Mechanistic Mathematical Models as a Basis for Digital Twins

Blockchain-secure patient Digital Twin in healthcare using smart contracts

Modern healthcare has a sharp focus on data aggregation and processing technologies. Consequently, from a data perspective, a patient may be regarded as a timestamped list of medical conditions and their corresponding corrective interventions. Technologies to securely aggregate and access data for individual patients in the quest for precision medicine have led to the adoption of Digital Twins in healthcare. Digital Twins are used in manufacturing and engineering to produce digital models of physical objects that capture the essence of device operation to enable and drive optimization. Thus, a patient's Digital Twin can significantly improve health data sharing. However, creating the Digital Twin from multiple data sources, such as the patient's electronic medical records (EMR) and personal health records (PHR) from wearable devices, presents some risks to the security of the model and the patient. The constituent data for the Digital Twin should be accessible only with permission from relevant entities and thus requires authentication, privacy, and provable provenance. This paper proposes a blockchain-secure patient Digital Twin that relies on smart contracts to automate the updating and communication processes that maintain the Digital Twin. The smart contracts govern the response the Digital Twin provides when queried, based on policies created for each patient. We highlight four research points: access control, interaction, privacy, and security of the Digital Twin and we evaluate the Digital Twin in terms of latency in the network, smart contract execution times, and data storage costs.

How Not to Make the Joint Extended Kalman Filter Fail with Unstructured Mechanistic Models

The unstructured mechanistic model (UMM) allows for modeling the macro-scale of a phenomenon without known mechanisms. This is extremely useful in biomanufacturing because using the UMM for the joint estimation of states and parameters with an extended Kalman filter (JEKF) can enable the real-time monitoring of bioprocesses with unknown mechanisms. However, the UMM commonly used in biomanufacturing contains ordinary differential equations (ODEs) with unshared parameters, weak variables, and weak terms. When such a UMM is coupled with an initial state error covariance matrix P(t=0) and a process error covariance matrix Q with uncorrelated elements, along with just one measured state variable, the joint extended Kalman filter (JEKF) fails to estimate the unshared parameters and state simultaneously. This is because the Kalman gain corresponding to the unshared parameter remains constant and equal to zero. In this work, we formally describe this failure case, present the proof of JEKF failure, and propose an approach called SANTO to side-step this failure case. The SANTO approach consists of adding a quantity to the state error covariance between the measured state variable and unshared parameter in the initial P(t = 0) of the matrix Ricatti differential equation to compute the predicted error covariance matrix of the state and prevent the Kalman gain from being zero. Our empirical evaluations using synthetic and real datasets reveal significant improvements: SANTO achieved a reduction in root-mean-square percentage error (RMSPE) of up to approximately 17% compared to the classical JEKF, indicating a substantial enhancement in estimation accuracy.

Hybrid modeling in bioprocess dynamics: Structural variabilities, implementation strategies, and practical challenges

Hybrid modeling, with an appropriate blend of the mechanistic and data-driven framework, is increasingly being adopted in bioprocess modeling, model-based experimental design (digital-twin), identification of critical process parameters, and optimization. However, the development of a hybrid model from experimental data is an inherently complex workflow, involving designed experiments, selection of the data-driven process, identification of model parameters, assessment fitness, and generalization capability. Depending on the complexity of the process system and purpose, each piece of these modules can flexibly be incorporated into the puzzle. However, this extra flexibility can be a cause of concern to trace an "optimal" model structure. In this paper, the development of hybrid models in a common bioprocess system, selection of data-driven components and their mapping to states, choice of parameter identification techniques, and model quality assurance are revisited. The challenges associated with hybrid-model development, and corrective actions have also been reviewed. The review also suggests the lack of data, and code sharing in communal repositories can be a hurdle in the exploration, and expansion of those tools in a bioprocess system.

