Neurodegenerative disorders, metabolic icebergs, and mitohormesis.

Neurodegenerative disorders are typically "split" based on their hallmark clinical, anatomical, and pathological features, but they can also be "lumped" by a shared feature of impaired mitochondrial biology. This leads us to present a scientific framework that conceptualizes Alzheimer's disease (AD), Parkinson's disease (PD), amyotrophic lateral sclerosis (ALS), and Huntington's disease (HD) as "metabolic icebergs" comprised of a tip, a bulk, and a base. The visible tip conveys the hallmark neurological symptoms, neurodegenerative regions, and neuronal protein aggregates for each disorder. The hidden bulk depicts impaired mitochondrial biology throughout the body, which is multifaceted and may be subdivided into impaired cellular metabolism, cell-specific mitotypes, and mitochondrial behaviours, functions, activities, and features. The underlying base encompasses environmental factors, especially modern industrial toxins, dietary lifestyles, and cognitive, physical, and psychosocial behaviours, but also accommodates genetic factors specific to familial forms of AD, PD, and ALS, as well as HD. Over years or decades, chronic exposure to a particular suite of environmental and genetic factors at the base elicits a trajectory of impaired mitochondrial biology that maximally impacts particular subsets of mitotypes in the bulk, which eventually surfaces as the hallmark features of a particular neurodegenerative disorder at the tip. We propose that impaired mitochondrial biology can be repaired and recalibrated by activating "mitohormesis", which is optimally achieved using strategies that facilitate a balanced oscillation between mitochondrial stressor and recovery phases. Sustainably harnessing mitohormesis may constitute a potent preventative and therapeutic measure for people at risk of, or suffering with, neurodegenerative disorders.

Prevent lumping during hot-water rehydration of lotus rhizome powder by restricted swelling treatment.

Lotus rhizome powder (LRP) tends to lump during hot-water rehydration, adversely affecting its edible quality. By utilizing a restricted swelling treatment (ST), where LRP was swollen at a temperature slightly below its onset gelatinization temperature (To), the lumping rate could be substantially reduced from 30.95% to 6.39%. This treatment induced an ordered-disordered structural transition of LRP without compromising its granule morphology and water dispersibility. This transition led to significant increases in thermal transition temperatures and a notable delay in peak pasting time by 86.6 s. These changes effectively delayed the formation of a gelatinous skin surrounding the dry granules, allowing them sufficient time to absorb water and paste completely, thereby preventing lumping. The prevention of lumping was beneficial for obtaining desired viscoelasticity of LRP paste. Conversely, ST treatments conducted at temperatures markedly deviating from To resulted in significantly higher lumping rates, underscoring the importance of carefully controlling the ST temperature.

An encompassed representation of timescale hierarchies in first-order reaction network.

Complex networks are pervasive in various fields such as chemistry, biology, and sociology. In chemistry, first-order reaction networks are represented by a set of first-order differential equations, which can be constructed from the underlying energy landscape. However, as the number of nodes increases, it becomes more challenging to understand complex kinetics across different timescales. Hence, how to construct an interpretable, coarse-graining scheme that preserves the underlying timescales of overall reactions is of crucial importance. Here, we develop a scheme to capture the underlying hierarchical subsets of nodes, and a series of coarse-grained (reduced-dimensional) rate equations between the subsets as a function of time resolution from the original reaction network. Each of the coarse-grained representations guarantees to preserve the underlying slow characteristic timescales in the original network. The crux is the construction of a lumping scheme incorporating a similarity measure in deciphering the underlying timescale hierarchy, which does not rely on the assumption of equilibrium. As an illustrative example, we apply the scheme to four-state Markovian models and Claisen rearrangement of allyl vinyl ether (AVE), and demonstrate that the reduced-dimensional representation accurately reproduces not only the slowest but also the faster timescales of overall reactions although other reduction schemes based on equilibrium assumption well reproduce the slowest timescale but fail to reproduce the second-to-fourth slowest timescales with the same accuracy. Our scheme can be applied not only to the reaction networks but also to networks in other fields, which helps us encompass their hierarchical structures of the complex kinetics over timescales.

A Nodal Immersed Finite Element-Finite Difference Method.

