Optimal control of bioproduction in the presence of population heterogeneity

Cell-to-cell variability, born of stochastic chemical kinetics, persists even in large isogenic populations. In the study of single-cell dynamics this is typically accounted for. However, on the population level this source of heterogeneity is often sidelined to avoid the inevitable complexity it introduces. The homogeneous models used instead are more tractable but risk disagreeing with their heterogeneous counterparts and may thus lead to severely suboptimal control of bioproduction. In this work, we introduce a comprehensive mathematical framework for solving bioproduction optimal control problems in the presence of heterogeneity. We study population-level models in which such heterogeneity is retained, and propose order-reduction approximation techniques. The reduced-order models take forms typical of homogeneous bioproduction models, making them a useful benchmark by which to study the importance of heterogeneity. Moreover, the derivation from the heterogeneous setting sheds light on parameter selection in ways a direct homogeneous outlook cannot, and reveals the source of approximation error. With view to optimally controlling bioproduction in microbial communities, we ask the question: when does optimising the reduced-order models produce strategies that work well in the presence of population heterogeneity? We show that, in some cases, homogeneous approximations provide remarkably accurate surrogate models. Nevertheless, we also demonstrate that this is not uniformly true: overlooking the heterogeneity can lead to significantly suboptimal control strategies. In these cases, the heterogeneous tools and perspective are crucial to optimise bioproduction.

Revisiting moment-closure methods with heterogeneous multiscale population models

Stochastic chemical kinetics at the single-cell level give rise to heterogeneous populations of cells even when all individuals are genetically identical. This heterogeneity can lead to nonuniform behaviour within populations, including different growth characteristics, cell-fate dynamics, and response to stimuli. Ultimately, these diverse behaviours lead to intricate population dynamics that are inherently multiscale: the population composition evolves based on population-level processes that interact with stochastically distributed single-cell states. Therefore, descriptions that account for this heterogeneity are essential to accurately model and control chemical processes. However, for real-world systems such models are computationally expensive to simulate, which can make optimisation problems, such as optimal control or parameter inference, prohibitively challenging. Here, we consider a class of multiscale population models that incorporate population-level mechanisms while remaining faithful to the underlying stochasticity at the single-cell level and the interplay between these two scales. To address the complexity, we study an order-reduction approximations based on the distribution moments. Since previous moment-closure work has focused on the single-cell kinetics, extending these techniques to populations models prompts us to revisit old observations as well as tackle new challenges. In this extended multiscale context, we encounter the previously established observation that the simplest closure techniques can lead to non-physical system trajectories. Despite their poor performance in some systems, we provide an example where these simple closures outperform more sophisticated closure methods in accurately, efficiently, and robustly solving the problem of optimal control of bioproduction in a microbial consortium model.

Beyond the chemical master equation: Stochastic chemical kinetics coupled with auxiliary processes

The chemical master equation and its continuum approximations are indispensable tools in the modeling of chemical reaction networks. These are routinely used to capture complex nonlinear phenomena such as multimodality as well as transient events such as first-passage times, that accurately characterise a plethora of biological and chemical processes. However, some mechanisms, such as heterogeneous cellular growth or phenotypic selection at the population level, cannot be represented by the master equation and thus have been tackled separately. In this work, we propose a unifying framework that augments the chemical master equation to capture such auxiliary dynamics, and we develop and analyse a numerical solver that accurately simulates the system dynamics. We showcase these contributions by casting a diverse array of examples from the literature within this framework and applying the solver to both match and extend previous studies. Analytical calculations performed for each example validate our numerical results and benchmark the solver implementation.

