Read out recent editorial on the need to control model methods.  And our review on computational models of TDS. pdf

In the technical “race” to produce the fanciest models, care must be taken to ensure that that the increasingly sophisiticated work-flow continues to produce meaningful predictions.

1) Beginning with high-resolution (e.g. 1 mm) anatomical scans, the entire model work flow should preserve precision.  Any Finite Elemet (FE) human head model is limited by the precision and accuracy of tissue dimensions (along with individual segmentation mask quality) and conductivity values incorporated (inhomogeneity and anisotropy). One hallmark of precision is that the cortical surface used in the final FEM solver should capture realistic sulci and gyri.

2) Simultaneously, a priori knowledge of tissue anatomy and factors known to shape current flow should be applied to further refine segmentation. Particularly critical are discontinuities not present in nature that result from limited scan resolution; notably both unnatural perforations in planar tissues (e.g. holes in CSF where brain contacts skull, misrepresented skull fissures, ventricular architecture….) and microstructures (e.g. incomplete or voxelized vessels) can produce significant aberrations in predicted current flow. Moreover, incorporation of multiple different tissue masks (e.g. eye sclera, cornea, glands, midbrain…) without reliable reported human conductivity values in literature (especially at DC frequency) may also lead to errors.

Thus addition of complexity without proper parameterization can evidently decrease prediction accuracy. An improper balance between these factors can lead to distortions in brain current flow of an order of magnitude or more, with the most appropriate methodology (ranging from concentric spheres to individualized models) ultimately depending on the clinical question being addressed.

 

From on paper on Computational models of tDCS:

 

Uses and need for computational models of non-invasive neuromodulation
Transcranial electrical stimulation is a promising tool in cognitive neuroscience and neuropsychiatric therapy based on the growing evidence that delivery of current to specific brain regions can modulate excitability1, 2 and, in some cases, promote desirable plastic changes3, 4.  Of particular interest are neurostimulation modalities that are low-cost, portable, and simple to implement. Furthermore, stimulation should be delivered in a manner that is safe, well tolerated, and can be applied concurrently with neuropsychological testing or even moderate physical activity.  Transcranial direct current stimulation (tDCS) has been gaining considerable interest because it possesses all these desired qualities5.
In contrast to pharmacotherapy, noninvasive electrotherapy offers the potential for both anatomically specific brain activation and complete temporal control-since electricity is delivered at the desired dose instantly and there is no electrical “residue” as the generated brain current disappears when stimulation is turned off.  Thus, transcranial Direct Current Stimulation can be customized and individualized to specific brain targets in ways not possible with other interventions in order to optimize a particular rehabilitative outcome. Specifically, the dose of electrotherapy is readily adjustable by determining the number, shape, size, and location of electrodes (which determines spatial targeting) and selecting the stimulation waveform (which determines the nature and timing of neuromodulation). Indeed, a single programmable electrotherapy device can be simply configured to provide a diversity of dosages.
Though this flexibility underpins the utility of neuromodulation, the myriad of potential dosages (e.g. stimulator settings and combinations of electrode placements) can lead to a great number of possibilities, thus making the optimal choice very difficult to readily ascertain. The essential issue in dose design is to relate each externally controlled dose with the associated brain regions targeted (and spared) by the resulting current flow – and hence the desired clinical outcome. Computational forward models aim to provide precisely these answers to the first part of this question (Figure 1), and thus represent a critical tool in the rational design, interpretation, and optimization of neuromodulation.
[FIGURE 1]
Methods for the generation of computational forward models of tDCS
Computational models of tDCS range in complexity from concentric sphere models to high-resolution models based on individuals MRIs.  The appropriate level of modeling detail depends on the clinical question being asked (as well as the available computational resources).  Whereas simple geometries (e.g. spheres) may be solved analytically6, realistic geometries employ specialized software, as described below,  including numerical solvers (namely Finite Element Methods, FEM).  Regardless of complexity, all forward models share the primary outcome of correctly predicting brain current flow during transcranial stimulation to guide clinical therapeutic delivery.
For clinicians interested in using computational forward models to inform study design or interpretation several options are available. 1) A collaboration with a modeling group6 or a company can allow for customized exploration of montage options; 2) referencing existing published reports or databases (Table 1) for comparable montages (with careful consideration of the role of individual variation and other caveats presented in the next section) (see also http://neuralengr.com/bonsai); 3) recently, a process where a desired brain target can be selected and the optimized stimulation electrode montage is proposed within seconds has been developed7.  If tDCS continues to emerge as an effective tool in clinical treatment and cognitive neuroscience, and concurrent modeling studies emphasize the need for rational (and in cases patient-specific) dose decisions, then it will become incumbent for clinical research teams to understand the applications (and limitations) of computational forward models, which motivates this section.
