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• W2998274393 abstract "Mathematical models are increasingly applied to characterize pathogen dynamics, to optimize dosage of antimicrobials and in translation from preclinical to clinical systems. While pharmacokinetic (PK) model building is conducted similarly regardless of pathogen, pharmacodynamic (PD) models for viruses and bacteria have been developed much in parallel. Models of bacteria dynamics have been established based on in vitro time kill data to gain translational value over single observation time point evaluations, empirical MIC-based indices, to support identification of optimal treatment regimens (dose, combination, duration). In contrast, viral dynamic models have put more focus on host–pathogen interactions. Such models were initially established to characterize human immunodeficiency virus (HIV) viral load during treatment, and showed that HIV was characterized by a high turnover rate and a short half-life in blood [[1]Perelson A.S. Ribeiro R.M. Introduction to modeling viral infections and immunity.Immunol Rev. 2018; 285: 5-8Crossref PubMed Scopus (15) Google Scholar]. These findings were key to change treatment paradigm towards ‘hit HIV, early and hard’, with the goal to minimize immune exhaustion and the risk to acquire deleterious mutations caused by the intense replication. The concepts developed in HIV modelling were later applied to other chronic (hepatitis C (HCV)) and acute (influenza) viral infections. Similarly, front load dosing to reduce the risk for emergence of resistance has been suggested based on bacterial infection models [[2]Bulitta J.B. Okusanya O.O. Forrest A. Bhavnani S.M. Clark K. Still J.G. et al.Population pharmacokinetics of fusidic acid: rationale for front-loaded dosing regimens due to autoinhibition of clearance.Antimicrob Agents Chemother. 2013; 57: 498-507Crossref PubMed Scopus (32) Google Scholar], but model complexity has been limited by the difficulty to measure bacterial kinetics in vivo, and the sparse information on bacteria–host interactions. The goal of this commentary is to highlight key aspects of bacteria and virus modelling and to emphasize what can be learnt from each other. We will here focus on acute infections, and we kindly refer to comprehensive reviews for more detailed aspects of modelling [[1]Perelson A.S. Ribeiro R.M. Introduction to modeling viral infections and immunity.Immunol Rev. 2018; 285: 5-8Crossref PubMed Scopus (15) Google Scholar,[3]Nielsen E.I. Friberg L.E. Pharmacokinetic-pharmacodynamic modeling of antibacterial drugs.Pharmacol Rev. 2013; 65: 1053-1090Crossref PubMed Scopus (210) Google Scholar]. Basic models rely on two main hypotheses: (1) pathogen and resources evolve in a single well-mixed environment and (2) pathogen replication is limited by the availability of host resources. For viral infections, the rate of encounter depends on both the number of target cells, and the number of free virus, and both vary over time (Fig. 1A). In the first days of infection, virus will grow exponentially and, at viral peak, target cells are largely depleted, leading to a phase of virus decline with a rate that reflects the progressive loss of infected cells caused by cure or death. This ‘target cell limited model’ has been successfully applied to influenza but also emerging viruses [[1]Perelson A.S. Ribeiro R.M. Introduction to modeling viral infections and immunity.Immunol Rev. 2018; 285: 5-8Crossref PubMed Scopus (15) Google Scholar]. Extracellular infections have been in focus for models describing bacteria dynamics. The initial bacterial growth is typically exponential. There is however also self-limiting growth, primarily due to lack of space in the studied system, which has been described by logistic growth models, or by more mechanistic approaches, e.g. with a growing and a resting state representing reduced replication when bacteria are present at high concentrations [[3]Nielsen E.I. Friberg L.E. Pharmacokinetic-pharmacodynamic modeling of antibacterial drugs.Pharmacol Rev. 2013; 65: 1053-1090Crossref PubMed Scopus (210) Google Scholar] (Figs. 1B–D). The latter component enables a so-called inoculum effect to be described (discussed below). When expanding into intracellular bacterial infections, model structures considering the target cells, such as those applied for viral dynamics, should be considered. Gaining a quantitative understanding of the immune response is difficult due to the short time scale of these infections, as well as by the natural complexity and intersubject variability of the immune system. It is therefore particularly crucial that experimentalists and modellers work together to design experiments that can leverage