Structural and practical identifiability analysis in bioengineering: a beginner's guide.

Advancements in digital technology have brought modelling to the forefront in many disciplines from healthcare to architecture. Mathematical models, often represented using parametrised sets of ordinary differential equations, can be used to characterise different processes. To infer possible estimates for the unknown parameters, these models are usually calibrated using associated experimental data. Structural and practical identifiability analyses are a key component that should be assessed prior to parameter estimation. This is because identifiability analyses can provide insights as to whether or not a parameter can take on single, multiple, or even infinitely or countably many values which will ultimately have an impact on the reliability of the parameter estimates. Also, identifiability analyses can help to determine whether the data collected are sufficient or of good enough quality to truly estimate the parameters or if more data or even reparameterization of the model is necessary to proceed with the parameter estimation process. Thus, such analyses also provide an important role in terms of model design (structural identifiability analysis) and the collection of experimental data (practical identifiability analysis). Despite the popularity of using data to estimate the values of unknown parameters, structural and practical identifiability analyses of these models are often overlooked. Possible reasons for non-consideration of application of such analyses may be lack of awareness, accessibility, and usability issues, especially for more complicated models and methods of analysis. The aim of this study is to introduce and perform both structural and practical identifiability analyses in an accessible and informative manner via application to well established and commonly accepted bioengineering models. This will help to improve awareness of the importance of this stage of the modelling process and provide bioengineering researchers with an understanding of how to utilise the insights gained from such analyses in future model development.

Smart Sensor Control and Monitoring of an Automated Cell Expansion Process.

Immune therapy for cancer patients is a new and promising area that in the future may complement traditional chemotherapy. The cell expansion phase is a critical part of the process chain to produce a large number of high-quality, genetically modified immune cells from an initial sample from the patient. Smart sensors augment the ability of the control and monitoring system of the process to react in real-time to key control parameter variations, adapt to different patient profiles, and optimize the process. The aim of the current work is to develop and calibrate smart sensors for their deployment in a real bioreactor platform, with adaptive control and monitoring for diverse patient/donor cell profiles. A set of contrasting smart sensors has been implemented and tested on automated cell expansion batch runs, which incorporate advanced data-driven machine learning and statistical techniques to detect variations and disturbances of the key system features. Furthermore, a 'consensus' approach is applied to the six smart sensor alerts as a confidence factor which helps the human operator identify significant events that require attention. Initial results show that the smart sensors can effectively model and track the data generated by the Aglaris FACER bioreactor, anticipate events within a 30 min time window, and mitigate perturbations in order to optimize the key performance indicators of cell quantity and quality. In quantitative terms for event detection, the consensus for sensors across batch runs demonstrated good stability: the AI-based smart sensors (Fuzzy and Weighted Aggregation) gave 88% and 86% consensus, respectively, whereas the statistically based (Stability Detector and Bollinger) gave 25% and 42% consensus, respectively, the average consensus for all six being 65%. The different results reflect the different theoretical approaches. Finally, the consensus of batch runs across sensors gave even higher stability, ranging from 57% to 98% with an average consensus of 80%.

Fluctuations in T cell receptor and pMHC interactions regulate T cell activation.

Adaptive immune responses depend on interactions between T cell receptors (TCRs) and peptide major histocompatibility complex (pMHC) ligands located on the surface of T cells and antigen presenting cells (APCs), respectively. As TCRs and pMHCs are often only present at low copy numbers their interactions are inherently stochastic, yet the role of stochastic fluctuations on T cell function is unclear. Here, we introduce a minimal stochastic model of T cell activation that accounts for serial TCR-pMHC engagement, reversible TCR conformational change and TCR aggregation. Analysis of this model indicates that it is not the strength of binding between the T cell and the APC cell per se that elicits an immune response, but rather the information imparted to the T cell from the encounter, as assessed by the entropy rate of the TCR-pMHC binding dynamics. This view provides an information-theoretic interpretation of T cell activation that explains a range of experimental observations. Based on this analysis, we propose that effective T cell therapeutics may be enhanced by optimizing the inherent stochasticity of TCR-pMHC binding dynamics.

