3.3.3. Monocytes

Due to their sizes, we hypothesise that monocytes do not have convection, but they experience diffusion in the arterial wall. Once monocytes are in the arterial wall, they differentiate into macrophages, and also, they suffer apoptosis. These two phenomena are represented by their reactive terms.

$$\frac{\partial \mathbb{C}\_{m,w}}{\partial t} + \nabla \cdot (-D\_{\mathbb{C}\_{m,w}} \nabla \mathbb{C}\_{m,w}) = -d\_{m} \mathbb{C}\_{m,w} - m\_{d} \mathbb{C}\_{m,w\_{\prime}} \tag{37}$$

where *Cm*,*<sup>w</sup>* is the monocyte concentration in the arterial wall. *dm* is the rate of monocytes that differentiate into macrophages and *md* is the apoptosis rate of monocytes.

In addition, a physiological monocyte inlet concentration in the lumen of 550 · 10−<sup>9</sup> *Monocyte m*<sup>3</sup> is imposed [48].

Monocyte flow through the endothelium is dependent on hemodynamics. Areas of low *TAWSS* are known to be atheroprone; particularly for carotid arteries, areas of *TAWSS* lower than 2 Pa can develop atheroma plaque [16,41,42]. For the case of *OSI*, according to our previous work [8], it can be determined that areas of *OSI* greater than 0.1910 are atheroprones. Monocyte flow across the endothelium can be defined as [8]:

$$\mathcal{I}\_{\rm{/s,m}}(TAWSS,OSI) = m\_{\rm{r}} \cdot (0.8588 \cdot e^{-0.6301 \cdot TAWSS} + 0.1295 \cdot e^{3.963 \cdot OSI}) \cdot \mathcal{C}\_{LDL,m,m} \cdot \mathcal{C}\_{m,I} \tag{38}$$

with *mr* being the monocyte recruitments from the lumen.