Populations of genetically identical cells tend to exhibit remarkable variability. This seemingly counter-intuitive observation has broad and fascinating implications, and has thus been a focal point of biological modeling. Many important processes act on this cellular heterogeneity at the population level, leading to an intricate coupling between the single-cell and the population-level dynamics. For example, selection pressures or growth rates may depend crucially on the expression of a particular gene (or gene family). Classical single-cell modeling approaches, such as the chemical master equation, can accurately describe the mechanisms driving cellular noise, however, they cannot encapsulate how the aforementioned auxiliary processes affect the population composition. In this work, we propose a unifying framework that extends the classical chemical master equation to faithfully capture the single-cell variability alongside the population-level evolution. We develop, analyse, and showcase an open-source numerical tool to simulate the dynamics of such populations in time. The tool is designed for straightforward use by a non-technical audience: a high-level description of the underlying chemical and population-level processes suffices to simulate complex system dynamics. Simultaneously, we retain high customisability of the underlying mathematical representation for the more advanced user. Ultimately, the unifying framework and the associated computational tool open new horizons in the study of how fundamental microscopic dynamics give rise to complex macroscopic phenomena.

Interstitial lung opacities in patients with severe COVID-19 pneumonia by bedside high-resolution ultrasound in association to CO2 retention

BACKGROUND

Coronavirus disease 2019 (COVID-19) can cause acute respiratory distress syndrome (ARDS).

OBJECTIVE

This single centre cross-section study aimed to grade the severity of pneumonia by bed-side lung ultrasound (LUS).

METHODS

A scoring system discriminates 5 levels of lung opacities: A-lines (0 points),≥3 B-line (1 point), coalescent B-lines (2 points), marked pleural disruptions (3 points), consolidations (4 points). LUS (convex 1-5 MHz probe) was performed at 6 defined regions for each hemithorax either in supine or prone position. A lung aeration score (LAS, maximum 4 points) was allocated for each patient by calculating the arithmetic mean of the examined lung areas. Score levels were correlated with ventilation parameters and laboratory markers.

RESULTS

LAS of 20 patients with ARDS reached from 2.58 to 3.83 and was highest in the lateral right lobe (Mean 3.67). Ferritin levels (Mean 1885μg/l; r = 0.467; p = 0.051) showed moderate correlation in spearman roh calculation. PaCO2 level (Mean 46.75 mmHg; r = 0.632; p = 0.005) correlated significantly with LAS, while duration of ventilation, Horovitz index, CRP, LDH and IL-6 did not.

CONCUSIONS

The proposed LAS describes severity of lung opacities in COVID-19 patients and correlates with CO2 retention in patients with ARDS.

Minimizing deformation of a thin fluid film driven by fluxes of momentum and heat

We consider a thin fluid film flowing down an inclined substrate subjected to localized external sources of momentum and heat flux that induce deformations of the fluid's free surface. This scenario is encountered in several industrial processes and of particular interest is the case where these deformations are undesirable. When the substrate is thin and the temperature along its underside is freely imposed by an active cooling mechanism, temperature gradients are generated at the fluid surface which drive a thermocapillary flow and influence the deformations. This naturally leads us to pose the optimal control problem of choosing the temperature profile that minimizes the unwanted free-surface deformations. Numerical computations reveal that the external forces generate deflections in a region near their peak beyond which all deflections are suppressed by the optimal control. Where nonzero deflections occur, the control is of bang-bang type (taking either its upper or lower bound), while the control is obtained in closed form for regions where the deflections are suppressed. Strikingly, in switching between these regions the optimal control chatters, that is, it switches infinitely many times over a finite interval. By appealing to Pontryagin's maximum principle and leveraging a symmetry embedded in the adjoint problem we uncover the underlying fractal structure of the chattering. Finally, we present practical approaches to avoid the infinite switching while retaining significantly reduced free-surface deformations.