The immersed finite element-finite difference (IFED) method is a computational approach to modeling interactions between a fluid and an immersed structure. The IFED method uses a finite element (FE) method to approximate the stresses, forces, and structural deformations on a structural mesh and a finite difference (FD) method to approximate the momentum and enforce incompressibility of the entire fluid-structure system on a Cartesian grid. The fundamental approach used by this method follows the immersed boundary framework for modeling fluid-structure interaction (FSI), in which a force spreading operator prolongs structural forces to a Cartesian grid, and a velocity interpolation operator restricts a velocity field defined on that grid back onto the structural mesh. With an FE structural mechanics framework, force spreading first requires that the force itself be projected onto the finite element space. Similarly, velocity interpolation requires projecting velocity data onto the FE basis functions. Consequently, evaluating either coupling operator requires solving a matrix equation at every time step. Mass lumping, in which the projection matrices are replaced by diagonal approximations, has the potential to accelerate this method considerably. This paper provides both numerical and computational analyses of the effects of this replacement for evaluating the force projection and for the IFED coupling operators. Constructing the coupling operators also requires determining the locations on the structure mesh where the forces and velocities are sampled. Here we show that sampling the forces and velocities at the nodes of the structural mesh is equivalent to using lumped mass matrices in the IFED coupling operators. A key theoretical result of our analysis is that if both of these approaches are used together, the IFED method permits the use of lumped mass matrices derived from nodal quadrature rules for any standard interpolatory element. This is different from standard FE methods, which require specialized treatments to accommodate mass lumping with higher-order shape functions. Our theoretical results are confirmed by numerical benchmarks, including standard solid mechanics tests and examination of a dynamic model of a bioprosthetic heart valve.

Spectral Analysis of High Order Continuous FEM for Hyperbolic PDEs on Triangular Meshes: Influence of Approximation, Stabilization, and Time-Stepping.

In this work we study various continuous finite element discretization for two dimensional hyperbolic partial differential equations, varying the polynomial space (Lagrangian on equispaced, Lagrangian on quadrature points (Cubature) and Bernstein), the stabilization techniques (streamline-upwind Petrov-Galerkin, continuous interior penalty, orthogonal subscale stabilization) and the time discretization (Runge-Kutta (RK), strong stability preserving RK and deferred correction). This is an extension of the one dimensional study by Michel et al. (J Sci Comput 89(2):31, 2021. 10.1007/s10915-021-01632-7), whose results do not hold in multi-dimensional frameworks. The study ranks these schemes based on efficiency (most of them are mass-matrix free), stability and dispersion error, providing the best CFL and stabilization coefficients. The challenges in two-dimensions are related to the Fourier analysis. Here, we perform it on two types of periodic triangular meshes varying the angle of the advection, and we combine all the results for a general stability analysis. Furthermore, we introduce additional high order viscosity to stabilize the discontinuities, in order to show how to use these methods for tests of practical interest. All the theoretical results are thoroughly validated numerically both on linear and non-linear problems, and error-CPU time curves are provided. Our final conclusions suggest that Cubature elements combined with SSPRK and OSS stabilization is the most promising combination.

Determination of the Number of Tissue Groups of Kinetically Distinct Transit Time in Whole-Body Physiologically Based Pharmacokinetic (PBPK) Models I: Theoretical Consideration of Bottom-Up Approach of Lumping Tissues in Whole-Body PBPK.

Minimal physiologically based pharmacokinetic (mPBPK) models, consisting of system-specific (e.g., tissue volume and blood flow) and drug-related (e.g., tissue-to-plasma partition coefficient) parameters, are practically useful for pharmacokinetic analyses. However, biopharmaceutical principles were not clear on how peripheral tissues, adopted in whole-body physiologically based pharmacokinetic (WB-PBPK) models, could be kinetically consolidated into one or two tissue groups in the mPBPK models. In this theoretical examination, we studied the relationship between the progressive tissue lumping in the direction from the longest mean transit time (MTTmax) to the shorter one(s) and the slopes of the terminal (λter)/distributional phases, assuming tissues with comparable MTTs are kinetically combined. The appropriateness of lumping was ascertained by evaluating the impact of difference in tissue MTTs during the lumping on the analytical solution of WB-PBPK models. We found that the ratio of MTTmax to the mean residence time in the body, viz., Kdet, is related to the change in λter by the progressive lumping and can serve as an index for the robustness of λter. Calculations with two extreme cases revealed that, for caffeine at Kdet < 0.03, the change in λter was minimal even when all peripheral tissues were collectively lumped, whereas for artesunic acid at Kdet > 50, the tissue of MTTmax could not be kinetically combined even with the tissue having the second-longest MTT without significantly affecting λter. Therefore, we proposed Kdet as an index for the robustness of λter during tissue lumping and for the number of tissue groups with distinct transit times in WB-PBPK.