The use of predictive models to develop chromatography-based purification processes

Chromatography is the workhorse of biopharmaceutical downstream processing because it can selectively enrich a target product while removing impurities from complex feed streams. This is achieved by exploiting differences in molecular properties, such as size, charge and hydrophobicity (alone or in different combinations). Accordingly, many parameters must be tested during process development in order to maximize product purity and recovery, including resin and ligand types, conductivity, pH, gradient profiles, and the sequence of separation operations. The number of possible experimental conditions quickly becomes unmanageable. Although the range of suitable conditions can be narrowed based on experience, the time and cost of the work remain high even when using high-throughput laboratory automation. In contrast, chromatography modeling using inexpensive, parallelized computer hardware can provide expert knowledge, predicting conditions that achieve high purity and efficient recovery. The prediction of suitable conditions in silico reduces the number of empirical tests required and provides in-depth process understanding, which is recommended by regulatory authorities. In this article, we discuss the benefits and specific challenges of chromatography modeling. We describe the experimental characterization of chromatography devices and settings prior to modeling, such as the determination of column porosity. We also consider the challenges that must be overcome when models are set up and calibrated, including the cross-validation and verification of data-driven and hybrid (combined data-driven and mechanistic) models. This review will therefore support researchers intending to establish a chromatography modeling workflow in their laboratory.

Introduction of a new flexible human resources planning system based on digital twin approach: A case study

Digital twin technology has become one of the key directions of intelligent manufacturing with a strong relationship to product lifecycle management. It contributes to increasing efficiency and flexibility in solving highly complex problems in constantly changing conditions. However, many circumstances make the real implementation of effective scenarios generated by simulation software tools difficult. One of them are rigid working schedules that complicate flexible human resources planning in accordance with optimal production and logistics plans. This article aims to examine the role of the digital factory twin in advanced human resources planning. Using the case study method, a solution for better coordination of internal logistics processes and utilization of logistics staff based on discrete-event simulation is presented. Several scenarios were tested and results showed the inevitability of using flexible working schedules for maximum utilization of logistics staff. The purpose of this study is not only to show one special case of one company, but to emphasize the potential of these software tools to achieve long-term synergies in coordinating logistics, production and human resources management activities. As a result of this study, an extended physical-digitalphysical loop model is presented. This extension consists in adding the second loop including communication with HR portal.

Development of a Digital Twin for Enzymatic Hydrolysis Processes

Enzymatic hydrolysis processes can be used to produce organic nutrient media from renewable raw materials. However, many of these processes are not optimally designed, so expensive enzymes and substrates are wasted. Mathematical models and Digital Twins (DTs) are powerful tools, which can be used to optimize bioprocesses and, thus, increase the yield of the desired products. Individual enzymatic hydrolysis processes have already been modeled, but models for the combined starch hydrolysis and proteolysis, or DTs, are not available yet. Therefore, an easily adaptable, dynamic, and mechanistic mathematical model representing the kinetics of the enzymatic hydrolysis process of the combined starch hydrolysis and proteolysis was developed and parameterized using experimental data. The model can simulate the starch hydrolysis process with an agreement of over 90% and the proteolysis process with an agreement of over 85%. Subsequently, this model was implemented into an existing DT of a 20 L stirred tank reactor (STR). Since the DT cannot only map the kinetics of the enzymatic process, but also the STR with the associated periphery (pumps, heating jacket, etc.), it is ideally suited for future process control strategy development and thus for the optimization of enzymatic hydrolysis processes.