[TABLE 1]
While the specific software applications used can vary across modeling groups, in general, the approach and workflow for model generation follow a similar pattern (Figure 2). The steps for generating high-resolution (anatomically specific) forward models of non-invasive neuromodulation are adapted from extensive prior work on computational modeling. These involve: Step 1) Demarcation of individual tissue types (masks) from high-resolution anatomical data using a combination of automated and manual segmentation tools. It is worth noting that the respective contribution of the automated/manual interventions depend on: a) sophistication of the particular automated algorithm employed since they are usually not optimized for forward transcranial modeling8 and b) the need for identification of anomalies in suspect populations like skull defects, lesions, shunts, etc. Consequently, as emphasized below, the number and precision of the individual masks obtained is pivotal for the generation of accurate 3D models in order to capture critical anatomical details that may influence current flow. Step 2) Modeling of the exact physical properties of the electrodes (e.g. shape and size) and precise placement within the segmented image data (i.e. along the skin mask outer surface). Step 3) Generation of accurate meshes (with high quality factor) from the tissue/electrode masks whilst preserving resolution of subject anatomical data.  Step 4) Resulting volumetric meshes are then imported into a commercial finite element (FE) solver. Step 5) At this step, resistivity is assigned to each mask and the boundary conditions are imposed. The standard Laplacian equation is solved using appropriate numerical solver and tolerance settings7, 9, 10. Step 6) Data is plotted as induced cortical electric field or current density maps.
[FIGURE 2]
Though each of the above steps is required for high-resolution modeling, there remains technical expertise and hence variation in protocols across groups and publications. These variations are relevant to clinical practice only in the sense that they change predictions in current flow that may eventually effect dose decisions. The sources and impact of these variations is addressed in the next section.
The precise pattern of current flow through the brain is determined not only by the stimulation dose (montage; the positions of the electrodes) but also by the underlying anatomy and tissue properties.  In predicting brain current flow using computational models, it is therefore important to precisely model both the stimulation condition itself and the relevant anatomy upon which it is delivered on an individual basis.  Modeling electrode geometry (e.g. pad shape and position) and stimulation intensity (e.g. total current applied) is relatively straightforward.  However, the representing tissue remains an area of ongoing technical development and is critical to establishing the clinical utility of these models. For example, cerebral spinal fluid (CSF) is highly conductive (a preferred “super highway” for current flow) such that the integrated details in CSF architecture profoundly shape current flow through adjacent brain regions (see supplementary figure in Datta et al., 2009) .
Initial models of transcranial current flow assumed simplified geometries such as concentric spheres that could be solved analytically11, 12 as well as numerically7, 12.  Such concentric sphere models are useful to address generic dose questions such as the global role of inter-electrode distance, electrode montage, or the relationship between electrode and brain current density, precisely because they exclude regional anatomical differences7, 12.   More realistic models started to include explicit representation of human anatomy9.  Datta et. al.,2009b13 published the first model of tDCS with gyri resolution, illustrating the importance of anatomical precision in determining complex brain current flow14. Addition of diffusion tensor imaging (DTI) incorporates anisotropic properties in the skull and the white matter regions13 Fine resolution of gyri/sulci lead to current “hotspots” in the sulci, thereby reinforcing the need for high-resolution modeling14. An open-source head model comprising of several different tissue types was adapted to analyze current flow through cortical, sub-cortical and brain stem structures15.
Recent studies have attempted to more directly link clinical outcomes and model predictions – and thus validate model utility. Clinical evaluation was combined with model predictions to investigate the effects of different montages in clinical conditions such as fibromyalgia16.  Recently, patient-specific models have been used to retrospectively analyze the therapeutic success of a given experimental stimulation montage9 and compare model predictions with patterns of activation revealed by functional magnetic resonance imaging (fMRI)17.
Recent effort has been directed towards increasing the precision of tDCS models by enhancing model sophistication. However, it is important to note that increased model complexity does not necessarily equate with greater accuracy or clinical value18. Indeed, to meaningfully guide clinical utility, attempts to enhance model precision must rationally balance detail (i.e. complexity) and accuracy. 1) Beginning with high-resolution anatomical scans, the entire model workflow should preserve precision.  Any human head model is limited by the precision and accuracy of tissue segmentation (i.e. “masks”) and of the assigned conductivity values. One hallmark of precision is that the cortical surface used in the final FEM solver should capture realistic sulci and gyri anatomy. 2) Simultaneously, a priori knowledge of tissue anatomy and factors known to influence current flow should be applied to further refine segmentation.  Particularly critical are discontinuities not present in nature that result from limited scan resolution; notably both unnatural perforations in planar tissues (e.g ventricular architecture. discontinuities in CSF where brain contacts skull, misrepresented skull fissures,) and microstructures (e.g. incomplete or voxelized vessels) can produce significant deviations in predicted current flow. Moreover, because of the sensitivity of current flow to any conductivity boundary, increasingly detailed segmentation (e.g. globe of the eye and related structures, glands, and deeper midbrain structures) without reliable reported human conductivity values in literature (especially at static frequency) may also lead to errors. Thus, addition of complexity without proper parameterization can evidently decrease prediction accuracy. An improper balance between these factors can introduce distortions in predicted brain current flow.
Finally, when clinicians are interpreting simulation predictions, it is important to recognize that the intensity of current flow in any specific brain region does not translate in any simple (linear) manner to the degree of brain activation or modulation (even when considering current direction7, 14). Moreover, recent neurophysiological studies indicate changes in “excitability” may not even be monotonic with stimulation dose and may infact reverse depending on background activity.  However, to a first approximation, it seems reasonable to predict that regions with more current flow are more likely to be “effected” by stimulation while regions with little or no current flow will be spared the direct effects of stimulation. As a first step to understand mechanism of action of tDCS, a relationship between model predicted regional current flow and changes in functional activation was recently demonstrated20. The central “quasi-uniform” assumption considers that if the electric field is uniform on the scale of a region (neuron) of interest, then “excitability/neuromodulation” may be indeed be considered to change directly with the local electric field intensity21 (see discussion in Datta et al., 200821 and Miranda et al., 200717).
