Models

Several models are already implemented in the CellBasedModels. You can use them by calling

CBMModels.NameOfModel

and introduced in the Agent using the baseModelInit or baseModelEnd keyord arguments. e.g.

ABM(2,
    baseModelInit=[CBMModels.Bacteria2D]
    #More arguments...
)

Soft spheres

The cells are spheroids that behave under the following equations:

\[m_i\frac{dv_i}{dt} =-bv_i+\sum_j F_{ij}\]

\[\frac{dx_i}{dt} =v_i\]

where the force is

\[F_{ij}= \begin{cases} f0(\frac{r_{ij}}{d_{ij}}-1)(\frac{\mu r_{ij}}{d_{ij}}-1)\frac{(x_i-x_j)}{d_{ij}}\hspace{1cm}if\;d_{ij}<\mu r_{ij}\\ 0\hspace{5cm}otherwise \end{cases}\]

where $d_{ij}$ is the Euclidean distance and $r_{ij}$ is the sum of both radius.

Functions assotiated with the model

Rod-shape agent

Model of physical interactions for bacteria modeled as 2D rod-shape like cells. This implementation follows the model of Volfson et al.

The forces that the rods feel are computed by the closest virtual spheres in contact. For a rod of mass $m$.

\[\bold{f}_{ij}=f_n\bold{n}_{ij}+f_t\bold{v}_t\]

where $\bold{n}_{ij}$ if the normal vector between between the center of the spheres, defined as $\bold{n}_{ij}=(\bold{r}_i-\bold{r}_j)/r_{ij}$; and the normal and tangential forces are defined as

\[\begin{aligned} f_n &= k_n\delta^{3/2}-\gamma_n \frac{m}{2}\delta v_n\\ f_t &= -\min(\gamma_t\frac{m}{2}\delta^{1/2},\mu_{cc}f_n) \end{aligned}\]

and $\delta=d-r_{ij}$, $v_n=\bold{v}_{ij}·\bold{n}_{ij}$ and $\bold{v}_t=\bold{v}_{ij}-v_n\bold{n}_{ij}$.

The equations of for a bacteria $i$ are given by

\[\begin{aligned} m\ddot{\bold{r}_i} &= \sum_s\bold{f}_{s}-\beta m \bold{v}\\ \bold{I}·\dot{\bold{\omega}}_i &= \sum_s(\bold{r}_s-\bold{r_i})\times\bold{f}_s - \beta_\omega\omega \end{aligned}\]

where $s$ denotes for the sum over the virtual interacting spheres acting on bacteria $i$ and $\bold{I}$ is the tensor of inertia of a cylinder.

Functions assotiated with the model

Here you may find functions that the defined model uses to compute it and can be used and modify it to make your own models.

function rodForces(
    x,y,d,l,theta,vx,vy,m,
    x2,y2,d2,l2,theta2,vx2,vy2,m2,
    kn,γn,γt,μcc,μcw
)