Key Concepts
SARS-CoV-2 particles infect an individual mainly through olfactory systems. Support cells in the olfactory tissue, called sustentacular cells, have ACE2 receptors, which provide a gateway through which viral particles can enter, hijack cellular machinery to produce more viral particles, lyse sustentacular cell and infect more cells in the vicinity. Death of these sustentacular cells upends the machinery powering olfactory sensory neurons (OSNs) [7]. Upon cell lysis, a certain number of viral particles enter into either the blood or the lymph. Increase in the permeability of the blood-brain barrier (BBB) by upregulation of IL-6 as well as enlargement of perivascular spaces (PVS) suggest that the SARS-CoV-2 virus might disseminate through the CNS [8,9,6]. Frontal lobe, temporal lobe, cerebellum, corpus callosum and thalamus is most liable to neural cell atrophy.
Model Building
The model was built using NetLogo 3D (version 6.2.0), which facilitates the three-dimensional representation of the system of interest [10]. The system has been divided into three distinct regions: the olfactory epithelium, circulatory system (the heart and the lungs), and the CNS), as seen in Figure 1. Steps are showcased within the NetLogo universe as a series of colorful blocks of varying sizes and shapes. Some blocks represent tissue, while others represent cells. Every effort to maintain a reasonable size ratio has been expended. In the model, the virus passes through the mucus barrier, travels through the olfactory epithelium and the circulatory system, moves past the blood-brain barrier to eventually reach the brain. The infection of the sustentacular cells and the atrophy of the cerebral regions have been depicted in order to represent the phenomena of anosmia as well as neuroinvasion by SARS-CoV-2.
Model Environment
The model was created on a rectangular coordinate system called the NetLogo world, and the x,y and z coordinates were set to -40 to +40, -30 to +30, and -20 to +20, respectively. However, the patches and frames were kept at their default settings of 13 pixels and 30 frames per second respectively. Each organ within the world was constructed with a distinct color to differentiate between systems. Further, the cells, represented as turtles were given different shapes to better visualize interactions and changes if any.
Model Assumptions and Rules
The model assumptions were first declared to design a plausible system and a corresponding model rule to simulate the same. These assumptions and rules were:
● The SARS-CoV-2 virus enters through the nose only. This assumption is to fit the model to the hypothesis that the neuroinvasion of the virus follows anosmia. The virus’ first entry point is thus, through the nasal cavity and into the olfactory epithelium after crossing the mucosal barrier.
● The mucus and blood brain barriers do not pose a physical resistance to the movement of the virus. The barriers’ effectivity and rate of clearance have not been established in the literature. The barriers are depicted by patches as a visual barrier only.
● The virus can infect only the sustentacular cells within the olfactory epithelium. Only the sustentacular cells possess the necessary entry molecules. When the distance between the virus and the sustentacular cells is less than 0.6, the virus attacks the sustentacular cells.
● From Bar-On et al [11], the virus burst size is approximately 1000. The burst size is appropriately scaled down during the simulation.
● The virus moves along the hematogenous route. The most convenient path for the virus’ movement to the central nervous system is through the bloodstream and not the olfactory bulb. This is because of the lack of a gateway molecule in the olfactory sensory neuron, in particular, the ACE2 receptors and primer protease TMPRSS2. The virus invades the lymphatic system from the sustentacular cells. The virus is then drained along with the lymph into the bloodstream. Through the bloodstream, it is then able to enter the heart and circulates through the system till it finally reaches the blood-brain barrier.
● Cells of a certain type are uniform in shape and size and the role of cilia and microvilli can be performed by the cell surface. The size of the cells varies and is therefore approximated to a uniform value (see Table 1).
● The immune system mounts a response 5 days after symptom onset. The approximate response by the immune system occurs 5 days after symptom onset. After 100 ticks (20 ticks = 1 day), 0-2 viruses are killed in each tick.
● The rate of immune response is lower in individuals aged 60 years and above. The number of viruses killed per tick is relatively lower.
Model Timescales, Variables, and Scaling-down
The values for the sizes and the counts of the model variables were obtained through literature mining; when specific data were not available, estimates based on present knowledge were utilized. As directly implementing the sizes and counts can result in the consumption of a large amount of computational time and resources, they were appropriately scaled down in the model environment so as to reflect realistic infection patterns. The sizes of the variables were scaled in terms of the relative ratios. For example, \(\frac{virus size}{sustentacular cell size}= \frac{0.1}{3}\). For scaling the counts, three mathematical functions were applied:
● For variables in the olfactory epithelium: log(count) * 10
● For variables in the brain: log(count) * 5
● For SARS-CoV-2: x1/3
Table 1 lists the sizes and counts of the variables [12–19]. The simulations were performed by changing the viral load using the slider and switching between different attributes (such as the age of the patient) using the choosers on the NetLogo interface. The results were analyzed by tracking the count of the sustentacular cells and brain atrophy via monitors on the interface, along with the number of ticks completed.
Visualization
In order to visualize the data, the viral count at the end of every tick was reported as output from NetLogo 3D; this was then plotted against the corresponding tick value. The plots this generated would help to generalize the trend of the virus’ count following infection over time. The plots were categorized according to the age group and further divided based on the initial viral load, resulting in six scenarios.
Table 1
Variable
|
Size (µm)
|
Count
|
Scaled Down Count
|
SARS-CoV-2
|
0.1
|
105 copies/mL
|
10-50
|
Sustentacular cells
|
3 - 5
|
3.33 x 106
|
65
|
Olfactory sensory neurons
|
3 - 5
|
107
|
70
|
Frontal lobe neurons
|
3 - 5
|
6.56 x 109
|
49
|
Temporal lobe neurons
|
3 - 5
|
3.52 x 109
|
48
|
Cerebellum neurons
|
3 - 5
|
69 x 109
|
54
|
Corpus callosum neurons
|
3 - 5
|
-
|
46
|
Thalamus neurons
|
3 - 5
|
-
|
43
|