Ilkka Laakso

Effects of coil orientation on the electric field induced by TMS over the hand motor area

Responses elicited by transcranial magnetic stimulation (TMS) over the hand motor area depend on the position and orientation of the stimulating coil. In this work, we computationally investigate the induced electric field for multiple coil orientations and locations in order to determine which parts of the brain are affected and how the sensitivity of motor cortical activation depends on the direction of the electric field. The finite element method is used for calculating the electric field induced by TMS in two individual anatomical models of the head and brain. The orientation of the coil affects both the strength and depth of penetration of the electric field, and the field strongly depends on the direction of the sulcus, where the target neurons are located. The coil position that gives the strongest electric field in the target cortical region may deviate from the closest scalp location by a distance on the order of 1xa0cm. Together with previous experimental data, the results support the hypothesis that the cortex is most sensitive to fields oriented perpendicular to the cortical layers, while it is relatively insensitive to fields parallel to them. This has important implications for targeting of TMS. To determine the most effective coil position and orientation, it is essential to consider both biological (the direction of the targeted axons) and physical factors (the strength and direction of the electric field).

Inter-subject variability in electric fields of motor cortical tDCS

BACKGROUNDnThe sources of inter-subject variability in the efficacy of transcranial direct current stimulation (tDCS) remain unknown. One potential source of variations is the brains electric field, which varies according to each individuals anatomical features.nnnOBJECTIVEnWe employed an approach that combines imaging and computational modeling to quantitatively study the extent and primary causes of inter-subject variation in tDCS electric fields.nnnMETHODSnAnatomically-accurate models of the head and brain of 24 males (age: 38.63xa0±xa011.24 years) were constructed from structural MRI. Finite-element method was used to computationally estimate the electric fields for tDCS of the motor cortex. Surface-based inter-subject registration of the electric field and functional MRI data was used for group level statistical analysis.nnnRESULTSnWe observed large differences in each individuals electric field patterns. However, group level analysis revealed that the average electric fields concentrated in the vicinity of the primary motor cortex. The variations in the electric fields in the hand motor area could be characterized by a normal distribution with a standard deviation of approximately 20% of the mean. The cerebrospinal fluid (CSF) thickness was the primary factor influencing an individuals electric field, thereby explaining 50% of the inter-individual variability, a thicker layer of CSF decreasing the electric field strength.nnnCONCLUSIONSnThe variability in the electric fields is related to each individuals anatomical features and can only be controlled using detailed image processing. Age was found to have a slight negative effect on the electric field, which might have implications on tDCS studies on aging brains.

Reducing the staircasing error in computational dosimetry of low-frequency electromagnetic fields

From extremely low frequencies to intermediate frequencies, the magnitude of induced electric field inside the human body is used as the metric for human protection. The induced electric field inside the body can be computed using anatomically realistic voxel models and numerical methods such as the finite-difference or finite-element methods. The computed electric field is affected by numerical errors that occur when curved boundaries with large contrasts in electrical conductivity are approximated using a staircase grid. In order to lessen the effect of the staircase approximation error, the use of the 99th percentile electric field, i.e. ignoring the highest 1% of electric field values, is recommended in the ICNIRP guidelines. However, the 99th percentile approach is not applicable to localized exposure scenarios where the majority of significant induced electric field values may be concentrated in a small volume. In this note, a method for removing the staircasing error is proposed. Unlike the 99th percentile, the proposed method is also applicable to localized exposure scenarios. The performance of the method is first verified by comparison with the analytical solution in a layered sphere. The method is then applied for six different exposure scenarios in two anatomically realistic human head models. The results show that the proposed method can provide conservative estimates for the 99th percentile electric field in both localized and uniform exposure scenarios.

Evaluation of SAR in a human body model due to wireless power transmission in the 10 MHz band

This study discusses a computational method for calculating the specific absorption rate (SAR) due to a wireless power transmission system in the 10 MHz frequency band. A two-step quasi-static method comprised of the method of moments and the scalar potential finite-difference method are proposed. The applicability of the quasi-static approximation for localized exposure in this frequency band is discussed by comparing the SAR in a lossy dielectric cylinder computed with a full-wave electromagnetic analysis and the quasi-static approximation. From the computational results, the input impedance of the resonant coils was affected by the existence of the cylinder. On the other hand, the magnetic field distribution in free space and considering the cylinder and an impedance matching circuit were in good agreement; the maximum difference in the amplitude of the magnetic field was 4.8%. For a cylinder-coil distance of 10 mm, the difference between the peak 10 g averaged SAR in the cylinder computed with the full-wave electromagnetic method and our quasi-static method was 7.8%. These results suggest that the quasi-static approach is applicable for conducting the dosimetry of wireless power transmission in the 10 MHz band. With our two-step quasi-static method, the SAR in the anatomically based model was computed for different exposure scenarios. From those computations, the allowable input power satisfying the limit of a peak 10 g averaged SAR of 2.0 W kg(-1) was 830 W in the worst case exposure scenario with a coil positioned at a distance of 30 mm from the chest.

