Electric circuit representation of the human circulatory system to estimate the position of nanosensors in vessels

Nanodevices are the focus of research enhancing the detection and treatment of diseases in the human body. Focusing on the scenario where nanosensors are flowing with the blood in the human circulatory system (HCS), in this work, we investigate a model to predict their distribution along the various vessel segments. Although various approaches report solutions for localizing nanosensors in the body, it is also relevant to derive their stationary distribution along the vessel segments as a prior step to assess their actuation and sensing capabilities in the body. We use a Markov chain formulation to derive the stationary distribution of nanosensors. We evaluate the transition probabilities relying on the representation of vessels with electric circuit components. We implement the electric circuit representation of the left ventricle in the heart and the arteries to find the blood flow at vessel bifurcations and then compute the Markov chain probabilities. Our system also allows to reveal the dynamics of the movement of nanosensors with the human activity. We illustrate results in two regimes, as low and high activity, to mimic the case when being at rest or doing sports.