Determination of the Number of Tissue Groups of Kinetically Distinct Transit Time in Whole-Body Physiologically Based Pharmacokinetic (PBPK) Models II: Practical Application of Tissue Lumping Theories for Pharmacokinetics of Various Compounds.

In our companion paper, we described the theoretical basis for tissue lumping in whole-body physiologically based pharmacokinetic (WB-PBPK) models and found that Kdet, a coefficient for determining the number of tissue groups of distinct transit time in WB-PBPK models, was related to the fractional change in the terminal slope (FCT) when tissues were progressively lumped from the longest transit time to shorter ones. This study was conducted to identify the practical threshold of Kdet by applying the lumping theory to plasma/blood concentration-time relationships of 113 model compounds collected from the literature. We found that drugs having Kdet < 0.3 were associated with FCT < 0.1 even when all peripheral tissues were lumped, resulting in comparable plasma concentration-time profiles between one-tissue minimal PBPK (mPBPK) and WB-PBPK models. For drugs with Kdet ≥ 1, WB-PBPK profiles appeared similar with two-tissue mPBPK models by applying the rule of FCT < 0.1 for lumping slowly equilibrating tissues. The two-tissue mPBPK model also appeared appropriate in terms of concentration-time profiles for drugs with 0.3 ≤ Kdet < 1, although, some compounds (15.9% of the total cases), but not all, in this range showed a slight (maximum of 18.9% of the total AUC) deviation from WB-PBPK models, indicating that the two-tissue model, with caution, could still be used for those cases. Comparison of kinetic parameters between traditional (model-fitting) and current (theoretical calculation) mPBPK analyses revealed their significant correlations. Collectively, these observations suggest that the number of tissue groups could be determined based on the Kdet/FCT criteria, and plasma concentration-time profiles from WB-PBPK could be calculated using equations significantly less complex.

A compatibility evaluation between the physiologically based pharmacokinetic (PBPK) model and the compartmental PK model using the lumping method with real cases.

Pharmacokinetic (PK) modeling is a useful method for investigating drug absorption, distribution, metabolism, and excretion. The most commonly used mathematical models in PK modeling are the compartment model and physiologically based pharmacokinetic (PBPK) model. Although the theoretical characteristics of each model are well known, there have been few comparative studies of the compatibility of the models. Therefore, we evaluated the compatibility of PBPK and compartment models using the lumping method with 20 model compounds. The PBPK model was theoretically reduced to the lumped model using the principle of grouping tissues and organs that show similar kinetic behaviors. The area under the concentration-time curve (AUC) based on the simulated concentration and PK parameters (drug clearance [CL], central volume of distribution [Vc], peripheral volume of distribution [Vp]) in each model were compared, assuming administration to humans. The AUC and PK parameters in the PBPK model were similar to those in the lumped model within the 2-fold range for 17 of 20 model compounds (85%). In addition, the relationship of the calculated Vd/fu (volume of distribution [Vd], drug-unbound fraction [fu]) and the accuracy of AUC between the lumped model and compartment model confirmed their compatibility. Accordingly, the compatibility between PBPK and compartment models was confirmed by the lumping method. This method can be applied depending on the requirement of compatibility between the two models.

[Critical quality attribute assessment of big brand traditional Chinese medicine: quality control of Tongren Niuhuang Qingxin Pills in texture and sensory attributes].

Texture sensory attributes are the key items in quality control of Chinese medicinal honeyed pills. The purpose of this study is to develop a quality control method for assessing the texture sensory attributes of Chinese medicinal honeyed pills based on real-world Tongren Niuhuang Qingxin pilular masses and finished products. First, parameters of texture profile analysis(TPA) were optimized through single factor and central composite design(CCD) experiments to establish a detection method for texture sensory attri-butes of Tongren Niuhuang Qingxin Pills. The results showed that the established detection method was stable and reliable, with the optimal parameters set up as follows: deformation percentage of 70%, detection speed at 30 mm·min~(-1), and interval time of 15 s. Furthermore, 540 data points yielded form six texture sensory attributes of pills from 30 batches were subjected to multivariate statistical process control(MSPC) with Hotelling T~2 and squared prediction error(SPE) control charts to establish the quality control method of Tongren Niuhuang Qingxin Pills. This study is expected to provide a reference for improving the quality control system of Chinese medicinal honeyed pills.