Future Directions
As computational models continue to evolve in sophistication new methodologies like diffusion tensor imaging (DTI) has been included to investigate anisotropic tissue resistivity contributions to current flow inside the brain22. This section, however, addresses how clinicians can directly leverage existing models to improve patient outcomes of stimulation.
Retrospectively computational models of tDCS provide a precise substrate to test mechanistic hypothesis about region specific effects on cognition or behavior.  In addition, computational models have contributed to the design and validation of new tDCS montages.  This includes variations of the conventional two electrode pad montage23 (one anode, one cathode) but also the introduction of new therapeutic approaches24, 25.
For example, High-Definition Transcranial Direct Current Stimulation (HD-tDCS) is a new modification of tDCS and uses arrays of specialized compact scalp electrodes to deliver current with no skin irritation and minimal discomfort26.  Using a computational model, the “4×1” HD-tDCS deployment – where a central ‘active’ electrode is surrounded by a ring of 4 ‘return’ electrodes – was predicted to allow unprecedented targeting of cortical regions with DC neuromodulation27 (Figure 3).  Subsequent to these model predictions, clinical studies to validate the focality and efficacy of 4×1 HD-tDCS are ongoing.  Still more sophisticated HD deployments, using up to 64 electrodes to focus current to targeted brain structures, have been proposed28.
[Figure 3]
Subject-to-subject variability is expected with any clinical intervention, neuromodulation, and especially tDCS allows for the potential individual customization of montage to normalize outcomes – specifically by controlling the amount of current delivered to a region(s) on interest.  The inverse question is: given the same montage is used across subjects, how different is the resulting brain current flow in each patent?  Notably, most published forward modeling studies and analysis are in-fact published as “case reports” with predictions only on a single head3, 29.  For a given electrode montage and stimulation dose, the sensitivity of global brain current to normal variation in anatomy (including across ages, gender) is poorly understood; however high-resolution modeling suggest gyri-specific dispersion of current flow, which could potentially account for individual variability14, 30-32.  More generally, gross differences in tissue dimensions, notably skull thickness, are expected to influence current flow.
There is increasing interest in the use of neuromodulation at the extremes of age including for aging-related disorders and in pediatric populations for indications including autism and epilepsy treatment33.  However, because the intensity of brain current generated during stimulation depend on both the tDCS dose (montage and current intensity) and the underlying brain anatomy, the same dose applied may produce different brain current in young or elderly subjects.34  For example, it would not be prudent to adjust stimulation dose for children through an arbitrary rule of thumb (e.g. reduce electrode size and current intensity by the ratio of head diameter). Computational forward models provide direct insight into the relation between external tDCS dose and resulting brain current and thus can inform dose design in such cases.  Figure 4 shows an example of a model of tDCS in a 12 year old. Both the peak and spatial distribution of current in the brain is altered compared to the typical adult case.  Though questions remain about the impact of gross anatomical (e.g. age, gender…) differences in altering generated brain current flow during neuromodulation, computational “forward” models provide direct insight into this question, and may ultimately be used to rationally adjust stimulation dose.
[Figure 4]
In more extreme cases, modeling efforts specifically addressed the role of individual anatomical pathology, such as skull defects35 or brain lesions8.   For example, tDCS has been shown to modulate cognitive, linguistic, and motor performance in both healthy and neurologically-impaired individuals with results supporting the feasibility of leveraging interactions between stimulation-induced neuromodulation and task execution17, 23, 36. However, while numerous reports have been published in recent years demonstrating the effects of tDCS upon task performance, there remain fundamental questions about the optimal design of electrode configuration, especially around lesioned tissue25. Several modeling studies have demonstrated the profound influence of stroke related brain lesions on resulting brain current produced by tDCS9, 10, 27. These studies demonstrate the potentially profound influence of lesions and skull defects on resulting current flow.
At the same time, there is clinical interest in the application of tDCS during rehabilitation of patients with brain lesions or skull defects (i.e. with or without skull plates) such traumatic brain injury (TBI) or patients undergoing neurosurgery.  As some of the neurological sequelae are presumably consequences of disrupted cortical activity following the traumatic event, the use tDCS to deliver current to both damaged and compensatory regions in such circumstances can be a useful tool to reactivate and restore activity in essential neural networks associated with cognitive or motor processing37. Modeling studies can provide insight into how skull defects and skull plates would affect current flow through the brain and how to modify tDCS dose and/or electrode locations in such cases (Figure 5, adapted from Datta et. al. 201026). It is precisely because these studies have shown the importance of specific defect/lesion details, that individual analysis of tDCS induced current flow seems warranted in such cases.
[Figure 5]
Conclusion
While numerous published reports have demonstrated the beneficial effects of transcranial direct-current stimulation (tDCS) upon task performance, fundamental questions remain regarding the optimal electrode montage.  Moreover, it is expected that individual anatomical differences, in the extreme case manifest as skull defects, and lesioned brain tissue, will influence current flow and should therefore be considered (and perhaps leveraged) in the optimization of neuromodulation therapies.  Computational models can underpin the design and evaluation of more effective tDCS montages and thus contribute to the validation of tDCS.
