key: cord-0936988-0ipyt9xq
authors: Goyal, Ashish; Duke, Elizabeth R.; Cardozo-Ojeda, E. Fabian; Schiffer, Joshua T.
title: Mathematical modeling explains differential SARS CoV-2 kinetics in lung and nasal passages in remdesivir treated rhesus macaques
date: 2020-06-22
journal: bioRxiv
DOI: 10.1101/2020.06.21.163550
sha: 3f1dc682ffea7e4901671716b4f71a3dc2f5408c
doc_id: 936988
cord_uid: 0ipyt9xq

Remdesivir was recently demonstrated to decrease recovery time in hospitalized patients with SARS-CoV-2 infection. In rhesus macaques, early initiation of remdesivir therapy prevented pneumonia and lowered viral loads in the lung, but viral loads increased in the nasal passages five days after therapy. We developed mathematical models to explain these results. We identified that 1) drug potency is slightly higher in nasal passages than in lungs, 2) viral load decrease in lungs relative to nasal passages during therapy because of infection-dependent generation of refractory cells in the lung, 3) incomplete drug potency in the lung that decreases viral loads even slightly may allow substantially less lung damage, and 4) increases in nasal viral load may occur due to a slight blunting of peak viral load and subsequent decrease of the intensity of the innate immune response, as well as a lack of refractory cells. We also hypothesize that direct inoculation of the trachea in rhesus macaques may not recapitulate natural infection as lung damage occurs more abruptly in this model than in human infection. We demonstrate with sensitivity analysis that a drug with higher potency could completely suppress viral replication and lower viral loads abruptly in the nasal passages as well as the lung. One Sentence Summary We developed a mathematical model to explain why remdesivir has a greater antiviral effect on SARS CoV-2 in lung versus nasal passages in rhesus macaques.

There is a desperate need for treatments for SARS CoV-2, the virus which causes COVID- 19 18 disease. 1 One unmet need for of antiviral therapy development is identification of virologic surrogates for 19

clinically meaningful endpoints such as death or need for hospitalization. In the case of SARS-CoV-2-20

infected people viral load can be routinely measured in nasal samples or saliva. 2 However, the primary 21 site of disease is lung tissue. Therefore, bronchoalveolar lavage (BAL) of the lungs would be an ideal 22

sample. However, BAL is usually not necessary for diagnosis, represents an infection risk to medical 23 personnel and is rarely performed in the care of COVID-19 patients. When BAL does occur, it is often 24 late during disease in critically ill patients rather than at early clinical presentation. Thus, the natural 25 kinetics of SARS CoV-2 in lungs are unknown in humans. 26

In humans, a double-blind, randomized, placebo-controlled trial showed that the nucleoside 27 analog remdesivir limited the duration of illness and approached statistical significance for reduction in 28 mortality when given later in disease 3 . In a separate study with an overall later time of treatment 29 initiation, remdesivir had no effect on viral load or clinical outcome. 4 A recent pre-print demonstrated that 30 remdesivir was highly effective when initiated 12 hours after infection in rhesus macaques. 5 In this 31 context, remdesivir prevented pneumonia and limited extent of clinical illness. While there was an effect 32 on viral shedding in serial BAL specimens, viral load in the nasal passage was unchanged relative to 33 animals treated with a vehicle during the first several days of infection and higher starting at day 5. A 34 critical question is whether nasal viral loads are potentially useful as a surrogate for the extent of lung 35 disease during COVID-19 infection. 36

Here, we develop mathematical models that recapitulate viral load trajectories in both anatomic 37 compartments of the infected rhesus macaques. The models explain these differences according to 38 different underlying viral kinetics off therapy in both compartments as well as differential drug potency in 39 nasal passage versus lung.

infiltrates on chest radiograph, lower viral load by nucleic acid and viral titer measurement in 48 bronchoalveolar lavage fluid on days 1, 3 and 7, and decreased volume of lung lesions, lung weight and 49 inflammation on histologic post-mortem exam. 5 50

We re-examined viral loads in BAL and nasal specimens, and noted that at days 1, 3 and 7 post-51

infection BAL viral loads were lower in the remdesivir arm relative to the vehicle arm by approximately a 52 single order of magnitude (Fig 1a) . Similar results were observed when viral load was measured using 53 viral culture. 5 In nasal specimens, there was no observed difference in viral loads at days 1, 2, 3 and 4; on 54 day 6, there was a trend towards higher viral loads in the remdesivir treated arm; on day 5 and 7, nasal 55 viral loads were statistically higher in the treated arm relative to vehicle (Fig. 1b) . 56