A new hierarchical approach to multi-level model abstraction for simplifying ODE models of biological networks and a case study: The G1/S Checkpoint/DNA damage signalling pathways of mammalian cell cycle.

Model reduction is an important topic in studies of biological systems. By reducing the complexity of large models through multi-level models while keeping the essence (biological meaning) of the model, model reduction can help answer many important questions about these systems. In this paper, we present a new reduction method based on hierarchical representation and a lumping approach. We used G1/S checkpoint pathway represented in Ordinary Differential Equations (ODE) in Iwamoto et al. (2011) as a case study to present this reduction method. The approach consists of two parts; the first part represents the biological network as a hierarchy (multiple levels) based on protein binding relations, which allowed us to model the biological network at different levels of abstraction. The second part applies different levels (level 1, 2 and 3) of lumping the species together depending on the level of the hierarchy, resulting in a reduced and transformed model for each level. The model at each level is a representation of the whole system and can address questions pertinent to that level. We develop and simulate reduced models for levels-1, 2 and 3 of lumping for the G1/S checkpoint pathway and evaluate the biological plausibility of the proposed method by comparing the results with the original ODE model of Iwamoto et al. (2011). The results for continuous dynamics of the G1/S checkpoint pathway with or without DNA-damage for reduced models of level- 1, 2 and 3 of lumping are in very good agreement and consistent with the original model results and with biological findings. Therefore, the reduced models (level-1, 2 and 3) can be used to study cell cycle progression in G1 and the effects of DNA damage on it. It is suitable for reducing complex ODE biological network models while retaining accurate continuous dynamics of the system. The 3 levels of the reduced models respectively achieved 20%, 26% and 31% reduction of the base model. Moreover, the reduced model is more efficient to run (30%, 44% and 52% time reduction for the three levels) and generate solutions than the original ODE model. Simplification of complex mathematical models is possible and the proposed reduction method has the potential to make an impact across many fields of biomedical research.

Using autoimmune strategically: Diagnostic lumping, splitting, and the experience of illness.

Experience of illness and sociology of diagnosis literatures offer valuable insights into how people live with chronic illness. In this article, we argue that investigating autoimmune illnesses contributes to the sociological understanding of illness experiences and diagnosis practices. Autoimmune is a broad category of illnesses in which a person's immune system identifies healthy cells as pathological. Drawing on 45 in-depth interviews with people who live with autoimmune illnesses, this article shows how both broad diagnostic classifications (lumping) and narrow diagnostic classifications (splitting) are integral to diagnostic work and illness experiences. Combining the illness experience and sociology of diagnosis literatures, we theorize diagnosis as an iterative process in which people strategically use broad illness categories such as autoimmune in combination with specific illness categories such as multiple sclerosis a way to negotiate heterogeneity and uncertainty and to make sense of what is happening in their bodies. In this article, we argue that in an era of specialization, broad diagnostic categories can help both patients and clinicians navigate the experience of illness.

Basic, simple and extendable kinetic model of protein synthesis.

Protein synthesis is one of the most fundamental biological processes. Despite existence of multiple mathematical models of translation, surprisingly, there is no basic and simple chemical kinetic model of this process, derived directly from the detailed kinetic scheme. One of the reasons for this is that the translation process is characterized by indefinite number of states, because of the structure of the polysome. We bypass this difficulty by applying lumping of multiple states of translated mRNA into few dynamical variables and by introducing a variable describing the pool of translating ribosomes. The simplest model can be solved analytically. The simplest model can be extended, if necessary, to take into account various phenomena such as the limited amount of ribosomal units or regulation of translation by microRNA. The introduced model is more suitable to describe the protein synthesis in eukaryotes but it can be extended to prokaryotes. The model can be used as a building block for more complex models of cellular processes. We demonstrate the utility of the model in two examples. First, we determine the critical parameters of the synthesis of a single protein for the case when the ribosomal units are abundant. Second, we demonstrate intrinsic bi-stability in the dynamics of the ribosomal protein turnover and predict that a minimal number of ribosomes should pre-exists in a living cell to sustain its protein synthesis machinery, even in the absence of proliferation.

