Studying the arterial hemodynamic response plays a crucial role in the understanding and the treatment of cardiovascular diseases. Due to the difficulty of measuring the arterial blood flow, its estimation through a particular arterial vessel, using non-invasive arterial pressure waveform measurements, has always been an important topic in physiology. For instance, knowing the blood flow in a specific site of the arterial network helps in the detection of arterial stenosis. It may also help in the diagnosis of heart valve's diseases. In this work, an algorithm based on modulating functions is proposed to estimate the arterial blood flow as well as to calibrate the conventional Windkessel model using arterial blood pressure signals measured in a particular site of the arterial system.

Studying the arterial hemodynamic response plays a crucial role in the understanding and the treatment of cardiovascular diseases. Due to the difficulty of measuring the arterial blood flow, its estimation through a particular arterial vessel, using non-invasive arterial pressure waveform measurements, has always been an important topic in physiology. For instance, knowing the blood flow in a specific site of the arterial network helps in the detection of arterial stenosis. It may also help in the diagnosis of heart valve's diseases. In this work, an algorithm based on modulating functions is proposed to estimate the arterial blood flow as well as to calibrate the conventional Windkessel model using arterial blood pressure signals measured in a particular site of the arterial system.

Arterial viscoelasticity assessment is extremely crucial for the prevention and early diagnosis of a wide range of cardiovascular diseases, such as Atherosclerosis. Accordingly, modeling the mechanical properties of the vessel wall tissue and the simulation of their effects on the arterial hemodynamic were considered of substantial role in clinical routine. Indeed, characterization and emulation of the arterial viscoelasticity deepen our understanding on the onset vascular pathology and causes. In addition, they can serve as reliable diagnosis tools. In this regard, over the last century, several mathematical models have been developed and extensively studied in order to emulate the real arterial viscoelasticity behavior and build a suitable non-invasive assessment tool. These models vary in their complexity and ease to be implemented. To date, lumped parametric model is thought to be the simplest representation that provides a convenient and computationally inexpensive tool. However, recent studies, have shown that conventional integer order lumped parameter models are not sufficient to simulate the viscoelastic properties of bio-tissues. Indeed, it doesn’t account for the power law demonstrated experimentally. The power-law like stress relaxation is expected to be seen in vascular tissue too. In order, to overcome this discrepancies, fractional-order constitutive laws have been proposed as an alternative. In fact, they provide more stable and realistic tool to simulate the viscoelastic materials since it can naturally capture such power-law effects.

Windkessel lumped parameter model (WK) is the most commonly used 0-Dimension characterization of the systemic arterial system. It presents the arterial hemodynamic by linking the blood flow, and blood pressure to the arterial resistance and compliance. It is formulated based on the mechanical-electrical analogies. As mentioned previously, recently, numerous studies have discussed the potential of describing the arterial wall viscoelasticity using fractional order models, reducing the number of parameters and exposing a natural response. Hence, a key missing item in the arterial Windkessel modeling is a fractional-order analog component that can provide a reliable, realistic representation of the viscoelasticity behavior. In this invention, we propose a mathematical biomarker for arterial viscoelasticity assessment. The biomarker is a key parameter in a new three-element fractional-order viscoelastic Windkessel model. The proposed model incorporates a fractional-order capacitor that substitutes the ideal capacitor of standard three- element WK model. The latter non-ideal element combines both resistive and capacitive properties which displays the viscoelastic behavior of the arterial vessel. The contribution of both properties is controlled by the fractional differentiation order (alpha) enabling an accurate and reliable physiological description. Based on our recent studies, the new proposed parameter will serve as a mathematical biomarker for arterial viscoelasticity assessment.

The proposed model is implemented in a small smart platform as illustrated in the following figure. It comprises:

• Hemodynamic data detector (Blood pressure, Blood flow, Cardiac output): It serve for the Hemodynamic data acquisition which are the input of the system.
• Processing Unit: the core of the proposed system where the developed fractional-order module is implemented.
• Display: All the evaluated parameters will be displayed in an adequate screen including the biomarker that will be analyzed.

Memristor TCAM (MTCAM) is considered as one of the promising alternatives for current generation CMOS-TCAM. In this work, we present a model of an MTCAM. The mathematical analysis is developed taking into consideration circuit parameters and effects such as 1) memristor ratio RH/RL, 2) transistor technology, 3) operating frequency, and 4) energy consumption. Moreover, the proposed model is validated using SPICE simulations for the memory array showing a close match with the presented mathematical formulations.