When nasal viral loads were compared longitudinally to BAL viral loads in vehicle treated 57 animals, viral loads were generally higher in BAL than in the nasal passages at days 1, 3 and 7 (Fig 1c) ; 58 in the remdesivir-treated animals, viral loads were equivalent on days 1 and 3, but higher in nasal 59 passages than BAL at day 7 (Fig 1d) . Overall, these results suggest that remdesivir lowered viral load in 60 the lung but appeared to have the opposite effect in nasal passages of rhesus macaques at late timepoints. molecule to achieve its active triphosphate form (NTP) as well as the distribution of these metabolites 69 from plasma to tissue. 70

For single-dose PK, we fit the model to data from healthy rhesus macaques in which various 71 intermediate metabolites were measured over time following a single injection of 10 mg/kg, including the 72 levels of NTP is PBMCs. 6, 7 We also simultaneously fit the model to multi-dose drug and metabolite 73 trough levels from the infected rhesus macaques (10 mg/kg at day 0.5 and thereafter, 5 mg/kg daily at 74 days 2 till 6 post-infection), including a day 7 level of the Nuc in tissue at the time of necropsy on day 7 75 in Fig 3b. 5 RDV PK parameters are listed in Table 1 . The PD models assumes an EC50 or concentration 76 of the active metabolite (NTP), at which replication is inhibited by 50%. 77

The model is able to recapitulate the levels of remdesivir and its metabolites in healthy (Fig 3a) 78 and infected rhesus macaques (Fig 3b) . 79

Lung and nasal mathematical model of SARS Co-V-2 in rhesus macaques. We developed a model of 81 viral replication in the nasal passage and lungs that includes multiple mechanisms that may occur 82 following infection in lungs and the nasal passages (Fig 4a) . This model is an adaptation of our previous 83 model of human COVID-19 infection and includes a density-dependent death of infected cells as a proxy 84

for an intensifying innate response to a higher burden of infection, proliferation of susceptible epithelial 85 cells, the conversion of susceptible and/or infected cells to an infection refractory state and the movement 86 of the virus between nasal passages and the lung. 8 We fit different versions of this model to the viral loads 87 in nasal passages and lung from 6 infected, remdesivir-treated animals, 5 Using model selection theory, we found that the model with minimal complexity necessary to 93 explain the observed data was the one in Fig. 4b . In this model, infected cell death and viral production 94 have different rates in lung compared to the nasal passage ( Table 2) . Furthermore, in the selected model, 95

susceptible lung cells proliferate and become refractory to infection, but cells in the nasal passages do not 96 (Table 3) . Interestingly, this model lacked viral interchange between lung and nasal passages. 97 98 Model fit to viral load data from untreated rhesus macaques. The best model fit recapitulated the 99 frequently observed trend of higher viral loads in BAL at late timepoints relative to the nasal passage in 100 untreated macaques (Fig 5a) . The model also closely captured the viral dynamics in BAL from untreated 101 animals and mostly captured nasal viral loads as well, though outlier datapoints compromised model fit 102 somewhat in several of the animals. 103

Infected cell death rates were generally higher while viral replication rates were uniformly lower 104 in the nasal passages relative to lungs in the untreated animals ( Table 4 ). The density-dependent exponent 105 had a similar value in both compartments (k=0.09), was similar to that predicted in humans, 8 and led to a suppressed viral replication varied somewhat across animals. Over the course of the treatment (from day 0.5 to day 7), the mean efficacy of the RDV treatment in nasal mucosa was estimated to be 88.4%, 91.4%, 119 86.9%, 81.0%, 86.2% and 83.5% in RM1, RM2, RM3, RM4, RM5 and RM6, respectively. Similarly, over 120 the course of the treatment (from day 0 to day 7), the mean efficacy of the RDV treatment in lung was 121 estimated to be 76.3%, 75.0%, 80.4%, 69.8%, 77.4% and 75.5% in RM1, RM2, RM3, RM4, RM5 and 122 RM6, respectively (Fig 6) . Brief reductions in RDV drug concentrations between doses related to lower 123 active metabolite levels in cells were associated with viral re-expansion after each dose (Fig 5b) . 124

The antiviral potency of remdesivir was estimated using "in vivo" EC50. Whereas "in vitro" IC50 125 estimate the antiviral concentration needed to inhibit 50% of viral replication based on in vitro 126 experiments, we estimate EC50 based on viral loads measured in vivo in animal or human experiments. 10 127

