Processes 2019, 7,37
Alfonso et al. developed an agent-based model of immune cell-epithelial cell interactions in breast
lobular epithelium [93]. The model investigated the effect of menstrual cycle length and hormone
status on inflammatory response to cell turnover in breast tissue. Blood vessels were homogeneously
distributed in the intra- and interlobular stroma. The model accounts for myoepithelial and luminal
cells. Cellular processes (i.e., epithelial cell proliferation, cell death via effector cells, programmed
cell death, removal of dead cells, immune cell motility, and inhibition of effector cells by regulatory
cells) are modeled as stochastic events. Effector CD8+ cells are the only cells responsible for killing of
damaged epithelial cells. Regulatory CD4+ and CD8+ cells act by inducing inactivation of effector
dependent response. Chemokines from damaged epithelial cells activate the immune cells. Immune
cells become ineffective when such chemokines are absent, or due to the suppression via regulatory
cells. The outcome of the model identified novel prognostic information for breast cancer, such as the
number of immune clusters being associated with the degree of epithelial damage.
3.3. Models Focusing on Tumor-Associated Lymphatics and Lymph Nodes
Reddy developed the first mathematical model of the lymphatic system in 1977 [94]. In
recent years, various computational modeling approaches have been used to study the lymphatic
vessels [95–99] and lymph nodes [100–102] in general, and in the application to infectious
disease [103,104], and simulating fluid and chemokine transport in the lymphatic system as it relates
to health and disease conditions [105]. Agent-based models have more recently been used to simulate
various processes that occur during an adaptive immune response in a lymph node. Meyer-Hermann
developed an ABM of germinal centers of the lymph node [106,107]. The authors studied B-cell
germinal center reactions and how they contribute to germinal center deregulation [106]. They
expanded this model to study B-cell affinity maturation in the lymph node germinal centers [108].
They found that competition for T-cell rescue and increased refractory time leads to a more robust
affinity maturation.
A series of studies on modeling of T-cell behavior in the lymph node have been conducted by
Bogle and Dunbar [44,109–112]. They modeled T-cell trafficking, activation, and proliferation in the
lymph node paracortex using an agent-based approach. The model included chemokine and cytokine
gradients. Using this lattice-based approach, they were able to model the movement and behavior of
T-cells in the lymph node paracortex [112]. In the next step, they expanded the agent-based model
of the lymph node paracortex in three dimensions to include T-cells and dendritic cells (DC). The
model allows simulation of a large number of T-cells at physiologic densities. The virtual lymph node
can shrink or swell, depending on the dynamics of cell trafficking. The model was able to simulate
T-cell activation in agreement with in-vivo observations, and provide new understanding on T-cell-DC
interactions. Not all the parameters of the model were experimentally measured; thus, the model
can be refined by more accurate measurement of those parameters [110]. Next, the authors built
on their previous models to simulate T-cell ingress and egress, as well as chemotaxis in the lymph
node, by incorporating new numerical methods. The new model allows simulation of expansion and
contraction of T-cells in the lymph node paracortex during an immune response. The ability to model
chemotaxis could be useful in studying other biological processes involving chemotaxis [111].
Moreau et al. constructed a virtual lymph node using agent-based modeling to study T-cell
activation by synapses (long-lasting contacts) and kinapses (transient interactions) [113]. The model
incorporated T-cell migration and T-cell-DC interactions. Additionally, virtual fluorescence-activated
cell sorting (FACs) profiles were obtained from modeling by visualizing T-cell proliferation. This
virtual lymph node model provides new opportunities for understanding the mechanisms of T-cell
regulation in infection or vaccine application [113].
