Project

Objectives: The main aim of the project is to develop a method for the identification of the TMS intensity and coil position needed for the effective stimulation of a given brain region. First, the hand area will be considered; it can be seen as a benchmark area because it is well studied in the literature. Based on the results of the hand area, the leg area will be then considered, being not as studied as the hand area, but belonging to the motor cortex for which a feedback in terms of motor evoked potential is possible. The proposed method aims at being the more general as possible, starting from brain areas easy to study as those considered in this project (areas in the motor cortex). The rationale is to transfer, in the future, the knowledge acquired in this research project to other brain areas, more difficult to stimulate. In particular, we refer to the prefrontal cortex, the different somatosensorial areas of the cortex, the cortex involved in the language and swallowing functions, or the associative areas of the cortex, that can be stimulated for treating severe depression as well as many other psychiatric and neurological disorders. For these areas a feedback of the stimulation can come only after many TMS sessions and time-consuming clinical protocols. This knowledge transfer will be developed in other research projects, which we aim to submit in the European context in the forthcoming years.

Methodologies: In this project, in order to identify the optimal coil position and TMS intensity, a cutting-edge approach is proposed. We will use personalized data (from MRI images) and consider the variability of tissue properties (in terms of Uncertainty Quantification), we will solve the forward field problem very fast by applying a Model Order Reduction (MOR) technique and finally we will solve the inverse problem in an accurate and challenging way thanks to DL techniques. Our method will be validated by means of TMS measurements. To this end, the project will be developed as follows. At the beginning of the project, 25 healthy, right-handed subjects, in the range 20-60 years will be recruited. The MRI scan of each volunteer will be acquired. T1- and T2-weighted MRIs will be performed with a 3 T scanner (Siemens Skyra), voxel size 1x1x1 mm.

The first motor threshold measurements for the hand region will be then acquired. The TMS will be delivered with a figure-of-eight coil, because of its focality with respect to the circular coil, characterized by a monophasic current. A neuronavigation system will be used during the TMS procedures. In this project, the DICOM system of coordinates (the origin is at the scanner origin, which is the center of the gradient coil, x increases from right to left, y increases from anterior to posterior, z increases from inferior to superior) will be used, so, because a neuronavigator has to be bought, a neuronavigator able to work with this system of coordinates will be considered. However, if a neuronavigation system working with the Montreal Neurological Institute (MNI) coordinates will be used for practical reasons, we plan to transform the coordinates from DICOM to MNI and vice versa by means of suitable matrices.

In this first phase of experiments, both the resting motor threshold (RMT) and the active motor threshold (AMT) will be measured by recording a Motor Evoked Potential (MEP) from a hand muscle (abductor pollicis brevis, ABP). The RMT is the lowest stimulus intensity required to elicit a MEP of at least 50μV in 5 out of 10 consecutive trials. Similarly, AMT is defined as the lowest stimulus intensity to elicit a MEP of at least 200μV in 5 out of 10 consecutive trials during an isometric contraction of ~10–20% of the maximum contraction in the target muscle.

The TMS experiments will give us the TMS intensity to elicit a MEP from the ABP muscle for each subject, which, coupled with the MRI scans, will be used for implementing the personalized field models. The MRI images will be completely anonymized and then copied on a mass storage device (e.g. CDs) following the procedures required by the ITT office of the Mondino Institute and transferred by hand to the POLIMI Unit. Starting from MRI images of a subject, the geometrical domain will be built by means of a segmentation procedure, made with the open source software SimNIBS [M1]. A Finite-Element Model (FEM) will be then implemented in SimNIBS, considering both head domain and coil geometry.

The eddy current problem will be solved with FEM coupled with Polynomial Chaos Expansion, able to consider the uncertainty in the knowledge of electrical conductivities [M2].

As a matter of fact, brain tissue characteristics vary among people, and this produces a relevant uncertainty in the results of the computation of the induced electric field in TMS. In particular, the most critical parameters are electrical conductivities, since biological tissues behave like air from the magnetic point of view. Tissue properties will be obtained from suitable databases, yet including specific uncertainty ranges to consider the high variability of parameters among patients and during the single patient lifetime [G2]. To this end, we will consider the literature data, e.g., findings from Gabriel and Gabriel [M3].

Moreover, starting from FEM and in order to obtain fast solutions of the forward eddy current problem, a Model Order Reduction (MOR) approach will be then applied [M4].

The MOR model will enable to simulate the coil in different positions around the target brain area with different orientations (overall 6 degrees of freedom, 3 for the position and 3 for the orientation are considered), with low computational costs. The obtained field maps (i.e. mean and standard deviation of the induced electric field in x-, y- and z-direction) with associated relevant positions and orientations of the coil can be collected in a database; moreover, a fast model for field simulation which considers tissue uncertainties and real head geometry will be available.

Moreover, the experiments performed by neurologists in the first phase of the project will be simulated with the help of FE models and, hence, the field map obtained during the experimental session will be computed. In this way, the field values which enable the stimulation of the cortical area of a given subject will be known.

The inverse problem can be formulated as follows: given the geometry of the head and the material properties (with their uncertainty ranges), find the optimal source position and intensity to obtain a given electric field map in a target brain area. In order to have a benchmark solution, we will solve this inverse problem with a classical optimization approach: we will use a genetic algorithm well known in literature e.g. NSGA-II [M5] coupled with the MOR field model implemented in the previous phase of the project.