A human time dose response model for Q fever.

The causative agent of Q fever, Coxiella burnetii, has the potential to be developed for use in biological warfare and it is classified as a bioterrorism threat agent by the Centers for Disease Control and Prevention (CDC) and as a category B select agent by the National Institute of Allergy and Infectious Diseases (NIAID). In this paper we focus on the in-host properties that arise when an individual inhales a dose of C. burnetii and establish a human time-dose response model. We also propagate uncertainty throughout the model allowing us to robustly estimate key properties including the infectious dose and incubation period. Using human study data conducted in the 1950's we conclude that the dose required for a 50% probability of infection is about 15 organisms, and that one inhaled organism of C. burnetti can cause infection in 5% of the exposed population. In addition, we derive a low dose incubation period of 17.6 days and an extracellular doubling time of half a day. In conclusion this paper provides a framework for detailing the parameters and approaches that would be required for risk assessments associated with exposures to C. burnetii that might cause human infection.

A review of back-calculation techniques and their potential to inform mitigation strategies with application to non-transmissible acute infectious diseases.

Back-calculation is a process whereby generally unobservable features of an event leading to a disease outbreak can be inferred either in real-time or shortly after the end of the outbreak. These features might include the time when persons were exposed and the source of the outbreak. Such inferences are important as they can help to guide the targeting of mitigation strategies and to evaluate the potential effectiveness of such strategies. This article reviews the process of back-calculation with a particular emphasis on more recent applications concerning deliberate and naturally occurring aerosolized releases. The techniques can be broadly split into two themes: the simpler temporal models and the more sophisticated spatio-temporal models. The former require input data in the form of cases' symptom onset times, whereas the latter require additional spatial information such as the cases' home and work locations. A key aspect in the back-calculation process is the incubation period distribution, which forms the initial topic for consideration. Links between atmospheric dispersion modelling, within-host dynamics and back-calculation are outlined in detail. An example of how back-calculation can inform mitigation strategies completes the review by providing improved estimates of the duration of antibiotic prophylaxis that would be required in the response to an inhalational anthrax outbreak.

Modelling mass casualty decontamination systems informed by field exercise data.

In the event of a large-scale chemical release in the UK decontamination of ambulant casualties would be undertaken by the Fire and Rescue Service (FRS). The aim of this study was to track the movement of volunteer casualties at two mass decontamination field exercises using passive Radio Frequency Identification tags and detection mats that were placed at pre-defined locations. The exercise data were then used to inform a computer model of the FRS component of the mass decontamination process. Having removed all clothing and having showered, the re-dressing (termed re-robing) of casualties was found to be a bottleneck in the mass decontamination process during both exercises. Computer simulations showed that increasing the capacity of each lane of the re-robe section to accommodate 10 rather than five casualties would be optimal in general, but that a capacity of 15 might be required to accommodate vulnerable individuals. If the duration of the shower was decreased from three minutes to one minute then a per lane re-robe capacity of 20 might be necessary to maximise the throughput of casualties. In conclusion, one practical enhancement to the FRS response may be to provide at least one additional re-robe section per mass decontamination unit.

Modeling inhalational tularemia: deliberate release and public health response.

Two epidemic modeling studies of inhalational tularemia were identified in the published literature, both demonstrating the high number of potential casualties that could result from a deliberate aerosolized release of the causative agent in an urban setting. However, neither study analyzed the natural history of inhalational tularemia nor modeled the relative merits of different mitigation strategies. We first analyzed publicly available human/primate experimental data and reports of naturally acquired inhalational tularemia cases to better understand the epidemiology of the disease. We then simulated an aerosolized release of the causative agent, using airborne dispersion modeling to demonstrate the potential number of casualties and the extent of their spatial distribution. Finally, we developed a public health intervention model that compares 2 mitigation strategies: targeting antibiotics at symptomatic individuals with or without mass distribution of antibiotics to potentially infected individuals. An antibiotic stockpile that is sufficient to capture all areas where symptomatic individuals were infected is likely to save more lives than treating symptomatic individuals alone, providing antibiotics can be distributed rapidly and their uptake is high. However, with smaller stockpiles, a strategy of treating symptomatic individuals alone is likely to save many more lives than additional mass distribution of antibiotics to potentially infected individuals. The spatial distribution of symptomatic individuals is unlikely to coincide exactly with the path of the dispersion cloud if such individuals are infected near their work locations but then seek treatment close to their homes. The optimal mitigation strategy will depend critically on the size of the release relative to the stockpile level and the effectiveness of treatment relative to the speed at which antibiotics can be distributed.