Table legends:
1.  Synopsis of tDCS Computer Models: Summary of tDCS forward head models.  Head models have progressed from being spherical based to being MRI derived. The most recent ones have employed patient-specific models. The second, third, and fourth columns list number of tissue types, the montage used, and particular model specifics, respectively. Abbreviations: C3, C4, F3, F4, O1, Oz, Cz correspond to 10/20 EEG system; SO: contralateral supra-orbital; LFC: left frontal cortex; RFC: right frontal cortex; RS: right shoulder; LS: left shoulder; pTC: posterior temporal cortex.
 Figure legends:
1. Role of computational models in rational electrotherapy: (left) Neuromodulation is a promising therapeutic modality as it allows affecting the brain in a way not possible with other techniques and a high degree of individualized optimization. The goal of computational models is to assist clinicians in leveraging the power and flexibility of neuromodulation. (right)  All computational forward models are used to predict brain current flow during transcranial stimulation to guide clinical practice.  As with pharmacotherapy, electrotherapy dose is controlled by the operator and leads a complex pattern of internal current flow that is described by the model.  In this way, clinicians can apply computational models to determine with dose will activate (or avoid) brain regions of interest.
2. Imaging and computational work-flow for the generation of high-resolution individualized models: Though the specific processes and software packages will vary across technical groups and applications, in each case high-resolution modeling initiated with precise anatomical scans that allow demarcation of key tissues. Tissues with distinct resistivity are used to form “masks”.  These masks along with the representation of the physical electrodes are “meshed” to allow FEM calculations.  The boundary conditions (generally simply reflecting how the electrodes are energized) and the governing equations (related to ohms law) are well established.  The reproduction of the stimulation dose and the underlying anatomy thus allow for the prediction of resulting brain current. These current flow patterns are represented in false-color map and analyzed through various post-processing tools.
3. High-Definition tDCS.  Comparison of current-density focality using the HD-tDCS 4×1-Ring deployment vs. a convention “pad” tDCS montage. (Left)  Some conventional tDCS montages can result in relatively diffuse and unfocal brain stimulation; in some cases, with peak currents between-not under-the electrodes (inset).  (Right) In contrast, HD-tDCS Ring stimulation results in highly targeted cortical area directly under the electrodes. (see Datta 2009).
4. Individualized head model of a 12 yr old: Segmentation masks and induced current flow for motor cortex tDCS.
5. Computational model of current flow in subjects with skull defects/plates. A defect in skull tissue, which is the most resistive tissue in the head, would hypothetically affect current flow in the underlying brain regions. Furthermore, the exact location of the defect (under/between the stimulation pads) in combination with the ‘material’ filling up the defect with the stimulation montage employed will influence induced current flow. Sample segmentation masks are shown on the left. A small defect under the anode pad (top right) leads to current flow in the cortex restricted to directly under the defect (avoiding the intermediate regions). A similar sized defect placed between the pads (bottom right) does not significantly alter current flow patterns in comparison with a healthy head with no defects26.
References:
1. Nitsche MA, Paulus W. Excitability changes induced in the human motor cortex by weak transcranial direct current stimulation. Journal of Physiology 2000;527:633-639.
2. Merton PA, Morton HB. Stimulation of the cerebral cortex in the intact human subject. Nature. May 22 1980;285(5762):227.
3. Nitsche MA, Paulus W. Sustained excitability elevations induced by transcranial DC motor cortex stimulation in humans Neurology. 2001;57:1899-1901.
4. Antal A, Lang N, Boros K, Nitsche M, Siebner HR, Paulus W. Homeostatic metaplasticity of the motor cortex is altered during headache-free intervals in migraine with aura. Cerebral cortex. Nov 2008;18(11):2701-2705.
5. Brunoni AR NM, Bolognini N, Bikson M, Wagner T, Merabet L, Edwards DJ, Valero-Cabre A, Rotenberg A, Pascual-Leone A, Ferrucci R, Priori A, Boggio PS, Fregni F. Clinical research with transcranial direct current stimulation (tDCS): Challenges and future directions. Brain Stimul. 2011;In Press.
6. Turkeltaub PE, Benson J, Hamilton RH, Datta A, Bikson M, Coslett HB. Left lateralizing transcranial direct current stimulation improves reading efficiency. Brain Stimul. 2011;In Press.
7. Datta A, Elwassif M, Battaglia F, Bikson M. Transcranial current stimulation focality using disc and ring electrode configurations:FEM analysis. Journal of neural engineering. 2008;5(2):163-174.
8. Datta A, Baker JM, Bikson M, Fridriksson J. Individualized model predicts brain current flow during transcranial direct-current stimulation treatment in responsive stroke patient. Brain Stimul 2011;In Press
9. Wagner T, Fregni F, Fecteau S, Grodzinsky A, Zahn M, Pascual-Leone A. Transcranial direct current stimulation:a computer-based human model study   Neuroimage. 2007;35(3):1113-1124.
10. Miranda PC, Lomarev M, Hallett M. Modeling the current distribution during transcranial direct current stimulation. Clin Neurophysiol. Jul 2006;117(7):1623-1629.
11. Stecker MM. Transcranial electric stimulation of motor pathways: a theoretical analysis. Comput Biol Med. Feb 2005;35(2):133-155.
12. Rush S, Driscoll DA. Current distribution in the brain from surface electrodes. Anesth Analg. Nov-Dec 1968;47(6):717-723.