Generic and specific recurrent neural network models: Applications for large and small scale biopharmaceutical upstream processes

The calculation of temporally varying upstream process outcomes is a challenging task. Over the last years, several parametric, semi-parametric as well as non-parametric approaches were developed to provide reliable estimates for key process parameters. We present generic and product-specific recurrent neural network (RNN) models for the computation and study of growth and metabolite-related upstream process parameters as well as their temporal evolution. Our approach can be used for the control and study of single product-specific large-scale manufacturing runs as well as generic small-scale evaluations for combined processes and products at development stage. The computational results for the product titer as well as various major upstream outcomes in addition to relevant process parameters show a high degree of accuracy when compared to experimental data and, accordingly, a reasonable predictive capability of the RNN models. The calculated values for the root-mean squared errors of prediction are significantly smaller than the experimental standard deviation for the considered process run ensembles, which highlights the broad applicability of our approach. As a specific benefit for platform processes, the generic RNN model is also used to simulate process outcomes for different temperatures in good agreement with experimental results. The high level of accuracy and the straightforward usage of the approach without sophisticated parameterization and recalibration procedures highlight the benefits of the RNN models, which can be regarded as promising alternatives to existing parametric and semi-parametric methods.

Modeling and Use of Inter-Criteria Decision Analysis for Selecting Growth Rate Models for Batch Cultivation of Yeast Kluyveromyces marxianus var. lactis MC 5

Ten unstructured models of Monod, Mink, Tessier, Moser, Aiba, Andrews, Haldane, Luong, Edward, and Han-Levenspiel are considered in this paper to explain the kinetics of cell growth for batch cultivation of the yeast Kluyweromyces marxianus var. lactis MC 5. For the first time, two independent kinetic models are used to model the process for the two basic substrates—lactose and oxygen. The selection of the most appropriate growth rate models has been made through a new multi-criteria decision-making approach called the Inter-Criteria Decision Analysis (ICDA) method. The application of ICDA to the growth rate of lactose and oxygen alone has shown that there have been many correlations between the studied models. Thus, the models for the growth rate, depending only on lactose, are reduced to one—Monod model and there are two models—Monod and Mink—depending on oxygen only. Separate kinetic process models have been developed for the combination of Monod–Monod and Monod–Mink models. For the first time, in addition to the multiplicative form, the additive form of a specific growth rate has been studied. The comparison of the obtained results has shown that the additive form has shown better results than the multiplicative one. For this reason, the additive form of the Monod–Monod model will be used to model the process.

A Digital Twins Machine Learning Model for Forecasting Disease Progression in Stroke Patients

Background: Machine learning methods have been developed to predict the likelihood of a given event or classify patients into two or more diagnostic categories. Digital twin models, which forecast entire trajectories of patient health data, have potential applications in clinical trials and patient management. Methods: In this study, we apply a digital twin model based on a variational autoencoder to a population of patients who went on to experience an ischemic stroke. The digital twin’s ability to model patient clinical features was assessed with regard to its ability to forecast clinical measurement trajectories leading up to the onset of the acute medical event and beyond using International Classification of Diseases (ICD) codes for ischemic stroke and lab values as inputs. Results: The simulated patient trajectories were virtually indistinguishable from real patient data, with similar feature means, standard deviations, inter-feature correlations, and covariance structures on a withheld test set. A logistic regression adversary model was unable to distinguish between the real and simulated data area under the receiver operating characteristic (ROC) curve (AUCadversary = 0.51). Conclusion: Through accurate projection of patient trajectories, this model may help inform clinical decision making or provide virtual control arms for efficient clinical trials.

Rational Design Method Based on Techno-Economic Principles for Integration of Organic/Organic Pervaporation with Lipase Catalyzed Transesterification

An engineering foundation is developed in this manuscript to allow the rational design of enzymatic transesterifications integrated with organic–organic pervaporation for the removal of methanol. In the first part, enzyme kinetics are elucidated for the solventless transesterification of two monoterpene alcohols with methyl acetate catalyzed by Novozym 435. Nonlinear regression revealed that three parameters (enzyme loading, forward and backward second-order reaction rate) sufficed to describe the entire conversion as a function of time. In the second part, a mathematical model for acetate ester production, integrated with organic–organic pervaporation, was developed based on a set of ordinary differential equations. To this end, empirical formulae for the pervaporation performance (of a PERVAP 2255-30 membrane and a standard HybSi^® membrane) were established, relating methyl acetate and methanol flux to the methanol concentration in the reactor. The resulting digital twin, “PervApp”, allows us to study the influence of the key design parameters “enzyme loading” and “membrane surface” on, e.g., catalyst productivity. Finally, a techno-economic assessment is made for an annual production of 100 tons of geranyl acetate. The described methodology allows producers to shift from laborious, expensive and often disappointing trial-and-error approaches to the rational design of such integrated units.

