dx [um]+0.076*D "internodal length-murray linear" dx2 "0.0037[um] *D *D^2[1/um]" "internodal length-murray quadratic" R2 3000[ohm] "typical chronic resistance" CC 10[uF] "coupling cap" discharge 2/(CC*R2) "discharge factor" electrode_area E-6[m^2] "constant electrode area for greater than 360 deg coverage" D14 14[um] "axon diameter 14 um" r14 (C_d*D14-D_d)/2 "axon radius-14 um" dx14 C_L*log(D14/D_L) "internodal length 14um-Wesselink" gamma14 dl/dx14 "internodal / nodal length-14um axon" dxs 1.4[mm] "A standardized nodal center-to-center length to use in 2nd finite difference calc" internodal_length "2354*(1-exp(-D14/16.26) )[m]" "" delta_8 dx8+dl "Internode+node length 8 um" delta_5 dx5+dl "Internode+node length 5 um" delta_14 dx14+dl "Internode+node length 14 um" ambient_factor_width 2.5 "Ambient cylinder/vn radius. Set to 2.5 for infinite elements domains to accommodate electrodes." ambient_factor_length 1.3 "Ambient cylinder/vn length. Set to 1.6 for infinite elements domains." sigma_fat 0.04 "From Veltink I tink"
8 Solve Laplace s equation once
9 Multiply V by waveform time series in PDE stim_wf stim*pw4(t[1/s]) "Stim amplitude over waveform"
10 Plot of membrane potential over time - spikes
11 Key Findings Identified ~5 fiber diameter groups implicated in VNS: ~8, 7, 5, 3, 2.5 μm Proposed correlations between fiber groups and functional fascicles responsible for efficacy and side effects 8, 7 μm: Recurrent laryngeal fascicle (hoarseness) 3 μm: P2ry1 pulmonary fascicle (cough, forced exhalation) 5 μm: Aortic baro/chemoreceptors (efficacy) Estimated numbers of fibers involved Proposed which fiber groups are activated at different amplitude levels Proposed a bandpass paradigm where both rostral activation and caudal blocking are considered as stim tools 1 At clinical stim amplitudes consistently found activation gaps in the nerve due to the <360 degree (270 degree) encirclement by the cathode 1. Anholt et al. Recruitment and blocking properties of the CardioFit stimulation lead J. Neural Eng. 8
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