On rapid oscillations driving biological processes at disparate timescales

We consider a generic biological process described by a dynamical system, subject to an input signal with a high-frequency periodic component. The rapid oscillations of the input signal induce inherently multiscale dynamics, motivating order-reduction techniques. It is intuitive that the system behaviour is well approximated by its response to the averaged input signal. However, changes to the high-frequency component that preserve the average signal are beyond the reach of such intuitive reasoning. In this study, we explore system response under the influence of such an input signal by exploiting the timescale separation between high-frequency input variations and system response time. Employing the asymptotic method of multiple scales, we establish that, in some circumstances, the intuitive approach is simply the leading-order asymptotic contribution. We focus on higher-order corrections that capture the response to the details of the high-frequency component beyond its average. This approach achieves a reduction in system complexity while providing valuable insight into the structure of the response to the oscillations. We develop the general theory for nonlinear systems, while highlighting the important case of systems affine in the state and the input signal, presenting examples of both discrete and continuum state spaces. Importantly, this class of systems encompasses biochemical reaction networks described by the chemical master equation and its continuum approximations. Finally, we apply the framework to a nonlinear system describing mRNA translation and protein expression previously studied in the literature. The analysis shines new light on several aspects of the system quantification and both extends and simplifies results previously obtained.

To quarantine, or not to quarantine: A theoretical framework for disease control via contact tracing

Contact tracing via smartphone applications is expected to be of major importance for maintaining control of the COVID-19 pandemic. However, viable deployment demands a minimal quarantine burden on the general public. That is, consideration must be given to unnecessary quarantining imposed by a contact tracing policy. Previous studies have modeled the role of contact tracing, but have not addressed how to balance these two competing needs. We propose a modeling framework that captures contact heterogeneity. This allows contact prioritization: contacts are only notified if they were acutely exposed to individuals who eventually tested positive. The framework thus allows us to address the delicate balance of preventing disease spread while minimizing the social and economic burdens of quarantine. This optimal contact tracing strategy is studied as a function of limitations in testing resources, partial technology adoption, and other intervention methods such as social distancing and lockdown measures. The framework is globally applicable, as the distribution describing contact heterogeneity is directly adaptable to any digital tracing implementation.

[Use of near-infrared spectroscopy for control of limb perfusion during venoarterial ECMO treatment : Application and limitations]

Patients undergoing peripheral venoarterial extracorporeal membrane oxygenation have a high risk of lower limb ischemia. In general, regular controls are carried out based on clinical and laboratory parameters in order to quickly detect and treat complications. These controls are challenging due to states of shock, nonpulsatile flow and vasopressor therapy. As additional monitoring the use of near-infrared spectroscopy (NIRS) is described in the literature as being very successful in detecting ischemia. The present article describes the use and possible limitations of NIRS for the diagnostics of peripheral ischemia.

The impact of venovenous extracorporeal membrane oxygenation on cytokine levels in patients with severe acute respiratory distress syndrome: a prospective, observational study

OBJECTIVE

The immunoinflammatory response is central to the pathogenesis of acute respiratory distress syndrome (ARDS). However, little is known how this is affected by venovenous (VV) extracorporeal membrane oxygenation (ECMO). Our objective was to investigate the factors that influence the inflammatory response of patients with ARDS undergoing VV ECMO, and to analyse the impact of this response on hospital mortality.

DESIGN AND SETTING

A prospective observational study of all consecutive patients with severe ARDS who had VV ECMO at a tertiary German ECMO centre from 2009 to 2015. Patients without complete datasets were excluded. Cytokines (interleukin [IL]6, IL8 and tissue necrosis factor [TNF]_α) and inflammatory markers (white cell count and C-reactive protein) were assessed before ECMO initiation and on Days 1, 5 and 10, before explantation and at explantation.

RESULTS

A total of 262 adult patients undergoing VV ECMO were analysed. Their median Sequential Organ Failure Assessment score was 12, PaO₂/FiO₂ ratio was 64 mmHg, and overall in-hospital mortality was 34%. Cytokine levels fell quickly within 24 hours and fell further over the first 5 days. Extra-pulmonary ARDS was associated with higher IL6 and IL8 levels compared with pulmonary ARDS. Mechanical ventilation with positive end-expiratory pressure ≥ 15 cmH₂O before ECMO was associated with higher IL6, IL8 and TNF_α levels. Driving pressures ≥ 19 cmH₂O before ECMO were associated with higher IL8 levels. Non-survivors had higher IL6 and IL8 levels for the duration of ECMO.