Downstream processing for influenza vaccines and candidates: An update

Seasonal and pandemic influenza outbreaks present severe health and economic burdens. To overcome limitations on influenza vaccines' availability and effectiveness, researchers chase universal vaccines providing broad, long-lasting protection against multiple influenza subtypes, and including pandemic ones. Novel influenza vaccine designs are under development, in clinical trials, or reaching the market, namely inactivated, or live-attenuated virus, virus-like particles, or recombinant antigens, searching for improved effectiveness; all these bring downstream processing (DSP) new challenges. Having to deal with new influenza strains, including pandemics, requires shorter development time, driving the development of faster bioprocesses. To cope with better upstream processes, new regulatory demands for quality and safety, and cost reduction requirements, new unit operations and integrated processes are increasing DSP efficiency for novel vaccine formats. This review covers recent advances in DSP strategies of different influenza vaccine formats. Focus is given to the improvements on relevant state-of-the-art unit operations, from harvest and clarification to purification steps, ending with sterile filtration and formulation. The development of more efficient unit operations to cope with biophysical properties of the new candidates is discussed: emphasis is given to the design of new stationary phases, 3D printing approaches, and continuous processing tools, such as continuous chromatography. The impact of the production platforms and vaccine designs on the downstream operations for the different influenza vaccine formats approved for this season are highlighted.

Digital Twins for Tissue Culture Techniques—Concepts, Expectations, and State of the Art

Techniques to provide in vitro tissue culture have undergone significant changes during the last decades, and current applications involve interactions of cells and organoids, three-dimensional cell co-cultures, and organ/body-on-chip tools. Efficient computer-aided and mathematical model-based methods are required for efficient and knowledge-driven characterization, optimization, and routine manufacturing of tissue culture systems. As an alternative to purely experimental-driven research, the usage of comprehensive mathematical models as a virtual in silico representation of the tissue culture, namely a digital twin, can be advantageous. Digital twins include the mechanistic of the biological system in the form of diverse mathematical models, which describe the interaction between tissue culture techniques and cell growth, metabolism, and the quality of the tissue. In this review, current concepts, expectations, and the state of the art of digital twins for tissue culture concepts will be highlighted. In general, DT’s can be applied along the full process chain and along the product life cycle. Due to the complexity, the focus of this review will be especially on the design, characterization, and operation of the tissue culture techniques.

Model-assisted DoE software: optimization of growth and biocatalysis in Saccharomyces cerevisiae bioprocesses

Bioprocess development and optimization are still cost- and time-intensive due to the enormous number of experiments involved. In this study, the recently introduced model-assisted Design of Experiments (mDoE) concept (Möller et al. in Bioproc Biosyst Eng 42(5):867, https://doi.org/10.1007/s00449-019-02089-7 , 2019) was extended and implemented into a software ("mDoE-toolbox") to significantly reduce the number of required cultivations. The application of the toolbox is exemplary shown in two case studies with Saccharomyces cerevisiae. In the first case study, a fed-batch process was optimized with respect to the pH value and linearly rising feeding rates of glucose and nitrogen source. Using the mDoE-toolbox, the biomass concentration was increased by 30% compared to previously performed experiments. The second case study was the whole-cell biocatalysis of ethyl acetoacetate (EAA) to (S)-ethyl-3-hydroxybutyrate (E3HB), for which the feeding rates of glucose, nitrogen source, and EAA were optimized. An increase of 80% compared to a previously performed experiment with similar initial conditions was achieved for the E3HB concentration.