Growth Rate of Plasmodium falciparum: Analysis of Parasite Growth Data from Malaria Volunteer Infection Studies

Background Growth rate of malaria parasites in the blood of infected subjects is an important measure of efficacy of drugs and vaccines. Methods We used log-linear and sine-wave models to estimate the parasite growth rate of the 3D7 strain of Plasmodium falciparum using data from 177 subjects from 14 induced blood stage malaria (IBSM) studies conducted at QIMR Berghofer. We estimated parasite multiplication rate per 48 hour (PMR48), PMR per life-cycle (PMRLC), and parasite life-cycle duration. We compared these parameters to those from studies conducted elsewhere with infections induced by IBSM (n=66), sporozoites via mosquito bite (n=336) or injection (n=51). Results The parasite growth rate of 3D7 in QIMR Berghofer studies was 0.75/day (95% CI: 0.73–0.77/day), PMR48 was 31.9 (95% CI: 28.7–35.4), PMRLC was 16.4 (95% CI: 15.1–17.8) and parasite life-cycle was 38.8 hour (95% CI: 38.3–39.2 hour). These parameters were similar to estimates from IBSM studies elsewhere (0.71/day, 95% CI: 0.67–0.75/day; PMR48 26.6, 95% CI: 22.2–31.8), but significantly higher (P < 0.001) than in sporozoite studies (0.47/day, 95% CI: 0.43–0.50/day; PMR48 8.6, 95% CI: 7.3–10.1). Conclusions Parasite growth rates were similar across different IBSM studies and higher than infections induced by sporozoite.

A c c e p t e d M a n u s c r i p t 5 The PMR48 may differ between malaria-naive individuals and individuals previously exposed to malaria [16], as well as between different parasite strains. The method used to measure parasitemia [17] and the statistical model used to estimate parasite growth rate [18,19] can also substantially affect PMR48estimates. Estimating parasite growth rate accurately is In this study, we analyzed data from IBSM studies conducted at QIMR Berghofer (QIMR-B) in which subjects were inoculated with P. falciparum 3D7 under similar experimental conditions [20-32] and parasitemia quantitated by a validated quantitative PCR (qPCR) assay [33]. We estimated the parasite growth rate and parasite life-cycle of P. falciparum 3D7, to then calculate PMR48 and PMRLC. We compared these estimates with our estimates using data from IBSM studies conducted by other research groups [14,15,[34][35][36][37], from mosquito bite sporozoite studies [17,19,34,38], and from cryopreserved sporozoite studies [8,10,[39][40][41][42].

IBSM Studies from QIMR Berghofer
We analyzed data from 177 malaria-naïve healthy subjects who participated in 14 IBSM studies across 27 cohorts between 2012 and 2017 at Q-Pharm Pty Ltd (Supplementary Table   Downloaded  A c c e p t e d M a n u s c r i p t 6 1). All studies were approved by the QIMR-B human research ethics committee and all subjects provided informed consent (Supplementary Table 1). Table 1 summarizes characteristics of the QIMR-B IBSM studies analyzed. Subjects were inoculated intravenously on Day 0 with human erythrocytes infected with approximately 1800, 2300, or 2800 viable P. falciparum 3D7 parasites. Subjects were treated with an antimalarial drug on Day 7,8,or 9.

Parasite Growth Monitoring and Data Processing of IBSM Studies from QIMR-B
Parasite growth was monitored using a qPCR assay targeting the P. falciparum 18S rRNA gene using a TaqMan probe [33]. Parasitemia was monitored twice daily after subjects were qPCR-positive until time of antimalarial drug administration. All samples from a subject were analyzed in duplicate or triplicate in a single assay at the end of study. Replicates were geometrically averaged on the log10 scale. The limit of detection of the qPOthCR assay was 64 parasites/mL [33]. However, the qPCR assay frequently detected parasite densities below this value; the measured parasite densities were used in the analysis. If one parasitemia replicate was not detected, and the other replicate was positive, the replicate non-detected value was set to 1 parasite/mL to give zero on the log scale and the geometric mean of the positive replicate values and 1 was taken. Non-detected sample values across all replicates before the first positive qPCR measurement were excluded from analysis. However, if parasitemia had been detected by qPCR at previous time points, non-detected parasitemia values were set to 32 parasites/mL (half the limit of detection of the qPCR assay). Other approaches to substitute non-detected values have been reported including substitution methods [12] and modeling techniques to handle censored observations [19,43]. Processed individual parasitemia data for the 177 subjects are presented in Supplementary Table 2.

IBSM and Sporozoite Studies from Other Research Groups
We analyzed parasitemia data from IBSM and sporozoite studies conducted by other research groups. These studies used a range of methodologies, including different means of infection (IBSM, mosquito bite, or cryopreserved sporozoites), different P. falciparum strains (3D7 or NF54), and different PCR methods to estimate parasitemia: TaqMan qPCR, SYBR Green qPCR, quantitative reverse transcription PCR (qRT-PCR), or nested PCR with fluorescence quantification of band intensity ( Table 2). The methodology used to process parasitemia data is summarized in Supplementary Table 3 and Supplementary Methods.

