One of the ubiquitous causes of deaths are the Cardio Vascular Diseases or CVDs. The implementation of nanotechnology in the treatment of CVDs has evinced better bio-compatibility and enhanced cell interactions. This provides a strong potential for their mathematical modeling with the diseased blood vessels. In our current study we have reported various mathematical models used for the treatment of CVDs employing nanotechnology. Mathematical modeling provides a tool to comprehend the type, shape and size of the nanoparticles that can be employed as possible drug delivery systems. Mathematical models help to predict how nano-drugs have many improvements like expanded drug loading capacity and programmable pharmo-kinetic properties over the conventional drugs. The amalgamation of mathematical models with clinical data provides for designing these optimal therapies. This review encapsulates the current state of mathematical modeling approaches to treat CVDs using nanoparticle targeted drug delivery.

The present work concerns the diffusion of nanoparticles in capillary-tissue exchange system. Nanoparticle are inoculated into the patient’s body by intertumoral administration. Thus, nanoparticles diffuse into tumoral tissues through diseased capillary walls. Blood in the capillaries is modelled as Jeffrey fluid. The resultant fluid is called Jeffrey nanofluid. In this model we have described diffusion occurring through the capillary walls into the surrounding tissue. The mathematical results are obtained analytically and have been compared with numerical solution. Graphs have been plotted using MATLAB. The effects of shape factor of nanoparticles, volume fraction of nanoparticles, Jeffrey fluid parameter, viscosity index and viscosity parameter has been observed on velocity and concentration of nanoparticles diffusing into the tissues. A noticeable observation states that brick shaped nanoparticles diffuse most rapidly i.e., have higher diffusion rates than other shapes

Arterioles are pivotal console of hemodynamics as they are significant contributors to pressure. Under various physiological conditions like administration of a drug, arterioles ascertain divergent mechanical forces. The current communication discusses the effect of different shapes of copper nanoparticles inoculated as nano drugs in arterioles. The blood is assumed to be a non-Newtonian fluid and is delineated as nanofluids. The three-layer model is used for modeling the blood flow as it aptly describes the flow of blood in narrow vessels of diameter less than 100 μm. The Hamilton-Crosser model is implemented to describe the thermal conductivity of nanofluid as this model holds in accordance with experimental as well as theoretical results. The expressions are also obtained for density, thermal expansion and viscosity of the considered nanofluid. The equations are solved analytically and graphs have been plotted using MATLAB. The relative consequence of various shapes of nanoparticles like platelets, blades, cylinders and bricks is observed in temperature, velocity and flow rate. It has been investigated through the graphs that brick-shaped nanoparticles have shown a maximum rise in temperature, velocity and flow rate. And reverse results are observed for blade-shaped nanoparticles. The effect of volume fraction, heat source parameter and Grashof number have also been inspected. The considered analysis shows that a suitable shape of nanoparticle can be used to develop the nano drug according to biomedical needs.

This paper investigates the aspects of dispersion of nanoparticles in blood capillaries linked to nanodrug delivery systems. Nanoparticles are injected intravenously in blood capillaries and the resultant fluid has been identified as nanofluid. The viscosity of nanofluid is modelled using the nanoparticle size dependent viscosity relation. The properties of blood are studied using power law fluid, owing to their physically close simulations. The dispersion model framed here has been solved applying the method used by Sankarsubramanian and Gill for deriving exchange coefficients. The study conducted gives an insight into temperature, velocity and three transport coefficients of nanoparticles dispersed in blood with respect to various parameters like heat source parameter, volume fraction, power law index, size of nanoparticles, Grashof number, Darcy number and slip parameter for small values of wall absorption parameter under steady state conditions. MATLAB software has been used to plot the graphs. The outcomes reveal that physical properties of nanoparticles like size chiefly govern their dispersion. Convergence analysis is also stated for the inhomogeneous Bessel differential equation obtained while solving the problem. The developed mathematical model has useful applications to understand the dispersion of nanodrugs in the treatment of cardio vascular diseases.