# Anomalous Angiogenesis in Retina

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Cellular Potts Model

#### 2.2. Continuum Fields at the Extracellular Scale

^{−1}, D

_{f}= 0.036 mm

^{2}/h, ν = 0.6498/h, S = 5 × 10

^{−7}pg/µm

^{2}(corresponding to 50 ng/mL for a sample with a 10 µm height [40,41]), and Γ = 0.02 pg/(µm

^{2}h) is the maximum amount of VEGF that could be consumed by a cell per hour [21,37,42]. In Equation (2), the VEGF source due to 320 the hypoxia caused by drusen and photoreceptors is

#### Durotaxis

#### 2.3. Signaling Processes and Cell Dynamics

#### 2.4. Retinal Configuration and Onset of Angiogenesis

_{pv}that may initiate sprouts and establish an external VEGF activation threshold for the sprouts to start. The parent vessels are randomly placed at the rectangle 0 < x < L, 0 < y < 0.3L = 120 µm and the concentration of external VEGF satisfies Equation (2). The 2 µm wide BM is a segment placed at y = 246 µm [5,43] and it is followed by RPE cells with interspersed drusen, which have Gaussian sources of VEGF representing hypoxic areas. These sources placed at y = 249 µm are farther than 100 µm from the choriocapillaries, which is consistent with the criterion for hypoxia to occur. New sprouts grow from the initial points only if the external VEGF concentration in them is larger than a threshold. The described CPM causes the sprouts to advance toward the drusen and they may or may not pass BM and RPE attracted by the VEGF sources at the photoreceptors.

_{photo}sources of VEGF associated with photoreceptors which are equally spaced on the x axis at y = 388 µm. We ignore the photoreceptors’ outer segments and their dynamics. As in the case of the sources associated with drusen, these VEGF sources are represented by Gaussian functions centered at (${x}^{{p}_{i}}$, ${y}^{{p}_{i}}$ = 388 µm) [45]. The holes divide BM into N

_{drusen}+ 1 pieces. Once VEGF sources are activated, new sprouts can start from the parent vessels at their predetermined sites if the external VEGF concentration there surpasses the activation threshold. VEGF sources stop emitting it when they are reached by ECs.

## 3. Results

#### 3.1. Impaired Adhesion

#### 3.1.1. Adhesion between RPE and BM

#### 3.1.2. RPE–RPE and EC–EC Adhesion

#### 3.2. Sources of VEGF

#### 3.3. Notch Signaling

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

2D | Two Dimensional |

AMD | Age-related Macular Degeneration |

BM | Bruch’s membrane |

CNV | Choroid Neo Vascularization |

CPM | Cellular Potts Model |

EC | Endothelial Cell |

ECM | Extra Cellular Matrix |

EMT | Epithelial to Mesenchymal Transition |

MC | Monte Carlo |

MCTS | Monte Carlo Time Step |

RPE | Retinal Pigmentation Epithelium |

VEGF | Vessel Endothelial Growth Factor |

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**Figure 1.**Sketch of a two-dimensional section of the macula, including choroid and choroid blood vessels, Bruch’s membrane, retinal pigment cells, drusen, outer retina, epithelial cells, and tip cells. Left panel: normal supply of oxygen. Right panel: hypoxia and incipient choroid neovascularization.

**Figure 2.**Effect of impaired adhesion between retinal pigmentation epithelium (RPE) and Bruch’s membrane (BM). Type 1 choroidal neovascularization (CNV) for ${\rho}_{adh}^{{\mathsf{\Sigma}}_{\sigma},{\mathsf{\Sigma}}_{{\sigma}^{\prime}}}$ (RPE-BM) = 30, snapshots at times: (

**a**) 601 Monte Carlos Time Step (MCTS), (

**d**) 1601 MCTS, (

**g**) 4501 MCTS, (

**j**) 9001 MCTS. Type 2 CNV for ${\rho}_{adh}^{{\mathsf{\Sigma}}_{\sigma},{\mathsf{\Sigma}}_{{\sigma}^{\prime}}}$ (RPE-BM) = 6, snapshots at times: (

**b**) 601 MCTS, (

**e**) 1601 MCTS, (

**h**) 4501 MCTS, (

**k**) 9001. MCTS. Type 2 CNV for ${\rho}_{adh}^{{\mathsf{\Sigma}}_{\sigma},{\mathsf{\Sigma}}_{{\sigma}^{\prime}}}$ (RPE-BM) = 0, snapshots at times: (

**c**) 601 MCTS, (

**f**) 1601 MCTS, (

**i**) 4501 MCTS, (

**l**) 9001 MCTS. We have represented the level curves of external VEGF as continuous lines.

**Figure 3.**Effect of impaired adhesion between RPE–RPE and EC–EC. Type 2 CNV for ${\rho}_{adh}^{{\mathsf{\Sigma}}_{\sigma},{\mathsf{\Sigma}}_{{\sigma}^{\prime}}}$ (EC-EC). = 70 and ${\rho}_{adh}^{{\mathsf{\Sigma}}_{\sigma},{\mathsf{\Sigma}}_{{\sigma}^{\prime}}}$ (RPE cell-RPE cell) = 90, snapshots at times: (

**a**) 601 MCTS, (

**d**) 1801 MCTS, (

**g**) 3601 MCTS, (

**j**) 8001 MCTS. Type 1 CNV for ${\rho}_{adh}^{{\mathsf{\Sigma}}_{\sigma},{\mathsf{\Sigma}}_{{\sigma}^{\prime}}}$ (EC-EC) = 70 and ${\rho}_{adh}^{{\mathsf{\Sigma}}_{\sigma},{\mathsf{\Sigma}}_{{\sigma}^{\prime}}}$ (RPE cell-RPE cell) = 80, snapshots at times: (