13. Suh HS, Kim SH, Lee WH, Kim TS. Realistic simulation of transcranial direct current stimulation via 3-d high resolution finite element analysis:Effect of tissue anisotropy Conf Proc IEEE Eng Med Biol Soc. 2009;2009:638-641.
14. Salvador R, Mekonnen A, Ruffini G, Miranda PC. Modeling the electric field induced in a high resolution head model during transcranial current stimulation. Conf Proc IEEE Eng Med Biol Soc. 2010;2010:2073-2076.
15. Parazzini M, Fiocchi S, Rossi E, Paglialonga A, Ravazzani P. Transcranial Direct Current Stimulation: Estimation of the Electric Field and of the Current Density in an Anatomical Head Model  IEEE Trans Biomed Eng. 2011;Epub.
16. Wolters CH, Anwander A, Tricoche X, Weinstein D, Koch MA, MacLeod RS. Influence of tissue conductivity anisotropy on EEG/MEG field and return current computation in a realistic head model: a simulation and visualization study using high-resolution finite element modeling. NeuroImage. Apr 15 2006;30(3):813-826.
17. Halko MA, Datta A, Plow EB, Scaturro J, Bikson M, Merabet LB. Neuroplastic changes following rehabilitative training correlate with regional electric field induced with tDCS  Neuroimage. 2011;In Press
18. Bikson M, Datta A. Guidelines for precise and accurate computational models of tDCS. Brain stimulation. Jul 3 2011.
19. Jefferys JG. Influence of electric fields on the excitability of granule cells in guinea-pig hippocampal slices. J Physiol. 1981;319:143-152.
20. Smith SM. Fast robust automated brain extraction. Hum Brain Mapp. Nov 2002;17(3):143-155.
21. Bikson M, Inoue M, Akiyama H, et al. Effects of uniform extracellular DC electric fields on excitability in rat hippocampal slices in vitro Journal of Physiology 2004;557:175-190.
22. Suh HS, Lee WH, Cho YS, Kim JH, Kim TS. Reduced spatial focality of electrical field in tDCS with ring electrodes due to tissue anisotropy. Conf Proc IEEE Eng Med Biol Soc. 2010;1:2053-2056.
23. Bikson M, Datta A, Rahman A, Scaturro J. Electrode montages for tDCS and weak transcranial electrical stimulation: role of “return” electrode’s position and size. Clin Neurophysiol. Dec 2010;121(12):1976-1978.
24. Miranda PC, Faria P, Hallett M. What does the ratio of injected current to electrode area tell us about current density in the brain during tDCS?  . Clinical Neurophysiology. 2009;120(6):1183-1187.
25. Im CH, Jung HH, Choi JD, Lee SY, Jung KY. Determination of optimal electrode positions for transcranial direct current stimulation (tDCS). Phys Med Biol. Jun 7 2008;53(11):N219-225.
26. Minhas P, Bansal V, Patel J, et al. Electrodes for high-definition transcutaneous DC stimulation for applications in drug delivery and electrotherapy, including tDCS. J Neurosci Methods. Jul 15 2010;190(2):188-197.
27. Datta A, Bansal V, Diaz J, Patel J, Reato D, Bikson M. Gyri-precise head model of transcranial direct current stimulation: Improved spatial focality using a ring electrode versus conventional rectangular pad Brain Stimulation 2009;2:201-207.
28. Dmochowski JP, Datta A, Bikson M, Su Y, Parra LC. Optimized multi-electrode stimulation increases focality and intensity at target. J Neural Eng. Jun 10 2011;8(4):046011.
29. Oostendorp TF, Hengeveld YA, Wolters CH, Stinstra J, van Elswijk G, Stegeman DF. Modeling transcranial DC stimulation. Conf Proc IEEE Eng Med Biol Soc. 2008;2008:4226-4229.
30. Fregni F, Thome-Souza S, Nitsche MA, Freedman SD, Valente KD, Pascual-Leone A. A controlled clinical trial of cathodal DC polarization in patients with refractory epilepsy. Epliepsia. 2006;47(2):335-342.
31. Thielscher A, Opitz A, Windhoff M. Impact of the gyral geometry on the electric field induced by transcranial magnetic stimulation. NeuroImage. Jan 1 2011;54(1):234-243.
32. Opitz A, Windhoff M, Heidemann RM, Turner R, Thielscher A. How the brain tissue shapes the electric field induced by transcranial magnetic stimulation. NeuroImage. Oct 1 2011;58(3):849-859.
33. Schneider HD, Hopp JP. The use of the Bilingual Aphasia Test for assessment and transcranial direct current stimulation to modulate language acquisition in minimally verbal children with autism. Clinical linguistics & phonetics. Jun 2011;25(6-7):640-654.
34. Freitas C, Mondragon-Llorca H, Pascual-Leone A. Noninvasive brain stimulation in Alzheimer’s disease: systematic review and perspectives for the future. Experimental gerontology. Aug 2011;46(8):611-627.
35. Datta A, Bikson M, Fregni F. Transcranial direct current stimulation in patients with skull defects and skull plates: high-resolution computational FEM study of factors altering cortical current flow. Neuroimage. Oct 1 2010;52(4):1268-1278.
