# Analysis of Unsteady Solute Dispersion in a Blood Flow of Herschel-Bulkley through a Catheterized Stenosed Artery

## Authors

• Intan Diyana Munir Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
• Nurul Aini Jaafar Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
• Sharidan Shafie Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia

## Abstract

Blockage of blood flow due to cholesterol deposits at the arterial wall, known as stenosis, can lead to conditions such as heart attack and stroke. Treatment such as balloon angioplasty involves the catheterization of an artery where a stented catheter is inflated at the stenosis site to open the narrowed artery. The catheterization of the stenosed artery affects the surrounding blood flow and dispersion process. The present study analyses the effect of catheter radius and stenosis height on the blood velocity and solute dispersion behavior. Herschel-Bulkley fluid is used to model the problem with stenosis as the boundary condition. The momentum equation and Herschel-Bulkley constitutive equation are solved analytically into integral forms. Simpson’s 3/8 rule and Regula-Falsi method were used to evaluate the integral numerically to obtain the velocity. The velocity was utilized to solve the unsteady convective-diffusion equation using the generalized dispersion model (GDM) to obtain the dispersion function. This present research can potentially help the medical field and industry in determining the suitable catheter radius for patients, calculating drug dosage and improving stent catheter design. Results show that the velocity decreases as the catheter radius and stenosis height increase. A decrease in velocity simultaneously increases the solute dispersion function.

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