Automated proper lumping for simplification of linear physiologically based pharmacokinetic systems.

Physiologically based pharmacokinetic (PBPK) models are an important type of systems model used commonly in drug development before commencement of first-in-human studies. Due to structural complexity, these models are not easily utilised for future data-driven population pharmacokinetic (PK) analyses that require simpler models. In the current study we aimed to explore and automate methods of simplifying PBPK models using a proper lumping technique. A linear 17-state PBPK model for fentanyl was identified from the literature. Four methods were developed to search the optimal lumped model, including full enumeration (the reference method), non-adaptive random search (NARS), scree plot plus NARS, and simulated annealing (SA). For exploratory purposes, it was required that the total area under the fentanyl arterial concentration-time curve (AUC) between the lumped and original models differ by 0.002% at maximum. In full enumeration, a 4-state lumped model satisfying the exploratory criterion was found. In NARS, a lumped model with the same number of lumped states was found, requiring a large number of random samples. The scree plot provided a starting lumped model to NARS and the search completed within a short time. In SA, a 4-state lumped model was consistently delivered. In simplify an existing linear fentanyl PBPK model, SA was found to be robust and the most efficient and may be suitable for general application to other larger-scale linear systems. Ultimately, simplified PBPK systems with fundamental mechanisms may be readily used for data-driven PK analyses.

Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

Selection and Qualification of Simplified QSP Models When Using Model Order Reduction Techniques.

Quantitative systems pharmacology (QSP) models are increasingly used in drug development to provide a deep understanding of the mechanism of action of drugs and to identify appropriate disease targets. Such models are, however, not suitable for estimation purposes due to their high dimensionality. Based on any desired and specific input-output relationship, the system may be reduced to a model with fewer states and parameters. However, any simplification process will be a trade-off between model performance and complexity. In this study, we develop a weighted composite criterion which brings together the opposing indices of performance and dimensionality. The weighting factor can be determined by qualification of the simplified model based on a visual predictive check (VPC) using the precision of each parameter. The weighted criterion and model qualification techniques were illustrated with three examples: a simple compartmental pharmacokinetic model, a physiologically based pharmacokinetic (PBPK) example, and a semimechanistic model for bone mineral density. When considering the PBPK example, this automated search identified the same reduced model which had been detected in a previous report, as well as a simpler model which had not been previously identified. The simpler bone mineral density model provided an adequate description of the response even after 1 year from the initiation of treatment. The proposed criterion together with a VPC provides a natural way for model order reduction that can be fully automated and applied to multiscale models.

Lumping kinetics of ABE fermentation wastewater treatment by oleaginous yeast Trichosporon cutaneum.

Lumping kinetics models were built for the biological treatment of acetone-butanol-ethanol (ABE) fermentation wastewater by oleaginous yeast Trichosporon cutaneum with different fermentation temperatures. Compared with high temperature (33°C, 306 K) and low temperature (23°C, 296 K), medium temperature (28°C, 301 K) was beneficial for the cell growth and chemical oxygen demand (COD) degradation during the early stage of fermentation but the final yeast biomass and COD removal were influenced little. By lumping method, the materials in the bioconversion network were divided into five lumps (COD, lipid, polysaccharide, other intracellular products, other extracellular products), and the nine rate constants (k1-k9) for the models can well explain the bioconversion laws. The Gibbs free energy (G) for this bioconversion was positive, showing that it cannot happen spontaneous, but the existence of yeast can after the chemical equilibrium and make the bioconversion to be possible. Overall, the possibility of using lumping kinetics for elucidating the laws of materials conversion in the biological treatment of ABE fermentation wastewater by T. cutaneum has been initially proved and this method has great potential for further application.

A combined model reduction algorithm for controlled biochemical systems.