Estimates for in ivio EC50 were roughly 2-fold higher (2-fold lower potency) in the lung relative to the 128 nasal passages (Table 4 ). Variability in nasal viral load peak and contemporaneous viral loads between 129 treated animals generally related to difference in in vivo EC50 rather than viral replication rate. RM2 had 130 complex kinetics with low peak viral load followed by viral rebound (which was not captured by the 131 model and may represent a drug resistant variant) 11 and was found to have the lowest EC50. One animal 132

with accelerated viral elimination in the lung (RM5) was found to have a higher infected cell death rate in 133 lung but similar EC50 relative to the other 5 treated animals (Table 4) . 134 135

We next performed counterfactual simulations in which the six treated animals were assumed to have not 137 received treatment (ϵ ! =0 and ϵ " =0). The viral load trajectories in these simulations (Fig. 7) appear 138 similar to those in untreated animals with BAL viral loads often exceeding nasal viral loads at later 139 timepoints (Fig 5a) . Comparisons of the counterfactual viral load tracings to the treated animals suggests 140 that a majority of viral load decrease in lungs is achieved following the first dose and is then carried 141 forward throughout the duration of therapy with unchanged decay slopes. On the other hand, in nasal 142

passages, viral load is decreased initially during therapy but then stabilizes or even increases, leading to 143 higher viral loads than counterfactual projections (Fig 7) .

In the nasal cavity, somewhere between day 2 and 6 of therapy, the tracings cross and viral loads 145 of the treated animals are predicted to exceed the counterfactual simulations of the same animals off 146 therapy (Fig. 7) . The model projects that early treatment reduces viral load, thereby decreasing new early 147 infection and preventing depletion of susceptible cells in the nasal passages (Fig 8) . Even without 148 assuming susceptible cell proliferation, there is an adequate population of these cells to establish a steady 149 state of viral replication (Fig 8) . In the lung where remdesivir is less potent and initially susceptible cells 150

can become refractory to infection, treatment leads to a slower depletion of susceptible cells. These cells 151 are nevertheless depleted in a linear fashion as they convert to a refractory state (Fig 8) . Inclusion of a 152 refractory cell compartment is therefore necessary to allow linear elimination of virus from serial BAL 153

Decreased cell death in the lungs of remdesivir treated animals. As an informal assessment of lung 156 damage, we longitudinally assessed cell death over time in our counterfactual simulations. In each case, 157 therapy decreased the degree of peak cell death by at least 33% (Fig. 9 ). While lung damage is multi-158 factorial during COVID-19, this finding is qualitatively compatible with the observation that early 159 remdesivir spared these 6 animals from severe clinical disease and abnormal lung histopathology. 160 161 Projected nasal and lung viral load trajectories at higher drug potency. Next, we performed sensitivity 162 analyses in which we assumed a more potent antiviral effect, which could arise either from different 163 dosing of remdesivir or a drug with a more potent drug. In nasal passages (Fig 10a) and in lungs ( Fig  164   10b) , the impact of the first dose is more profound with higher potency leading to a more abrupt decline 165 in viral load. 166

We estimate that minimum drug efficacies of 99.99% and 99.5% would be required to eliminate 167 virus from nasal passages and lungs within 5 days for a drug that is given 12 hours after infection. The 168 need for such high potency reflects the lack of a concurrent immune response at this early stage of 169 infection.

modeling of human infection that antiviral treatment with moderate potency would not clear viral 173 infection in the nasal passage (or sputum) if dosed prior to the peak viral load but would clear infection if 174 dose several days later. 8 Our simulations of the rhesus macaque data arrive at a similar conclusion in the 175 nasal passage, that, paradoxically, later treatment with a moderate potency drug results in lower viral 176 loads, whereas treatment started before peak results in increased late viral loads (Fig 11a) . In contrast, in 177 the lungs, later treatment at days 2 or 4 leads to a subsequent viral load trajectory similar to that of the 178 earlier treated animals during the later stages of infection (Fig 11b) . 179

We estimate that minimum drug efficacies of 50% and 99.5% would be required to eliminate 180 virus from nasal passages and lungs within 5 days for a drug that is given 4 days after infection. This 181 result is due to the higher remaining viral load in the lungs of animals during the first untreated 5 days of 182 infection.

