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Method of moments analysis of planar multilayer circuits typically assumes that conductors are infinitely thin and only surface currents need be modeled. Modern fabrication techniques, especially for high-frequency integrated circuits, can easily create structures that require modeling volume current. We present here a complete volume current-based method of moments analysis of arbitrary structures embedded in shielded multilayer media. The volume rooftop, uniform via, and tapered via basis functions that we present are key for such an analysis. The embedding layered media is not meshed as it is automatically included in the Green's function. The required integrations (in six dimensions) of the Green's function have been evaluated analytically with full results presented as a two-dimensional infinite summation that is rapidly evaluated to full precision using the FFT algorithm. Planar circuits using thick metal are typically analyzed to high accuracy one to three orders of magnitude faster due to reduced subsection count.

Parkinson’s Disease (PD) is the second most common neurodegenerative disease in the United States, affecting at least one million people. The cardinal symptoms of PD are tremor, rigidity, slowed movement, and impaired balance. While some symptoms of PD are responsive to anti-PD medications, other symptoms, are less medication responsive, especially walking and balance. Moreover, daily activities, such as writing, using tools, and walking, affect the quality of life (QoL) of people with PD (PwPD). Monitoring PD symptoms is essential for clinical evaluations and adjusting medication to help maintain QoL for PwPD. we are developing a mobile app to conduct at-home PD symptom monitoring with the goal of providing more timely and frequent measurements of PD symptoms for both patients and clinicians. While the tremor and finger tapping results collected in the mobile app have been discussed in previous publications, this paper focuses on the design and testing of postural stability (balance) tests in the app and the validation of the reliability of the mobile embedded accelerometers. During the test, a dual-purpose shaker was employed to provide vibration in amplitude and frequency range similar to human postural stability signals. A head expander was attached to the shaker and the smartphone holder is screwed to it. The tilt and yaw angles of the smartphone holder are adjustable, therefore the smartphone could be tested in an angled position relative to the shaker. Various types of input signals were tested, including sweep and multiple real postural stability data previously collected from a volunteer. Two models of smartphones were used to measure the signal through multiple trials and the results were compared to the input benchmark signal to verify the accuracy of the smartphone measurements. Besides the evaluation of the time domain raw data, we have also employed several signal processing algorithms to extract postural stability factors, such as the root mean square (RMS) value, the derivative of acceleration, frequency factors, etc., with the goal of identifying the patterns of motion signals which could be used as a summary measures of balance for PD. These signal processing algorithms were used to process raw measurement data from multiple trials, on different input signals, and on different devices. The results were compared, and the consistency of these factors through multiple trials with different smartphone models is tested and summarized. These results help us to find the most reliable measure to be used in the smartphone application. Both the results in raw acceleration signals and calculated factors will be discussed to further the current understanding of the reliability of smartphone measurements with embedded accelerometers.