BACKGROUND: Systems Biology continues to produce increasingly large models of complex biochemical reaction networks. In applications requiring, for example, parameter estimation, the use of agent-based modelling approaches, or real-time simulation, this growing model complexity can present a significant hurdle. Often, however, not all portions of a model are of equal interest in a given setting. In such situations methods of model reduction offer one possible approach for addressing the issue of complexity by seeking to eliminate those portions of a pathway that can be shown to have the least effect upon the properties of interest. METHODS: In this paper a model reduction algorithm bringing together the complementary aspects of proper lumping and empirical balanced truncation is presented. Additional contributions include the development of a criterion for the selection of state-variable elimination via conservation analysis and use of an 'averaged' lumping inverse. This combined algorithm is highly automatable and of particular applicability in the context of 'controlled' biochemical networks. RESULTS: The algorithm is demonstrated here via application to two examples; an 11 dimensional model of bacterial chemotaxis in Escherichia coli and a 99 dimensional model of extracellular regulatory kinase activation (ERK) mediated via the epidermal growth factor (EGF) and nerve growth factor (NGF) receptor pathways. In the case of the chemotaxis model the algorithm was able to reduce the model to 2 state-variables producing a maximal relative error between the dynamics of the original and reduced models of only 2.8% whilst yielding a 26 fold speed up in simulation time. For the ERK activation model the algorithm was able to reduce the system to 7 state-variables, incurring a maximal relative error of 4.8%, and producing an approximately 10 fold speed up in the rate of simulation. Indices of controllability and observability are additionally developed and demonstrated throughout the paper. These provide insight into the relative importance of individual reactants in mediating a biochemical system's input-output response even for highly complex networks. CONCLUSIONS: Through application, this paper demonstrates that combined model reduction methods can produce a significant simplification of complex Systems Biology models whilst retaining a high degree of predictive accuracy. In particular, it is shown that by combining the methods of proper lumping and empirical balanced truncation it is often possible to produce more accurate reductions than can be obtained by the use of either method in isolation.

Reduction of a Whole-Body Physiologically Based Pharmacokinetic Model to Stabilise the Bayesian Analysis of Clinical Data.

Whole-body physiologically based pharmacokinetic (PBPK) models are increasingly used in drug development for their ability to predict drug concentrations in clinically relevant tissues and to extrapolate across species, experimental conditions and sub-populations. A whole-body PBPK model can be fitted to clinical data using a Bayesian population approach. However, the analysis might be time consuming and numerically unstable if prior information on the model parameters is too vague given the complexity of the system. We suggest an approach where (i) a whole-body PBPK model is formally reduced using a Bayesian proper lumping method to retain the mechanistic interpretation of the system and account for parameter uncertainty, (ii) the simplified model is fitted to clinical data using Markov Chain Monte Carlo techniques and (iii) the optimised reduced PBPK model is used for extrapolation. A previously developed 16-compartment whole-body PBPK model for mavoglurant was reduced to 7 compartments while preserving plasma concentration-time profiles (median and variance) and giving emphasis to the brain (target site) and the liver (elimination site). The reduced model was numerically more stable than the whole-body model for the Bayesian analysis of mavoglurant pharmacokinetic data in healthy adult volunteers. Finally, the reduced yet mechanistic model could easily be scaled from adults to children and predict mavoglurant pharmacokinetics in children aged from 3 to 11 years with similar performance compared with the whole-body model. This study is a first example of the practicality of formal reduction of complex mechanistic models for Bayesian inference in drug development.

Simplification of a pharmacokinetic model for red blood cell methotrexate disposition.

PURPOSE: A pharmacokinetic (PK) model is available for describing the time course of the concentrations of methotrexate (MTX or MTXGlu1) and its active polyglutamated metabolites (MTXGlu2-5) in red blood cells (RBCs). In this study, we aimed to simplify the MTX PK model and to optimise the blood sampling schedules for use in future studies. METHODS: A proper lumping technique was used to simplify the original MTX RBC PK model. The sum of predicted RBC MTXGlu3-5 concentrations in both the simplified and original models was compared. The sampling schedules for MTXGlu3-5 or all MTX polyglutamates in RBCs were optimised using the Population OPTimal design (POPT) software. RESULTS: The MTX RBC PK model was simplified into a three-state model. The maximum of the absolute value of relative difference in the sum of predicted RBC MTXGlu3-5 concentrations over time was 6.3 %. A five blood sample design was identified for estimating parameters of the simplified model. CONCLUSIONS: This study illustrates the application of model simplification processes to an existing model for MTX RBC PK. The same techniques illustrated in our study may be adopted by other studies with similar interest.