36. Mendonca ME, Santana MB, Baptista AF, et al. Transcranial DC Stimulation in Fibromyalgia: Optimized Cortical Target Supported by High-Resolution Computational Models. Journal of Pain 2011;12(5):610-617.
37. Liebetanz D, Klinker F, Hering D, et al. Anticonvulsant effects of transcranial direct-current stimulation (tDCS) in the rat cortical ramp model of focal epilepsy. Epliepsia. 2006;47(7):1216-1224.

 

Uses and need for computational models of non-invasive neuromodulation
Transcranial electrical stimulation is a promising tool in cognitive neuroscience and neuropsychiatric therapy based on the growing evidence that delivery of current to specific brain regions can modulate excitability1, 2 and, in some cases, promote desirable plastic changes3, 4.  Of particular interest are neurostimulation modalities that are low-cost, portable, and simple to implement. Furthermore, stimulation should be delivered in a manner that is safe, well tolerated, and can be applied concurrently with neuropsychological testing or even moderate physical activity.  Transcranial direct current stimulation (tDCS) has been gaining considerable interest because it possesses all these desired qualities5.
In contrast to pharmacotherapy, noninvasive electrotherapy offers the potential for both anatomically specific brain activation and complete temporal control-since electricity is delivered at the desired dose instantly and there is no electrical “residue” as the generated brain current disappears when stimulation is turned off.  Thus, transcranial Direct Current Stimulation can be customized and individualized to specific brain targets in ways not possible with other interventions in order to optimize a particular rehabilitative outcome. Specifically, the dose of electrotherapy is readily adjustable by determining the number, shape, size, and location of electrodes (which determines spatial targeting) and selecting the stimulation waveform (which determines the nature and timing of neuromodulation). Indeed, a single programmable electrotherapy device can be simply configured to provide a diversity of dosages.Though this flexibility underpins the utility of neuromodulation, the myriad of potential dosages (e.g. stimulator settings and combinations of electrode placements) can lead to a great number of possibilities, thus making the optimal choice very difficult to readily ascertain. The essential issue in dose design is to relate each externally controlled dose with the associated brain regions targeted (and spared) by the resulting current flow – and hence the desired clinical outcome. Computational forward models aim to provide precisely these answers to the first part of this question (Figure 1), and thus represent a critical tool in the rational design, interpretation, and optimization of neuromodulation.
[FIGURE 1]
Methods for the generation of computational forward models of tDCS
Computational models of tDCS range in complexity from concentric sphere models to high-resolution models based on individuals MRIs.  The appropriate level of modeling detail depends on the clinical question being asked (as well as the available computational resources).  Whereas simple geometries (e.g. spheres) may be solved analytically6, realistic geometries employ specialized software, as described below,  including numerical solvers (namely Finite Element Methods, FEM).  Regardless of complexity, all forward models share the primary outcome of correctly predicting brain current flow during transcranial stimulation to guide clinical therapeutic delivery.
For clinicians interested in using computational forward models to inform study design or interpretation several options are available. 1) A collaboration with a modeling group6 or a company can allow for customized exploration of montage options; 2) referencing existing published reports or databases (Table 1) for comparable montages (with careful consideration of the role of individual variation and other caveats presented in the next section) (see also http://neuralengr.com/bonsai); 3) recently, a process where a desired brain target can be selected and the optimized stimulation electrode montage is proposed within seconds has been developed7.  If tDCS continues to emerge as an effective tool in clinical treatment and cognitive neuroscience, and concurrent modeling studies emphasize the need for rational (and in cases patient-specific) dose decisions, then it will become incumbent for clinical research teams to understand the applications (and limitations) of computational forward models, which motivates this section.
[TABLE 1]
While the specific software applications used can vary across modeling groups, in general, the approach and workflow for model generation follow a similar pattern (Figure 2). The steps for generating high-resolution (anatomically specific) forward models of non-invasive neuromodulation are adapted from extensive prior work on computational modeling. These involve: Step 1) Demarcation of individual tissue types (masks) from high-resolution anatomical data using a combination of automated and manual segmentation tools. It is worth noting that the respective contribution of the automated/manual interventions depend on: a) sophistication of the particular automated algorithm employed since they are usually not optimized for forward transcranial modeling8 and b) the need for identification of anomalies in suspect populations like skull defects, lesions, shunts, etc. Consequently, as emphasized below, the number and precision of the individual masks obtained is pivotal for the generation of accurate 3D models in order to capture critical anatomical details that may influence current flow. Step 2) Modeling of the exact physical properties of the electrodes (e.g. shape and size) and precise placement within the segmented image data (i.e. along the skin mask outer surface). Step 3) Generation of accurate meshes (with high quality factor) from the tissue/electrode masks whilst preserving resolution of subject anatomical data.  Step 4) Resulting volumetric meshes are then imported into a commercial finite element (FE) solver. Step 5) At this step, resistivity is assigned to each mask and the boundary conditions are imposed. The standard Laplacian equation is solved using appropriate numerical solver and tolerance settings7, 9, 10. Step 6) Data is plotted as induced cortical electric field or current density maps.
[FIGURE 2]
Though each of the above steps is required for high-resolution modeling, there remains technical expertise and hence variation in protocols across groups and publications. These variations are relevant to clinical practice only in the sense that they change predictions in current flow that may eventually effect dose decisions. The sources and impact of these variations is addressed in the next section.