Viral load is a valid surrogate endpoint for treatment efficacy of several viruses including HIV, 185 hepatitis B, hepatitis C and cytomegalovirus. [12] [13] [14] [15] [16] It is plausible that SARS CoV-2 lung viral load is also 186 predictive of disease severity in humans. Viral loads from swabs of infected tissue provide an 187 approximation of the number of infected cells at a given point in time, and therefore the surface area of 188 infected tissue. 17, 18 Unfortunately, it is less certain whether viral load measurements can be leveraged for 189 SARS CoV-2 treatment response in humans because BAL is required to measure lung viral loads but 190 these are never performed longitudinally in infected people as part of routine clinical care. Experience 191 from other respiratory viruses suggests that viral load measures in the upper airway by nasal swab or 192 saliva may or may not be representative of those in the lung. 19 193 Here we apply mathematical models to remdesivir treatment data in rhesus macaques in which 194 both lung and nasal viral load were measured. We identify that the relationship between lung and nasal On the other hand, in rhesus macaques, extensive lung damage and clinic illness is observed 215 within two days of infection, which is not in keeping with severe illness in humans which emerges at least 216 a week after the initial phase of illness. 5, 21 We hypothesize that direct intratracheal inoculation of 217 macaques with a high viral titer results in more immediate infection of lung. In humans, a more common 218 pattern is for respiratory viruses to start replicating in the upper airway and then transmit to the lungs in a 219 second stage of infection. 22 An alternative, and not mutually exclusive explanation is that the degree of 220 viral replication in the lung can also be established extremely early in humans, but that the more extensive 221

immune-mediated damage which may be correlated with the extent of early viral replication, occurs 1-2 222 weeks later. Had the rhesus macaques with the highest lung viral loads been followed for a longer period 223 of time, it is possible that a more severe pneumonia would have developed at later timepoints. 224 A counterintuitive result predicted by our model is that remdesivir is slightly more potent in the 225 nasal cavity than in the lung on a per cell level (assuming that drug levels are indeed equivalent in the two 226 compartments). Nevertheless, SARS CoV-2 is not cleared in nasal passages as effectively as in the lungs 227 while on treatment, because the effectiveness of antiviral therapies is never independent of the concurrent 228 intensity of the immune response to infection. 10, 23 We previously predicted that a more potent therapy is 229 needed after 2 days of SARS CoV-2 infection relative to >5 days after infection because there is little 230 innate immune pressure against the virus during its early expansion phase. 8 As a result, despite a slight 231 blunting of initial viral loads, virus will rebound or stabilize and end up at a higher viral level in the nose 232 than in the absence of treatment. 233

Here, we recapitulate this finding in the nasal passages, but also predict why this does not occur 234 in the lungs of macaques. In the lung as in the nasal cavity, we assume density dependent killing as a proxy for an intensifying innate response to a higher burden of infection. However, our model also 236 suggests that ongoing infection drives a percentage of lung cells to become temporarily refractory to 237 infection. Inclusion of this assumption is required to recapitulate lung viral load data and to explain the 238 observation that lung damage is severely blunted in animals receiving treatment. This assumption is 239 supported by modeling of influenza infection. 24 

There are several limitations of our approach. First, our approximation of lung damage is 241 relatively coarse based on the complexity of this post-viral inflammatory process which may be mediated 242 by factors other than number of infected cells. This is therefore a qualitative target of our modeling. 243

Second, our fits to nasal viral load are imperfect which may be due to imprecision in viral load 244 measurements as well as missed components within the model. In the case of RM2, there is substantial 245 viral rebound that may be due to incomplete innate responses to the first pulse of infection, or to de novo 246 drug resistance. Third, we only model early infection and therefore neglect the critical impact of the late 247 acquired immune response. 25-27 248

In conclusion, we demonstrate that in rhesus macaques, the non-linear forces governing SARS 249

CoV-2 viral load trajectories in the lung and nasal passages differ substantially in the presence of a 250 partially effective antiviral therapy. To the extent that the rhesus macaque model approximates human 251 infection, nasal viral load remains a promising surrogate endpoint marker, but perhaps only in the context 252 of a highly potent antiviral therapy.