Modeling Legionnaires' disease outbreaks: estimating the timing of an aerosolized release using symptom-onset dates.

BACKGROUND: Over the last 30 years, there have been a number of reported Legionnaires' disease outbreaks resulting from the release of causative organisms from aerosol-producing devices. METHODS: We model a Legionnaires' disease epidemic curve as the convolution of an infection-time distribution (representing the aerosolized release) and an incubation-period distribution. The model is fitted to symptom-onset data from specific outbreaks to estimate the start and end dates of the release. We also develop this retrospective "back-calculation" model into a prospective "real-time" model that can estimate the final size of an ongoing outbreak, in addition to the timing of its release. RESULTS: In the retrospective analysis, the estimated release end dates were generally earlier than reported end dates. This suggests that, in many outbreaks, the release might have already ended by the time the source was reportedly cleaned or closed. Prospective analysis showed that valid estimates of the release start date could be achieved early in the outbreak, the total number of cases could be reasonably determined shortly after the release had ended, and estimates of the release end date could be satisfactorily achieved in the latter stages of the outbreak. CONCLUSIONS: This model could be used in the course of a Legionnaires' disease outbreak to provide early estimates of the total number of cases, thus helping to inform public-health planning. Toward the end of the outbreak, estimates of the release end date could help corroborate standard epidemiologic, environmental, and microbiologic investigations that seek to identify the source.

Stamping out fires! Controlling smallpox with targeted mass vaccination.

BACKGROUND: More than 30 years have now passed since the last naturally occurring case of smallpox; however, the variola virus still exists in at least 2 locations. The possibility that any clandestine stocks could be used for bioterrorism is a continuing concern for the public health community. OBJECTIVE: . Mathematical modeling is used to assess the impact of mass vaccination following a smallpox release when either standard public health controls are failing or political/public opinion is urging more comprehensive methods. Two mass vaccination strategies are considered: a blanket nationwide campaign v. an approach targeted only at those geographic areas that experience smallpox cases. The study evaluates which intervention strategy results in the fewest combined disease and vaccine-related deaths. RESULTS: . Outbreaks that go unnoticed until up to 50 cases have occurred are optimally controlled with targeted mass vaccination of the affected administrative districts in the majority of scenarios considered. The number of people vaccinated is approximately two thirds fewer than when implementing a nationwide campaign. Similar results arise when contact tracing is either highly unsuccessful or reduced in favor of reallocating limited resources for a policy of mass vaccination. CONCLUSIONS: . Reactive nationwide mass vaccination remains a suboptimal strategy for controlling an expanding smallpox outbreak in all but the most extreme circumstances. Rather, targeted mass vaccination of affected areas is likely to result in fewer deaths. The vaccines administered are also likely to be much fewer because they would probably be distributed to a much smaller number of districts, thus relieving pressure on potentially stretched public health systems.

A plague on five of your houses--statistical re-assessment of three pneumonic plague outbreaks that occurred in Suffolk, England, between 1906 and 1918.