**b**) 601 MCTS, (

**e**) 1801 MCTS, (

**h**) 3601 MCTS, (

**k**) 8001 MCTS. Type 2 CNV for ${\rho}_{adh}^{{\mathsf{\Sigma}}_{\sigma},{\mathsf{\Sigma}}_{{\sigma}^{\prime}}}$ (EC–EC) = 80 and ${\rho}_{adh}^{{\mathsf{\Sigma}}_{\sigma},{\mathsf{\Sigma}}_{{\sigma}^{\prime}}}$ (RPE cell-RPE cell) = 80, snapshots at times: (

**c**) 601 MCTS, (

**f**) 1801 MCTS, (

**i**) 3601 MCTS, (

**l**) 8001 MCTS.

**Figure 4.**Effect of the VEGF concentration at the sources. For αi = 4.01 × 10

^{−4}= 0.000401, snapshots at times: (

**a**) 601 MCTS, (

**d**) 1201 MCTS, (

**g**) 3001 MCTS, (

**j**) 5201 MCTS. For αi = 1.203 × 10

^{−3}= 0.001203, snapshots at times: (

**b**) 601 MCTS, (

**e**) 1201 MCTS, (

**h**) 3001 MCTS, (

**k**) 5201 MCTS. For αi = 2.005 × 10

^{−3}= 0.002005, snapshots at times: (

**c**) 601 MCTS, (

**f**) 1201 MCTS, (

**i**) 3001 MCTS, (

**l**) 5201 MCTS.

**Figure 5.**Type 1 CNV due to the lack of VEGF in the point where the tip cell of the sprout tries to cross the RPE (left column: (

**a**), (

**c**), (

**e**)). Amount of VEGF receptors of ECs (right column: (

**b**), (

**d**), (

**f**)). Snapshots at times: (

**a**), (

**b**) 1501 MCTS, (

**c**), (

**d**) 4501 MCTS, (

**e**), (

**f**) 9001 MCTS.

**Figure 6.**Type 2 CNV favored by the point where the sprout cross the RPE (left column: (

**a**), (

**c**), (

**e**)). Amount of VEGF receptors of ECs (right column: (

**b**), (

**d**), (

**f**)). Snapshots at times: (

**a**), (

**b**) 1201 MCTS, (

**c**), (

**d**) 1501 MCTS, (

**e**), (

**f**) 3001 MCTS.

**Figure 7.**Effect of Jagged and Delta production on CNV. Type 1 CNV for ${r}_{J}$ = 500 molec/h, ${r}_{D}$ = 1000 molec/h, snapshots at times: (

**a**) 601 MCTS, (

**d**) 1601 MCTS, (

**g**) 4501 MCTS, (

**j**) 9001 MCTS. Type 2 CNV (reference simulation) for ${r}_{J}$ = 2000 molec/h, ${r}_{D}$ = 1000 molec/h, snapshots at times: (

**b**) 601 MCTS, (

**e**) 1601 MCTS, (

**h**) 4501 MCTS, (

**k**) 9001 MCTS. Type 2 CNV for ${r}_{J}$ = 2000 molec/h, ${r}_{D}$ = 7500 molec/h, snapshots at times: (

**c**) 601 MCTS, (

**f**) 1601 MCTS, (

**i**) 4501 MCTS, (

**l**) 9001 MCTS. Left column extracted from Supplementary Material: Video S1. Middle column extracted from Supplementary Material: Video S2.

**Figure 8.**Effect of Jagged and Delta production on CNV. Type 1 CNV for ${r}_{J}$ = 500 molec/h, ${r}_{D}$ = 1000 molec/h, snapshots at times: (

**a**) 601 MCTS, (

**d**) 1801 MCTS, (

**g**) 3601 MCTS, (

**j**) 8001 MCTS. Type 2 CNV (reference simulation) for ${r}_{J}$ = 2000 molec/h, ${r}_{D}$ = 1000 molec/h, snapshots at times: (

**b**) 601 MCTS, (

**e**) 1801 MCTS, (

**h**) 3601 MCTS, (

**k**) 8001 MCTS. Type 2 CNV for ${r}_{J}$ = 2000 molec/h, ${r}_{D}$ = 7500 molec/h, snapshots at times: (

**c**) 601 MCTS, (

**f**) 1801 MCTS, (

**i**) 3601 MCTS, (

**l**) 8001 MCTS.

Param. | A_{EC} | P_{EC} | L_{EC} | A_{RPE} | P_{RPE} | A_{druse} | P_{druse} |
---|---|---|---|---|---|---|---|

Value | 78 µm^{2} | 50 µm | 60 µm | 169 µm^{2} | 52 µm | 2827 µm^{2} | 188 µm |

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Vega, R.; Carretero, M.; Bonilla, L.L. Anomalous Angiogenesis in Retina. *Biomedicines* **2021**, *9*, 224.
https://doi.org/10.3390/biomedicines9020224

**AMA Style**

Vega R, Carretero M, Bonilla LL. Anomalous Angiogenesis in Retina. *Biomedicines*. 2021; 9(2):224.
https://doi.org/10.3390/biomedicines9020224

**Chicago/Turabian Style**

Vega, Rocío, Manuel Carretero, and Luis L Bonilla. 2021. "Anomalous Angiogenesis in Retina" *Biomedicines* 9, no. 2: 224.
https://doi.org/10.3390/biomedicines9020224