Fast multigrid-based computation of the induced electric field for transcranial magnetic stimulation

In transcranial magnetic stimulation (TMS), the distribution of the induced electric field, and the affected brain areas, depends on the position of the stimulation coil and the individual geometry of the head and brain. The distribution of the induced electric field in realistic anatomies can be modelled using computational methods. However, existing computational methods for accurately determining the induced electric field in realistic anatomical models have suffered from long computation times, typically in the range of tens of minutes or longer. This paper presents a matrix-free implementation of the finite-element method with a geometric multigrid method that can potentially reduce the computation time to several seconds or less even when using an ordinary computer. The performance of the method is studied by computing the induced electric field in two anatomically realistic models. An idealized two-loop coil is used as the stimulating coil. Multiple computational grid resolutions ranging from 2 to 0.25xa0mm are used. The results show that, for macroscopic modelling of the electric field in an anatomically realistic model, computational grid resolutions of 1xa0mm or 2xa0mm appear to provide good numerical accuracy compared to higher resolutions. The multigrid iteration typically converges in less than ten iterations independent of the grid resolution. Even without parallelization, each iteration takes about 1.0xa0s or 0.1xa0s for the 1 and 2xa0mm resolutions, respectively. This suggests that calculating the electric field with sufficient accuracy in real time is feasible.

Dominant factors affecting temperature rise in simulations of human thermoregulation during RF exposure

Numerical models of the human thermoregulatory system can be used together with realistic voxel models of the human anatomy to simulate the body temperature increases caused by the power absorption from radio-frequency electromagnetic fields. In this paper, the Pennes bioheat equation with a thermoregulatory model is used for calculating local peak temperatures as well as the body-core-temperature elevation in a realistic human body model for grounded plane-wave exposures at frequencies 39, 800 and 2400 MHz. The electromagnetic power loss is solved by the finite-difference time-domain (FDTD) method, and the discretized bioheat equation is solved by the geometric multigrid method. Human thermoregulatory models contain numerous thermophysiological and computational parameters--some of which may be subject to considerable uncertainty--that affect the simulated core and local temperature elevations. The goal of this paper is to find how greatly the computed temperature is influenced by changes in various modelling parameters, such as the skin blood flow rate, models for vasodilation and sweating, and clothing and air movement. The results show that the peak temperature rises are most strongly affected by the modelling of tissue blood flow and its temperature dependence, and mostly unaffected by the central control mechanism for vasodilation and sweating. Almost the opposite is true for the body-core-temperature rise, which is however typically greatly lower than the peak temperature rise. It also seems that ignoring the thermoregulation and the blood temperature increase is a good approximation when the local 10 g averaged specific absorption rate is smaller than 10 W kg(-1).

Computational dosimetry of induced electric fields during realistic movements in the vicinity of a 3 T MRI scanner.

Medical staff working near magnetic resonance imaging (MRI) scanners are exposed both to the static magnetic field itself and also to electric currents that are induced in the body when the body moves in the magnetic field. However, there are currently limited data available on the induced electric field for realistic movements. This study computationally investigates the movement induced electric fields for realistic movements in the magnetic field of a 3 T MRI scanner. The path of movement near the MRI scanner is based on magnetic field measurements using a coil sensor attached to a human volunteer. Utilizing realistic models for both the motion of the head and the magnetic field of the MRI scanner, the induced fields are computationally determined using the finite-element method for five high-resolution numerical anatomical models. The results show that the time-derivative of the magnetic flux density (dB/dt) is approximately linearly proportional to the induced electric field in the head, independent of the position of the head with respect to the magnet. This supports the use of dB/dt measurements for occupational exposure assessment. For the path of movement considered herein, the spatial maximum of the induced electric field is close to the basic restriction for the peripheral nervous system and exceeds the basic restriction for the central nervous system in the international guidelines. The 99th percentile electric field is a considerably less restrictive metric for the exposure than the spatial maximum electric field; the former is typically 60-70% lower than the latter. However, the 99th percentile electric field may exceed the basic restriction for dB/dt values that can be encountered during tasks commonly performed by MRI workers. It is also shown that the movement-induced eddy currents may reach magnitudes that could electrically stimulate the vestibular system, which could play a significant role in the generation of vertigo-like sensations reported by people moving in a strong static magnetic field.