BACKGROUND: Plague is a re-emerging disease and its pneumonic form is a high priority bio-terrorist threat. Epidemiologists have previously analysed historical outbreaks of pneumonic plague to better understand the dynamics of infection, transmission and control. This study examines 3 relatively unknown outbreaks of pneumonic plague that occurred in Suffolk, England, during the first 2 decades of the twentieth century. METHODS: The Kolmogorov-Smirnov statistical test is used to compare the symptomatic period and the length of time between successive cases (i.e. the serial interval) with previously reported values. Consideration is also given to the case fatality ratio, the average number of secondary cases resulting from each primary case in the observed minor outbreaks (termed R(minor)), and the proportion of individuals living within an affected household that succumb to pneumonic plague via the index case (i.e. the household secondary attack rate (SAR)). RESULTS: 2 of the 14 cases survived giving a case fatality ratio of 86% (95% confidence interval (CI) = {57%, 98%}). For the 12 fatal cases, the average symptomatic period was 3.3 days (standard deviation (SD) = 1.2 days) and, for the 11 non index cases, the average serial interval was 5.8 days (SD = 2.0 days). R(minor) was calculated to be 0.9 (SD = 1.0) and, in 2 households, the SAR was approximately 14% (95% CI = {0%, 58%}) and 20% (95% CI = {1%, 72%}), respectively. CONCLUSIONS: The symptomatic period was approximately 1 day longer on average than in an earlier study but the serial interval was in close agreement with 2 previously reported values. 2 of the 3 outbreaks ended without explicit public health interventions; however, non-professional caregivers were particularly vulnerable - an important public health consideration for any future outbreak of pneumonic plague.

Re-assessment of mitigation strategies for deliberate releases of anthrax using a real-time outbreak characterization tool.

Responding rapidly and appropriately to a covert anthrax release is an important public health challenge. A methodology to assist the geographical targeting of such a response has recently been published; as have a number of independent studies that investigate mitigation strategies. Here, we review and combine some of these published techniques to more realistically assess how key aspects of the public health response might impact on the outcomes of a bioterrorist attack. We combine a within-host mathematical model with our spatial back-calculation method to investigate the effects of a number of important response variables. These include how previously reported levels of adherence with taking antibiotics might affect the total outbreak size compared to assuming full adherence. Post-exposure vaccination is also considered, both with and without the use of antibiotics. Further, we investigate a range of delays (2, 4 and 8 days) before interventions are implemented, following the last day of symptomatic onset of some number of observed initial cases (5, 10 and 15). Our analysis confirms that outbreak size is minimised by implementing prophylactic treatment after having estimated the exposed area based on 5 observed cases; however, imperfect (rather than full) adherence with antibiotics results in approximately 15% additional cases. Moreover, of those infected individuals who only partially adhere with a prophylactic course of antibiotics, 86% remain disease free; a result that holds for scenarios in which infected individuals inhale much higher doses than considered here. Increasing logistical delays have a particularly detrimental effect on lives saved with an optimal strategy of early identification and analysis. Our analysis shows that it is critical to have systems and processes in place to rapidly identify, geospatially analyse and then swiftly respond to a deliberate anthrax release.

Estimating the location and spatial extent of a covert anthrax release.

Rapidly identifying the features of a covert release of an agent such as anthrax could help to inform the planning of public health mitigation strategies. Previous studies have sought to estimate the time and size of a bioterror attack based on the symptomatic onset dates of early cases. We extend the scope of these methods by proposing a method for characterizing the time, strength, and also the location of an aerosolized pathogen release. A back-calculation method is developed allowing the characterization of the release based on the data on the first few observed cases of the subsequent outbreak, meteorological data, population densities, and data on population travel patterns. We evaluate this method on small simulated anthrax outbreaks (about 25-35 cases) and show that it could date and localize a release after a few cases have been observed, although misspecifications of the spore dispersion model, or the within-host dynamics model, on which the method relies can bias the estimates. Our method could also provide an estimate of the outbreak's geographical extent and, as a consequence, could help to identify populations at risk and, therefore, requiring prophylactic treatment. Our analysis demonstrates that while estimates based on the first ten or 15 observed cases were more accurate and less sensitive to model misspecifications than those based on five cases, overall mortality is minimized by targeting prophylactic treatment early on the basis of estimates made using data on the first five cases. The method we propose could provide early estimates of the time, strength, and location of an aerosolized anthrax release and the geographical extent of the subsequent outbreak. In addition, estimates of release features could be used to parameterize more detailed models allowing the simulation of control strategies and intervention logistics.