The ABM developed for studies of the lymphatic system thus far mainly focus on the lymph
node, and in particular, T-cell processes. Folcik et al. developed the basic immune simulator (BIS),
which is an agent-based platform that includes parenchymal tissue, secondary lymphoid tissue and the
lymphatic/humoral circulation [114]. Using agent-based and hybrid models, lymph node dynamics are
47
Alfonso et al. developed an agent-based model of immune cell-epithelial cell interactions in breast
lobular epithelium [93]. The model investigated the effect of menstrual cycle length and hormone
status on inflammatory response to cell turnover in breast tissue. Blood vessels were homogeneously
distributed in the intra- and interlobular stroma. The model accounts for myoepithelial and luminal
cells. Cellular processes (i.e., epithelial cell proliferation, cell death via effector cells, programmed
cell death, removal of dead cells, immune cell motility, and inhibition of effector cells by regulatory
cells) are modeled as stochastic events. Effector CD8+ cells are the only cells responsible for killing of
damaged epithelial cells. Regulatory CD4+ and CD8+ cells act by inducing inactivation of effector
dependent response. Chemokines from damaged epithelial cells activate the immune cells. Immune
cells become ineffective when such chemokines are absent, or due to the suppression via regulatory
cells. The outcome of the model identified novel prognostic information for breast cancer, such as the
number of immune clusters being associated with the degree of epithelial damage.
3.3. Models Focusing on Tumor-Associated Lymphatics and Lymph Nodes
Reddy developed the first mathematical model of the lymphatic system in 1977 [94]. In
recent years, various computational modeling approaches have been used to study the lymphatic
vessels [95–99] and lymph nodes [100–102] in general, and in the application to infectious
disease [103,104], and simulating fluid and chemokine transport in the lymphatic system as it relates
to health and disease conditions [105]. Agent-based models have more recently been used to simulate
various processes that occur during an adaptive immune response in a lymph node. Meyer-Hermann
developed an ABM of germinal centers of the lymph node [106,107]. The authors studied B-cell
germinal center reactions and how they contribute to germinal center deregulation [106]. They
expanded this model to study B-cell affinity maturation in the lymph node germinal centers [108].
They found that competition for T-cell rescue and increased refractory time leads to a more robust
affinity maturation.
A series of studies on modeling of T-cell behavior in the lymph node have been conducted by
Bogle and Dunbar [44,109–112]. They modeled T-cell trafficking, activation, and proliferation in the
lymph node paracortex using an agent-based approach. The model included chemokine and cytokine
gradients. Using this lattice-based approach, they were able to model the movement and behavior of
T-cells in the lymph node paracortex [112]. In the next step, they expanded the agent-based model
of the lymph node paracortex in three dimensions to include T-cells and dendritic cells (DC). The
model allows simulation of a large number of T-cells at physiologic densities. The virtual lymph node
can shrink or swell, depending on the dynamics of cell trafficking. The model was able to simulate
T-cell activation in agreement with in-vivo observations, and provide new understanding on T-cell-DC
interactions. Not all the parameters of the model were experimentally measured; thus, the model
can be refined by more accurate measurement of those parameters [110]. Next, the authors built
on their previous models to simulate T-cell ingress and egress, as well as chemotaxis in the lymph
node, by incorporating new numerical methods. The new model allows simulation of expansion and
contraction of T-cells in the lymph node paracortex during an immune response. The ability to model
chemotaxis could be useful in studying other biological processes involving chemotaxis [111].
Moreau et al. constructed a virtual lymph node using agent-based modeling to study T-cell
activation by synapses (long-lasting contacts) and kinapses (transient interactions) [113]. The model
incorporated T-cell migration and T-cell-DC interactions. Additionally, virtual fluorescence-activated
cell sorting (FACs) profiles were obtained from modeling by visualizing T-cell proliferation. This
virtual lymph node model provides new opportunities for understanding the mechanisms of T-cell
regulation in infection or vaccine application [113].
The ABM developed for studies of the lymphatic system thus far mainly focus on the lymph
node, and in particular, T-cell processes. Folcik et al. developed the basic immune simulator (BIS),
which is an agent-based platform that includes parenchymal tissue, secondary lymphoid tissue and the
lymphatic/humoral circulation [114]. Using agent-based and hybrid models, lymph node dynamics are
47