quantitative information. Various experiments have been conducted in animal models where viral dynamics was scrutinized across changes in experimental conditions, such as inoculum size, treatment regimen, multiple viral challenges, and immunologically modified animals. These rich data allowed one to elaborate models integrating key components of the immune response and to fit them to data to tease out the major mechanisms involved in pathogen control (e.g. neutrophils, cytokines, CD8+ T-cells, antibodies) [[4]Dobrovolny H.M. Reddy M.B. Kamal M.A. Rayner C.R. Beauchemin C.A. Assessing mathematical models of influenza infections using features of the immune response.PloS One. 2013; 8e57088Crossref PubMed Scopus (76) Google Scholar,[5]Madelain V. Baize S. Jacquot F. Reynard S. Fizet A. Barron S. et al.Ebola viral dynamics in nonhuman primates provides insights into virus immuno-pathogenesis and antiviral strategies.Nat Commun. 2018; 9: 4013Crossref PubMed Scopus (42) Google Scholar]. Corresponding data for bacterial infections are scarce, i.e. most experiments are performed in neutropenic mice, resulting in only few studies describing the impact of immune cells, e.g. neutrophils, on bacterial infections [[3]Nielsen E.I. Friberg L.E. Pharmacokinetic-pharmacodynamic modeling of antibacterial drugs.Pharmacol Rev. 2013; 65: 1053-1090Crossref PubMed Scopus (210) Google Scholar]. Antibiotics typically enhance the bacterial killing where the Emax parameter describes the maximum killing rate (i.e. not the maximum effect observed in a system). The bacterial density can have a large impact on the killing rate of antibiotics with a less than proportional kill at bacteria densities >107 CFU/mL [[3]Nielsen E.I. Friberg L.E. Pharmacokinetic-pharmacodynamic modeling of antibacterial drugs.Pharmacol Rev. 2013; 65: 1053-1090Crossref PubMed Scopus (210) Google Scholar]. Models including a compartment of non-growing, non-susceptible resting or persistent bacteria (Fig. 1D) takes this aspect into account, where the transfer from the growing, susceptible state depend on the bacteria population size. A fast treatment initiation is consequently indicated for efficient antibiotic therapy, as predicted from PKPD models where expected concentration-time profiles in patients are driving the bacterial killing. Antivirals typically block viral production or de novo infection, and thus their effects are also more dramatic when they are given before susceptible cells are depleted (i.e. peak viremia). In chronic viral infections, drug efficacy needs to be high (typically >90%) to drive virus to extinction and to compensate for the slow rate of elimination of infected cells and/or the constant replenishment of target cells (Fig. 2A). In acute infections, the immune response, when fully mounted, is capable of clearing the infection. Therefore, antiviral treatment can be beneficial even if it does not fully block viral infection, as long as it can reduce viraemia to such extent that clinical symptoms and/or the risk of transmission are reduced (Fig. 2B). For instance, in macaques treated with favipiravir and subsequently infected with Ebola virus, 2 days later a ~50% blockage of viral production was sufficient to reduce peak viraemia by 2–3 logs (Fig. 2B), which led to reduced cytokine inflammation and an increased survival [[5]Madelain V. Baize S. Jacquot F. Reynard S. Fizet A. Barron S. et al.Ebola viral dynamics in nonhuman primates provides insights into virus immuno-pathogenesis and antiviral strategies.Nat Commun. 2018; 9: 4013Crossref PubMed Scopus (42) Google Scholar]. While modelling resistance has played a great role in optimizing antiviral treatments against HIV and HCV (see more examples in [[1]Perelson A.S. Ribeiro R.M. Introduction to modeling viral infections and immunity.Immunol Rev. 2018; 285: 5-8Crossref PubMed Scopus (15) Google Scholar]), it has been much more scarcely used for acute viral infections for which fewer data are available and most efforts have relied on in vitro or simulation data [[6]Canini L. Conway J.M. Perelson A.S. Carrat F. Impact of different oseltamivir regimens on treating influenza A virus infection and resistance emergence: insights from a modelling study.PLoS Comput Biol. 2014; 10e1003568Crossref PubMed Scopus (50) Google Scholar]. On the other hand, modelling activities for bacteria have often emphasized this aspect, motivated by the fact that bacterial resistance to antibiotics is a major threat to public health. Models are developed to explore if treatments can overcome existing resistance, i.e. clear bacteria with an elevated MIC, or to characterize the emergence of resistance observed in in vitro time-kill systems. Rapid (within 24 hr) emergence could be because of a