CONCLUSION

Cytokine levels, on average, fall rapidly after initiation of VV ECMO, which may be related to the reduction of invasiveness of mechanical ventilation. Higher cytokine levels are associated with extrapulmonary causes of ARDS, more aggressive mechanical ventilation before VV ECMO, and mortality.

Pitfalls in percutaneous ECMO cannulation

INTRODUCTION

This observational report depicts typical problems of extracorporeal membrane oxygenation cannulation from a large case series of a single center.

METHODS

We analysed our experience with 720 consecutive patients receiving veno-venous or veno-arterial extracorporeal membrane oxygenation focusing on the spectrum of complications occurring in a subset of 159 patients treated with percutaneous veno-arteria extracorporeal membrane oxygenation in our institution between January 2009 to December 2014.

RESULTS

The main problems were: vascular complications or ischemia of the corresponding extremity (leading to surgical revision in 16.9 % of patients); blood loss and/or relocation of cannulas. Hypoxia of the upper body (Harlequin syndrome) occurred in 8.8 % of patients. Cannulation failure and malfunction were infrequent. Careful insertion technique, close surveillance and monitoring are compelling.

CONCLUSIONS

As lack of experience is the trigger of many complications, adequate training of cannulation techniques is essential to minimize adverse events.

[Intensive care unit-acquired weakness in the critically ill : critical illness polyneuropathy and critical illness myopathy]

Intensive care unit-acquired weakness (ICUAW) is a severe complication in critically ill patients which has been increasingly recognized over the last two decades. By definition ICUAW is caused by distinct neuromuscular disorders, namely critical illness polyneuropathy (CIP) and critical illness myopathy (CIM). Both CIP and CIM can affect limb and respiratory muscles and thus complicate weaning from a ventilator, increase the length of stay in the intensive care unit and delay mobilization and physical rehabilitation. It is controversially discussed whether CIP and CIM are distinct entities or whether they just represent different organ manifestations with common pathomechanisms. These basic pathomechanisms, however, are complex and still not completely understood but metabolic, inflammatory and bioenergetic alterations seem to play a crucial role. In this respect several risk factors have recently been revealed: in addition to the administration of glucocorticoids and non-depolarizing muscle relaxants, sepsis and multi-organ failure per se as well as elevated levels of blood glucose and muscular immobilization have been shown to have a profound impact on the occurrence of CIP and CIM. For the diagnosis, careful physical and neurological examinations, electrophysiological testing and in rare cases nerve and muscle biopsies are recommended. Nevertheless, it appears to be difficult to clearly distinguish between CIM and CIP in a clinical setting. At present no specific therapy for these neuromuscular disorders has been established but recent data suggest that in addition to avoidance of risk factors early active mobilization of critically ill patients may be beneficial.

Prognostic value of 99m Tc leukocyte scintigraphy in diabetic pedal osteomyelitis

While leukocyte scintigraphy is accurate in detection of pedal osteomyelitis, there has been little data relating the technique to outcomes. We designed a trial to examine the prognostic value of sequential 99m Tc labeled leukocyte scans to establish the diagnosis of osteomyelitis and after three to four weeks of culture-guided antibiotic therapy. Twenty-three diabetic patients with proven pedal osteomyelitis (21/23) or persistent uptake (2/23) on the sequence of scans were studied. Five additional episodes of osteomyelitis developed in the group over the period of the study. Eleven patients demonstrated persistent uptake in the sequential scans. Nine progressed to amputation. The remaining two patients were biopsy-negative for infection, did not have cutaneous ulceration and were thought to have rapidly progressive arthropathy. Sequential leukocyte scintigraphy accurately predicts the need for amputation and can circumvent ineffective prolonged antibiotic therapy.