The precise pattern of current flow through the brain is determined not only by the stimulation dose (montage; the positions of the electrodes) but also by the underlying anatomy and tissue properties.  In predicting brain current flow using computational models, it is therefore important to precisely model both the stimulation condition itself and the relevant anatomy upon which it is delivered on an individual basis.  Modeling electrode geometry (e.g. pad shape and position) and stimulation intensity (e.g. total current applied) is relatively straightforward.  However, the representing tissue remains an area of ongoing technical development and is critical to establishing the clinical utility of these models. For example, cerebral spinal fluid (CSF) is highly conductive (a preferred “super highway” for current flow) such that the integrated details in CSF architecture profoundly shape current flow through adjacent brain regions (see supplementary figure in Datta et al., 2009) .
Initial models of transcranial current flow assumed simplified geometries such as concentric spheres that could be solved analytically11, 12 as well as numerically7, 12.  Such concentric sphere models are useful to address generic dose questions such as the global role of inter-electrode distance, electrode montage, or the relationship between electrode and brain current density, precisely because they exclude regional anatomical differences7, 12.   More realistic models started to include explicit representation of human anatomy9.  Datta et. al.,2009b13 published the first model of tDCS with gyri resolution, illustrating the importance of anatomical precision in determining complex brain current flow14. Addition of diffusion tensor imaging (DTI) incorporates anisotropic properties in the skull and the white matter regions13 Fine resolution of gyri/sulci lead to current “hotspots” in the sulci, thereby reinforcing the need for high-resolution modeling14. An open-source head model comprising of several different tissue types was adapted to analyze current flow through cortical, sub-cortical and brain stem structures15.
Recent studies have attempted to more directly link clinical outcomes and model predictions – and thus validate model utility. Clinical evaluation was combined with model predictions to investigate the effects of different montages in clinical conditions such as fibromyalgia16.  Recently, patient-specific models have been used to retrospectively analyze the therapeutic success of a given experimental stimulation montage9 and compare model predictions with patterns of activation revealed by functional magnetic resonance imaging (fMRI)17.
Recent effort has been directed towards increasing the precision of tDCS models by enhancing model sophistication. However, it is important to note that increased model complexity does not necessarily equate with greater accuracy or clinical value18. Indeed, to meaningfully guide clinical utility, attempts to enhance model precision must rationally balance detail (i.e. complexity) and accuracy. 1) Beginning with high-resolution anatomical scans, the entire model workflow should preserve precision.  Any human head model is limited by the precision and accuracy of tissue segmentation (i.e. “masks”) and of the assigned conductivity values. One hallmark of precision is that the cortical surface used in the final FEM solver should capture realistic sulci and gyri anatomy. 2) Simultaneously, a priori knowledge of tissue anatomy and factors known to influence current flow should be applied to further refine segmentation.  Particularly critical are discontinuities not present in nature that result from limited scan resolution; notably both unnatural perforations in planar tissues (e.g ventricular architecture. discontinuities in CSF where brain contacts skull, misrepresented skull fissures,) and microstructures (e.g. incomplete or voxelized vessels) can produce significant deviations in predicted current flow. Moreover, because of the sensitivity of current flow to any conductivity boundary, increasingly detailed segmentation (e.g. globe of the eye and related structures, glands, and deeper midbrain structures) without reliable reported human conductivity values in literature (especially at static frequency) may also lead to errors. Thus, addition of complexity without proper parameterization can evidently decrease prediction accuracy. An improper balance between these factors can introduce distortions in predicted brain current flow.
Finally, when clinicians are interpreting simulation predictions, it is important to recognize that the intensity of current flow in any specific brain region does not translate in any simple (linear) manner to the degree of brain activation or modulation (even when considering current direction7, 14). Moreover, recent neurophysiological studies indicate changes in “excitability” may not even be monotonic with stimulation dose and may infact reverse depending on background activity.  However, to a first approximation, it seems reasonable to predict that regions with more current flow are more likely to be “effected” by stimulation while regions with little or no current flow will be spared the direct effects of stimulation. As a first step to understand mechanism of action of tDCS, a relationship between model predicted regional current flow and changes in functional activation was recently demonstrated20. The central “quasi-uniform” assumption considers that if the electric field is uniform on the scale of a region (neuron) of interest, then “excitability/neuromodulation” may be indeed be considered to change directly with the local electric field intensity21 (see discussion in Datta et al., 200821 and Miranda et al., 200717).
Future Directions As computational models continue to evolve in sophistication new methodologies like diffusion tensor imaging (DTI) has been included to investigate anisotropic tissue resistivity contributions to current flow inside the brain22. This section, however, addresses how clinicians can directly leverage existing models to improve patient outcomes of stimulation.
Retrospectively computational models of tDCS provide a precise substrate to test mechanistic hypothesis about region specific effects on cognition or behavior.  In addition, computational models have contributed to the design and validation of new tDCS montages.  This includes variations of the conventional two electrode pad montage23 (one anode, one cathode) but also the introduction of new therapeutic approaches24, 25.
For example, High-Definition Transcranial Direct Current Stimulation (HD-tDCS) is a new modification of tDCS and uses arrays of specialized compact scalp electrodes to deliver current with no skin irritation and minimal discomfort26.  Using a computational model, the “4×1” HD-tDCS deployment – where a central ‘active’ electrode is surrounded by a ring of 4 ‘return’ electrodes – was predicted to allow unprecedented targeting of cortical regions with DC neuromodulation27 (Figure 3).  Subsequent to these model predictions, clinical studies to validate the focality and efficacy of 4×1 HD-tDCS are ongoing.  Still more sophisticated HD deployments, using up to 64 electrodes to focus current to targeted brain structures, have been proposed28.