heterogeneous bacteria population in the infectious inoculum, where the more resistant bacteria are selected under antibiotic pressure, or that bacteria develop tolerance upon antibiotic exposure (adaptive resistance). Genetic studies may clarify on the most likely mechanism, although there are experimental challenges, given that bacteria can rapidly change/revert the genotype and phenotype when exposed to a new experimental environment. Moreover, given that the immune system is likely to clear bacteria irrespective of their MIC, and resistance emergence rates may differ in the microenvironment of a host infection, both qualitative and quantitative aspects of resistance emergence need to be better understood to improve translation from in vitro to clinical systems. Anyhow, the ‘hit hard paradigm’ is likely to also be one of the most important success factors to clear bacterial infections [[2]Bulitta J.B. Okusanya O.O. Forrest A. Bhavnani S.M. Clark K. Still J.G. et al.Population pharmacokinetics of fusidic acid: rationale for front-loaded dosing regimens due to autoinhibition of clearance.Antimicrob Agents Chemother. 2013; 57: 498-507Crossref PubMed Scopus (32) Google Scholar]. Antimicrobial drug combinations are frequently adopted to overcome existing resistance and/or to minimize the risk of resistance emergence during therapy. Modelling can be particularly useful to identify the most promising combinations, given that the number of possible scenarios to explore experimentally easily become unfeasible, and the impact of various dosing regimens, resulting in various concentration-time profiles, can be explored [[7]Brill M.J. Kristoffersson A.N. Zhao C. Nielsen E.I. Friberg L.E. Semi-mechanistic pharmacokinetic–pharmacodynamic modelling of antibiotic drug combinations.Clin Microbiol Infect. 2018; 24: 697-706Abstract Full Text Full Text PDF PubMed Scopus (29) Google Scholar]. Such dynamic characterizations of interactions to define the level of synergy typically relies on in vitro experiments, with a large range of concentrations, that go beyond a simple determination of MIC or IC50 [[8]Koizumi Y. Ohashi H. Nakajima S. Tanaka Y. Wakita T. Perelson A.S. et al.Quantifying antiviral activity optimizes drug combinations against hepatitis C virus infection.Proc Natl Acad Sci. 2017; : 201610197Google Scholar,[9]Wicha S.G. Chen C. Clewe O. Simonsson U.S. A general pharmacodynamic interaction model identifies perpetrators and victims in drug interactions.Nat Commun. 2017; 8: 2129Crossref PubMed Scopus (44) Google Scholar]. We believe that modelling can evolve into the key approach for translation from preclinical infection systems to patient outcomes, and will progress to further support study design and optimize clinical usage by considering patient's individual characteristics. In that perspective it is crucial to consider the dynamics and time courses of infection and efficacy and move away from summary metrics when developing treatments, especially when translating from in vitro to in vivo to patients. In the future, the incorporation of growth characteristics at infection site, impact of the immune system, and clinical aspects of the infection, will be key to improve the predictive ability and translational relevance of these models. Moreover, because pathogens may be localized in several tissues or organs, models that can consider the concentration-time profile at different infectious sites, i.e. physiology-based pharmacokinetic (PBPK) models, may become an important asset for development of antimicrobial therapies [[10]Sadiq M.W. Nielsen E.I. Khachman D. Conil J.-M. Georges B. Houin G. et al.A whole-body physiologically based pharmacokinetic (WB-PBPK) model of ciprofloxacin: a step towards predicting bacterial killing at sites of infection.J Pharmacokinet Pharmacodyn. 2017; 44: 69-79Crossref PubMed Scopus (28) Google Scholar]. In that perspective, more collaborations between modelers focusing on mechanistic detail (systems), PBPK, data-driven approaches (pharmacometrics) but also disease transmission at the epidemiological level, will be essential to bridge in vitro and in vivo experiments and to accelerate the development of relevant antimicrobial strategies against emerging pathogens. Drs Friberg and Guedj have nothing to disclose in relation to this manuscript. No external funding was received for this commentary. The two authors contributed equally to this work. Both drafted the manuscript and accepted the final version of the manuscript." @default.
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• W2998274393 title "Acute bacterial or viral infection—What's the difference? A perspective from PKPD modellers" @default.
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