Statistical Models
Pre-treatment parasitemia data from QIMR-B IBSM studies were used to fit log-linear and sine-wave growth models. Data were fitted overall by simultaneously analyzing data from the 177 subjects. Data were also fitted by subject (177 subjects individually) and by cohort (27 cohorts individually). Data from IBSM and sporozoite studies conducted by other research groups were only analyzed overall for all data presented in each of the original publications.
Model selection for the random effects structure in mixed-effects models was assessed using the Bayesian Information Criterion and the stability of the parameter estimates.
Log-linear parasite growth model. The log-linear model used to estimate parasite growth was: where Y = parasitemia (parasites/mL) measured by qPCR; a = y-intercept, m = parasite growth rate per day; time = days from inoculation, ranging from first positive PCR timepoint to treatment. The model was fitted by subject using simple log-linear regression, and by Downloaded from https://academic.oup.com/jid/advance-article-abstract/doi/10.1093/infdis/jiz557/5611305 by guest on 30 November 2019 A c c e p t e d M a n u s c r i p t 8 cohort and overall using a linear mixed-effects model with a random effect for estimated using maximum likelihood. The models fitted by cohort assumed that the random effect for was independent for each subject. For the model fitted overall, a nested random effect for was included to capture the variability at cohort and subjects-within-cohort levels.
Sine-wave parasite growth model. The sine-wave model used to estimate parasite growth was: where Y, a, m, and time are as above, and c = sine-wave amplitude; period = duration of the parasite life-cycle in days; k = sine-wave phase shift. This model was fitted by subject using non-linear regression, and by cohort and overall using a non-linear mixed-effects model. The same random effects described in the log-linear model were applied. Additionally, as each subject within a cohort received inoculum from the same batch, but the inoculum was not synchronized between cohorts, the model fitted overall included a random effect for the sinewave phase shift modeled at the cohort level and assumed to be independent of the random effect for a.
Model convergence and parameter estimation for the sine-wave models fitted by subject were sensitive to the starting values of the model, which were chosen as the estimated parasite growth parameters of the sine-wave model fitted by cohort, for the cohort the subject belonged to. For all models, the time variable was centered by its corresponding mean to aid model convergence, calculated either at the overall or cohort levels as per the respective analysis group (calculated at cohort level for subject level analysis).

PMR estimation
PMR48 was estimated as follows: where m is the parasite growth rate per day estimated by the log-linear or sine-wave growth models, and 2 days is the accepted parasite life-cycle of 48 h.
PMRLC was estimated as follows: where m is the parasite growth rate per day and period is the duration of the parasite lifecycle in days, both estimated by the sine-wave model.

Effect of Gender, Age, and Inoculum Size on Parasite Growth Parameters
The log-linear and sine-wave growth models described above were fitted to data from QIMR-B studies stratified by subject gender and age, and by inoculum size (Supplementary Table   1). The inoculum size of 2300 viable parasites was excluded for analysis because of its small sample size (n = 9) ( Table 1). The same random effects described above for the log-linear and sine-wave models were applied.

Statistical Analysis
Parasite growth models were fitted using the package nlme, version 3. were included in the pooled analysis (   Parasite growth and shape parameters estimated overall were similar to parameters obtained by fitting the data by subject and by cohort (Supplementary Tables 5-7). The mean parasite growth rates estimated using log-linear models were significantly different to parasite growth rates estimated using sine-wave models when fitted by subject (P < 0.001) and by cohort (P = 0.007). This difference was not significant when only subjects treated on Day 7 were included in the analysis by cohort (Supplementary Table 8). Analysis of data stratified by gender, age and inoculum size is presented in Supplementary   Table 9. The mean parasite growth rate and amplitude in female subjects were significantly higher than in male subjects when using a sine-wave model (P < 0.001), but not when using a log-linear model (P = 0.10). Subject age did not significantly affect parasite growth or shape parameters. The parasite life-cycle of the 2800 viable parasites inoculum was marginally longer than that of the 1800 viable parasites inoculum when using a sine-wave model (P = 0.033), but the opposite pattern was found for amplitude (P = 0.025).

Sporozoite Studies Conducted by Other Research Groups
Parasite growth and shape parameters estimated using log-linear and sine-wave models fitted overall for data from IBSM and sporozoite studies conducted by other research groups are presented in Table 3. parasitemia is typically measured for four to five parasite life-cycles before treatment. It is possible that the preceding liver stage of sporozoite studies more strongly initiates innate or adaptive immunity that serves to slow subsequent growth in blood stage. Estimates of parasite growth rate will be more accurate as the duration of infection increases, as more data above the limit of detection are available for analysis. In the IBSM studies reported here, all inocula were effectively identical and prepared as the product of a single mosquito infection.
The parasite growth rates estimated using log-linear models appeared to be sensitive to the phase of the growth cycle of the last observation included in analyses. Although the log-            M a n u s c r i p t 36 a Studies that used a Plasmodium 18S rRNA PCR-based methodology that had been analytically validated and compared in an EQA program were included in the meta-analysis (see Table 2  Days after inoculation Log 10 (parasites/mL)