This thesis focuses on developing a novel brain stimulation methodology by using temporally interfering gigahertz (GHz) electromagnetic (EM) waves, termed EMvelop stimulation. Our work on EMvelop stimulation addresses two key aspects of developing this novel methodology: obtaining high electric field intensity and focality at target regions deep inside the brain tissue and fast and robust data-driven electric field estimation.

First, we validate the idea of EMvelop stimulation using multi-physics modeling and algorithmic optimization simulations. We show that at GHz frequencies, we can create antenna arrays at the scale of a few centimeters or less that can be endocranially implanted to enable longitudinal stimulation and circumvent signal attenuation due to the scalp and skull. Furthermore, owing to the small wavelength of GHz EM waves, we can optimize both amplitudes and phases of the EM waves to achieve high intensity and focal stimulation at targeted regions. We develop a simulation framework investigating the propagation of GHz EM waves and the corresponding heat generated in the brain tissue. We propose two optimization flows to identify antenna current amplitudes and phases for either maximal intensity or maximal focality transmission of the interfering electric fields with EM waves safety constraint. A representative result of our study is that with two endocranially implanted arrays of size 4.2 cm x 4.7 cm each, we can achieve an intensity of 12 V/m with a focality of 3.6 cm at a target deep in the brain tissue. To the best of our knowledge, this is the first time the idea of EMvelop stimulation was proposed and investigated, and we demonstrated its benefits over prior methodologies of electrical stimulation.

Second, a common factor across electromagnetic methodologies of brain stimulation is the optimization of essential dosimetry parameters, like amplitude, phase, and the location of one or more transducers, which controls the stimulation strength and targeting precision. Since obtaining in-vivo measurements for the electric field distribution inside the biological tissue is challenging, physics-based simulators are used. However, these physics-based simulators are computationally expensive and time-consuming, making computing the electric field repeatedly for optimization purposes computationally prohibitive. To overcome this issue, we trained a U-Net model using 14 segmented human magnetic resonance images (MRIs). Once trained, the model inputs a segmented human MRI and the antenna location and outputs the corresponding electric field. At 1.5 GHz, on the validation dataset consisting of 6 patients, we can estimate the electric field with the magnitude of complex correlation coefficient of 0.978. Additionally, we could calculate the electric field with a mean time of 4.4 ms for a potential antenna location. On average, this is at least 1200 times faster than the time required by state-of-the-art physics-based simulator COMSOL. The significance of this work is that it shows the possibility of real-time calculation of the electric field from the patient MRI and coordinates for the antenna, making it possible to optimize the amplitude, phase, and location of several different transducers with stochastic gradient descent since our model is a continuous function.

Our work shows the potential of EMvelop stimulation to be portable, discreet, and continuously operable brain stimulation technology while being minimally invasive. The aim of our work is to expand the therapeutic options available to an even larger number of patients with neurological and psychiatric disorders.