[Figure 3]
Subject-to-subject variability is expected with any clinical intervention, neuromodulation, and especially tDCS allows for the potential individual customization of montage to normalize outcomes – specifically by controlling the amount of current delivered to a region(s) on interest.  The inverse question is: given the same montage is used across subjects, how different is the resulting brain current flow in each patent?  Notably, most published forward modeling studies and analysis are in-fact published as “case reports” with predictions only on a single head3, 29.  For a given electrode montage and stimulation dose, the sensitivity of global brain current to normal variation in anatomy (including across ages, gender) is poorly understood; however high-resolution modeling suggest gyri-specific dispersion of current flow, which could potentially account for individual variability14, 30-32.  More generally, gross differences in tissue dimensions, notably skull thickness, are expected to influence current flow.
There is increasing interest in the use of neuromodulation at the extremes of age including for aging-related disorders and in pediatric populations for indications including autism and epilepsy treatment33.  However, because the intensity of brain current generated during stimulation depend on both the tDCS dose (montage and current intensity) and the underlying brain anatomy, the same dose applied may produce different brain current in young or elderly subjects.34  For example, it would not be prudent to adjust stimulation dose for children through an arbitrary rule of thumb (e.g. reduce electrode size and current intensity by the ratio of head diameter). Computational forward models provide direct insight into the relation between external tDCS dose and resulting brain current and thus can inform dose design in such cases.  Figure 4 shows an example of a model of tDCS in a 12 year old. Both the peak and spatial distribution of current in the brain is altered compared to the typical adult case.  Though questions remain about the impact of gross anatomical (e.g. age, gender…) differences in altering generated brain current flow during neuromodulation, computational “forward” models provide direct insight into this question, and may ultimately be used to rationally adjust stimulation dose.
[Figure 4]
In more extreme cases, modeling efforts specifically addressed the role of individual anatomical pathology, such as skull defects35 or brain lesions8.   For example, tDCS has been shown to modulate cognitive, linguistic, and motor performance in both healthy and neurologically-impaired individuals with results supporting the feasibility of leveraging interactions between stimulation-induced neuromodulation and task execution17, 23, 36. However, while numerous reports have been published in recent years demonstrating the effects of tDCS upon task performance, there remain fundamental questions about the optimal design of electrode configuration, especially around lesioned tissue25. Several modeling studies have demonstrated the profound influence of stroke related brain lesions on resulting brain current produced by tDCS9, 10, 27. These studies demonstrate the potentially profound influence of lesions and skull defects on resulting current flow.
At the same time, there is clinical interest in the application of tDCS during rehabilitation of patients with brain lesions or skull defects (i.e. with or without skull plates) such traumatic brain injury (TBI) or patients undergoing neurosurgery.  As some of the neurological sequelae are presumably consequences of disrupted cortical activity following the traumatic event, the use tDCS to deliver current to both damaged and compensatory regions in such circumstances can be a useful tool to reactivate and restore activity in essential neural networks associated with cognitive or motor processing37. Modeling studies can provide insight into how skull defects and skull plates would affect current flow through the brain and how to modify tDCS dose and/or electrode locations in such cases (Figure 5, adapted from Datta et. al. 201026). It is precisely because these studies have shown the importance of specific defect/lesion details, that individual analysis of tDCS induced current flow seems warranted in such cases.
[Figure 5]
Conclusion
While numerous published reports have demonstrated the beneficial effects of transcranial direct-current stimulation (tDCS) upon task performance, fundamental questions remain regarding the optimal electrode montage.  Moreover, it is expected that individual anatomical differences, in the extreme case manifest as skull defects, and lesioned brain tissue, will influence current flow and should therefore be considered (and perhaps leveraged) in the optimization of neuromodulation therapies.  Computational models can underpin the design and evaluation of more effective tDCS montages and thus contribute to the validation of tDCS.
Table legends:1.  Synopsis of tDCS Computer Models: Summary of tDCS forward head models.  Head models have progressed from being spherical based to being MRI derived. The most recent ones have employed patient-specific models. The second, third, and fourth columns list number of tissue types, the montage used, and particular model specifics, respectively. Abbreviations: C3, C4, F3, F4, O1, Oz, Cz correspond to 10/20 EEG system; SO: contralateral supra-orbital; LFC: left frontal cortex; RFC: right frontal cortex; RS: right shoulder; LS: left shoulder; pTC: posterior temporal cortex.
Figure legends:1. Role of computational models in rational electrotherapy: (left) Neuromodulation is a promising therapeutic modality as it allows affecting the brain in a way not possible with other techniques and a high degree of individualized optimization. The goal of computational models is to assist clinicians in leveraging the power and flexibility of neuromodulation. (right)  All computational forward models are used to predict brain current flow during transcranial stimulation to guide clinical practice.  As with pharmacotherapy, electrotherapy dose is controlled by the operator and leads a complex pattern of internal current flow that is described by the model.  In this way, clinicians can apply computational models to determine with dose will activate (or avoid) brain regions of interest.
2. Imaging and computational work-flow for the generation of high-resolution individual

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