Experimental data. We analyzed viral load observations from nasal passages and BAL, and remdesivir and 255 its metabolites plasma concentrations from 12 SARS-CoV-2-infected rhesus macaques in which 6 were 256 treated with remdesivir and 6 received a vehicle control. 5 Remdesivir was infused 12 hours after infection 257 at a dose 10mg/kg with subsequent daily doses of 5 mg/kg for 6 day., We also added viral loads from nasal 258 passages and BAL from 8 additional untreated animals from Muster et al. 7, 21 In both studies, rhesus 259 macaques were infected with 2.6x10 6 TCID50 of SARS-CoV-2 strain. Details about the infection and 260 treatment protocol can be found in these two pre-prints. 261

We also analyzed more frequently sampled observations of remdesivir and its metabolites averaged 262 from three healthy animals after a single IV infusion of 10mg/kg of remdesivir. 28 263 264 Remdesivir pharmakinetics model. We used a compartmental and metabolism pharmacokinetics (PK) 265 model for remdesivir. The goal of this model was to recapitulate the sparse data from remdesivir and its 266 metabolites after several doses to the SARS-CoV-2-infected animals, 5 along with the very frequently 267 sampled data after a single dose in healthy animals. 6 The PK model (depicted in Fig 2) 2 is produced at a rate π 0 and cleared with rate γ 0 . 24 Free virus is exchanged between the lungs and nasal 296 passages at rates 12 and 21 . 297

We also considered the possibility of the emergence of refractory cells. Due to antiviral actions of 298 cytokines such as interferon, it has been experimentally demonstrated that uninfected lung airway cells may 299 become refractory ( . ) at rate . , 24 and that infected cells may convert directly to refractory cells ( . ) at 300 rate . . Refractory cells may lose their refractory state and become susceptible at rate . . 24 Since we were only interested in the viral dynamics in a short span of ~7 days (with or without treatment), we ignored the 302 death rate of uninfected and refractory cells in the lung, that are usually long-lived. 303

We also included the possibility of regeneration of susceptible cells during infection. Innate 304 immune cells eliminate virus but can also induce pulmonary tissue damage or endothelium damage as part 305 of this process. 31, 32 The restoration of the respiratory epithelial barrier after an injury is important and may 306 happens within days after viral clearance, 33-35 depending on the severity of the infection and the extent of 307 lung involvement. Indeed, the proliferation of epithetical cells and progenitor stem cells (or, distal airway 308 stem cells or DASCs) is critical for barrier repair following an inflammatory insult. Following lung injury, 309 the tissue repair process is promoted by immune cells including innate lymphoid cells (ILC-IIs) and 310 macrophages. 36 Epithelial restoration is initiated locally by proliferating alveolar type II (AT2) cells. 37 We 311 modeled this restoration by adding a logistic proliferation of susceptible and refractory (but not infected 38 ) 312 epithetical cells with maximum rate . . All the previous mechanisms are modeled by the following 313 Taking derivative on both sides, we obtain 335

Notice that this definition of 1 is equivalent to 1 = 1 − 1 − 1 − 1 . Under this assumption, the 337 fraction of the lung covered with dead cells would be: Table 2 . 360

We next fit models to viral load and lung lesion observations from treated and untreated animals. 361

Here, we explored different competing models listed in Table 3 and described below. We explored models 362 that included cell proliferation and refractory cells in the lungs, fixing 2 = 0, 42 2 = 0 and 2 = 0. We 363 explored the possibility that AT2 cells proliferate with maximum rate 1 after some delay, 33 i.e. 1 = 0 if 364 < . We also included models assuming that the antiviral activity of remdesivir in nasal passages occurs 365 after its activity in the lungs by a delay . For comprehensiveness, we checked two models where refractory 366

(1) with rate . . . and (2) with rate

. Notice that for the latter when 781~0 then \ for each compartment . Since we were estimating 371 both 78. and . together we explored fixing the standard deviation of the random effects of 78. to 0.1, 372 0.2 and 1. Finally, we only estimated the fixed effects of 1 , and , when applicable. Here, we also 373 assumed = 0 as the time of infection with same initial values and fixed parameters 1 , 2 , 1 and 2 as 374 before. We estimated the remaining parameters depending on each model assumptions. 375

To determine the best and most parsimonious model among the instances above, we computed the 376 log-likelihood (log L) and the Akaike Information Criteria (AIC=-2log L+2m, where m is the number of 377 parameters estimated). We assumed a model has similar support from the data if the difference between its 378

AIC and the best model (lowest) AIC is less than two. 43 379 assuming no treatment. In the case of the lung (BAL specimens), therapy is projected to lead to consistently 432 lower viral loads. In the case of nasal viral load, therapy temporarily lowers viral load, but viral load is 433 predicted to ultimately persist at higher levels than in the absence of treatment. Simulations are based on 434 data from RM1-6. Time is in days from infection. 435 

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