In-situ electric field in human body model in different postures for wireless power transfer system in an electrical vehicle.

The in-situ electric field of an adult male model in different postures is evaluated for exposure to the magnetic field leaked from a wireless power transfer system in an electrical vehicle. The transfer system is located below the centre of the vehicle body and the transferred power and frequency are 7u2009kW and 85u2009kHz, respectively. The in-situ electric field is evaluated for a human model (i) crouching near the vehicle, (ii) lying on the ground with or without his arm stretched, (iii) sitting in the drivers seat, and (iv) standing on a transmitting coil without a receiving coil. In each scenario, the maximum in-situ electric fields are lower than the allowable limit prescribed by international guidelines, although the local magnetic field strength in regions of the human body is higher than the allowable external magnetic field strength. The highest in-situ electric field is observed when the human body model is placed on the ground with his arm extended toward the coils, because of a higher magnetic field around the arm.

Analysis of in situ electric field and specific absorption rate in human models for wireless power transfer system with induction coupling

This study investigates the specific absorption rate (SAR) and the in situ electric field in anatomically based human models for the magnetic field from an inductive wireless power transfer system developed on the basis of the specifications of the wireless power consortium. The transfer system consists of two induction coils covered by magnetic sheets. Both the waiting and charging conditions are considered. The transfer frequency considered in this study is 140xa0kHz, which is within the range where the magneto-quasi-static approximation is valid. The SAR and in situ electric field in the chest and arm of the models are calculated by numerically solving the scalar potential finite difference equation. The electromagnetic modelling of the coils in the wireless power transfer system is verified by comparing the computed and measured magnetic field distributions. The results indicate that the peak value of the SAR averaged over a 10xa0g of tissue and that of the in situ electric field are 72 nW kg(-1)xa0and 91xa0mV m(-1)xa0for a transmitted power of 1xa0W, Consequently, the maximum allowable transmitted powers satisfying the exposure limits of the SAR (2 W kg(-1)) and the in situ electric field (18.9 V m(-1)) are found to be 28 MW and 43 kW. The computational results show that the in situ electric field in the chest is the most restrictive factor when compliance with the wireless power transfer system is evaluated according to international guidelines.

The relationship between specific absorption rate and temperature elevation in anatomically based human body models for plane wave exposure from 30 MHz to 6 GHz

According to the international safety guidelines/standard, the whole-body-averaged specific absorption rate (Poljak et al 2003 IEEE Trans. Electromagn. Compat. 45 141-5) and the peak spatial average SAR are used as metrics for human protection from whole-body and localized exposures, respectively. The IEEE standard (IEEE 2006 IEEE C95.1) indicates that the upper boundary frequency, over which the whole-body-averaged SAR is deemed to be the basic restriction, has been reduced from 6 to 3xa0GHz, because radio-wave energy is absorbed around the body surface when the frequency is increased. However, no quantitative discussion has been provided to support this description especially from the standpoint of temperature elevation. It is of interest to investigate the maximum temperature elevation in addition to the core temperature even for a whole-body exposure. In the present study, using anatomically based human models, we computed the SAR and the temperature elevation for a plane-wave exposure from 30xa0MHz to 6xa0GHz, taking into account the thermoregulatory response. As the primary result, we found that the ratio of the core temperature elevation to the whole-body-averaged SAR is almost frequency independent for frequencies below a few gigahertz; the ratio decreases above this frequency. At frequencies higher than a few gigahertz, core temperature elevation for the same whole-body averaged SAR becomes lower due to heat convection from the skin to air. This lower core temperature elevation is attributable to skin temperature elevation caused by the power absorption around the body surface. Then, core temperature elevation even for whole-body averaged SAR of 4xa0Wxa0kg(-1)xa0with the duration of 1xa0h was at most 0.8xa0°C, which is smaller than a threshold considered in the safety guidelines/standard. Further, the peak 10xa0g averaged SAR is correlated with the maximum body temperature elevations without extremities and pinna over the frequencies considered. These findings were confirmed for seven models, including models of a child and a pregnant female. Thus, the current basic restriction for whole-body exposure in the international guidelines is conservative. Peak spatial-averaged SAR can be used as a metric for estimating local temperature elevation even for whole-body exposure. Our computational results also support the description in the IEEE standard about the reduction of the upper applicable frequency of whole-body-averaged SAR from 6 and 3xa0GHz; the power density reference level is more conservative than the basic restriction limit for the whole-body averaged SAR from the standpoint of temperature elevation.