A key point will be that to properly define the wanted electric field map in the target area. Many papers devoted to the identification of the induced electric field in the hand region (also called hand knob) have been published in the past years. The most recent ones identified the electric field normal to the interface between white and grey matter as the most probable cause of neuronal stimulation. In particular, for the hand region, the pre-central cortical gyrus and the anterior wall of the central sulcus are considered as target area and the preferred direction for the induced electric field is that perpendicular to the central sulcus [M6]. To solve the inverse problem, a suitable formulation has to be defined: the aim is to maximize the induced electric field (normal component) in the target areas and minimize the electric field in the regions around, which should not be stimulated. We think that a multi-objective optimization problem arises, and the NSGA-II method could be able to solve it in a very efficient way. In order to solve the same inverse problem in a new and efficient way, we plan to make use of DL [D1, D2]. With this approach we will work with images of the electric field maps.

The proposed approach is characterized by the implementation of a cascade of two Deep Neural Networks (DNNs): a Variational Autoencoder (VA) [D3, D4] and a Convolutional Neural Network (CNN) [D2, D5] (see Fig. 1). This model will be denoted as DNN model.

Starting from an image of the desired electric field map highlighted by the neurologist (we call it 'raw image'), the VA will be able to generate a FEM-like electric field map, which will be used as input for the CNN. Then, the CNN will return the coil position for obtaining the desired electric field map.

Fig. 1 - Online use of the DL approach

The following remarks can be done: the role of the VA is important because the area highlighted by the neurologist (by hand or with a simple tool) needs to be transformed in an image which resembles the result of a field analysis. Moreover, one of the main challenges of the project is to transfer the results obtained by the proposed method to the medical practice, hence the research group aims to make it user-friendly, and this is the scope of the VA. Finally, it is worth to notice that the CNN will identify the coil position only. Once the position is known and the value of the electric field for stimulating the hand area of the given subject is known too (thanks to the FE model simulating the experiments of TMS), the TMS intensity can be scaled because of the linearity of the field model. Before using this DL approach, both VA and CNN must be trained. For this purpose we will use the fast MOR surrogate model to generate the training dataset consisting in a large number (tens of thousands) of FEM-like images and the corresponding coil positions. In a first moment, we plan to train one DNN model for each subject, acting as a straightforward inverse model personalized to the subject. The dataset of the images from one patient will be split in training and test data. This personalized DNN model can be directly compared with the benchmark approach previously mentioned that uses NSGA-II together with the MOR surrogate model in order to solve the inverse problem. This comparison will give us a first feedback on the DL approach. In a second phase we plan to investigate a completely new approach that cannot be addressed using the optimization approach, that is to train a DNN model using the data from different subjects simultaneously. In particular we plan to train our DNN model with 20 out of 25 subjects and to use the 5 remaining subjects (called "test set") for the model validation. For training the VA, the dataset of field maps obtained with the MOR model will be used (see Fig. 2).

Fig. 2 - VA training

It is worth to notice that the choice of the image for representing the electric field distribution in the best way is a critical issue. However, using VAs, there are degrees of freedom from this point of view: because VAs can treat all kind of images, it possible to choose a 2D image as represented in Fig. 2 or 2D slices of the head centered on the region of interest or even a 3D image (representing a volume). The CNN will then be trained using the dataset of field maps performed with the MOR model. For each field map we know the position of the coil which generated it, so we can train the CNN with the field maps as input and the corresponding TMS coil position as output (see Fig. 3).

Fig. 3 - CNN training

Moreover, an experimental validation is planned: starting from the MRI image, the raw image with the desired field distribution in the hand area overlapped to the brain geometry is drawn for each subject; the DL approach (see Fig. 1) is applied; the coil position is identified and hence the TMS intensity is tuned. The information on coil position and TMS intensity are then given to the neurologists who will apply on each subject the personalized TMS. When the TMS is delivered to the 20 subjects belonging to the training set, we expect to find a lower TMS intensity with respect to the TMS delivered in the first session of experiments. This is due to the optimization procedure which should find a better location, allowing to reduce the intensity for obtaining the same stimulation. In this way we will obtain a more effective TMS, personalized on the subject. The personalized TMS applied to the 5 subjects belonging to the test set will let us understand if our DL method is able to generalize: being the head geometry of these subjects unknown to the NNs during the training phase, if we will obtain a stimulation, setting the coil position and intensity to the values found out with our approach, it means that our DNN approach is able to generalize over the domain geometry. Once the method is validated for the hand area, we aim at solving a similar problem for the leg area, which is located in a different, deeper position in the brain. The hypothesis we assume is that the electric field value needed for stimulating the motor cortex in the leg area is similar to that needed for stimulating the hand area, especially when evaluating the value of the AMT. In fact, although differences in baseline excitability may exist between the motor area of the hand and the motor area of the leg, the level of cortical activation in conditions of muscle preactivation (such as that determined by the slight voluntary activation) should be considered quite comparable. To this end, we will create the database of field maps and raw images for the leg region, based on the MOR model already implemented for solving the hand region problem (no new segmentation process neither new MOR model is needed). We have to train the NNs from scratch and in particular both VA and CNN have to be trained for the new area, based only on the field model results, for 20 out of 25 subjects. For each subject we will obtain the optimal coil position and intensity given by the DL approach. Their values will be given to the neurologists who will perform the personalized TMS to each subject, recording the AMT for the leg stimulation. If we are able to elicit a MEP with the settings given by our DL approach, it means that our method is able to generalize by varying the area to stimulate. This would be a good result, because it probably means that our approach could be applied to other brain areas not belonging to the motor cortex, for which it is difficult to obtain a feedback like MEPs are for the motor cortex stimulation. On the other hand, the personalized TMS applied to the 5 subjects belonging to the test set will let us understand if our DL method is able to generalize on the geometry also for the leg area.