• Korean Journal of Clinical Pharmacy
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• v.31 no.2
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• pp.125-135
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• 2021

Background: Generally, pharmacokinetics (PK) models could be stratified into two models. The compartment PK model uses the concept of simple compartmentalization to describe complex bodies, and the physiologically based pharmacokinetic (PBPK) model describes the body using multi-compartment networking. Notwithstanding sharing a theoretical background in both models, there was still a lack of knowledge to enhance compatibility in both models. Objective: This study aimed to evaluate the compatibility among PBPK, lumping model and compartment PK model with voriconazole PK case study. Methods: The number of compartments and blood flow on each tissue in the PBPK model were modified using the lumping method, considering physiological similarities. The concentration-time profiles and area under the concentration-time curve (AUC) parameters were simulated at each model, assuming taken voriconazole oral 400 mg single dose. After that, those mentioned PK parameters were compared. Results: The PK profiles and parameters of voriconazole in the three models were similar that proves their compatibility. The AUC of central compartment in the PBPK and lumping model was within a 2-fold range compared to those in the 2- compartment model. The AUC of non-eliminating tissues compartment in the PBPK model was similar to those in the lumping model. Conclusion: Regarding the compatibility of the three PK models, the utilization of the lumping method was confirmed by suggesting its reliable PK parameters with PBPK and compartment PK models. Further case studies are recommended to confirm our findings.

• Steel and Composite Structures
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• v.23 no.6
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• pp.683-690
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• 2017

In the stability and sensitivity design and diagnosis approaches, there are various methodologies available. Bond graph modeling by lumping technique is one of the universal methodologies in methodical analysis used by many researchers in all over the world. The accuracy of the method is validated in different arenas. Bond graphs are a concise, pictorial representation of the energy storage, dissipation and exchange mechanisms of interacting dynamic systems, subsystems and components. This paper proposes a bond graph modeling for distributed parameter systems using lumping techniques. Therefore, a steel frame structure was modeled to analyze employing bond graph modeling of distributed system using lumping technique. In the analytical part, the effectiveness of bond graphs to model this system is demonstrated. The dynamic responses of the system were computed and compared with those computed from the finite element analysis. The calculated maximum deflection time histories were found to be comparable. The sensitivity and the stability of the steel frame structure was also studied in different aspects. Thus, the proposed methodology, with its simplicity, can be used for stability and sensitivity analyses as alternative to finite element method for steel structures. The major value brought in the practical design is the simplicity of the proposed method for steel structures.

• Journal of Welding and Joining
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• v.11 no.3
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• pp.34-47
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• 1993

Finite element models were developed for thermal and residual stress analysis for the specific welding problems. They were used to evaluate the effectiveness of the various welding heat input models, such as ramp heat input function and lumped pass models. Through the parametric studies, thermal-mechanical modeling sensitivity to the ramp function and lumping techniques was determined by comparing the predicted results with experimental data. The kinetics for residual stress formation during welding can be developed by iteration of various proposed mechanisms in the parametric study. A ramp heat input function was developed to gradually apply the heat flux with variable amplitude to the model. This model was used to avoid numerical convergence problems due to an instantaneous increase in temperature near the fusion zone. Additionally, it enables the model to include the effect of a moving arc in a two-dimensional plane. The ramp function takes into account the variation in the out of plane energy flow in a 2-D model as the arc approaches, travels across, and departs from each plane under investigation. A lumped pass model was developed to reduce the computation cost in the analysis of multipass welds. Several weld passes were assumed as one lumped pass in this model. Recommendations were provided about ramp lumping techniques and the optimum number of weld passes that can be combined into a single thermal input.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.22 no.1
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• pp.47-57
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• 2010

Subgrid scale stabilization method is applied to Woo and Liu(2004)'s extended Boussinesq FEM numerical model to eliminate the 2dx wiggles. In order to optimize the computational efficiency, Hessian operator is introduced and the matrix of velocity vector is combined to one matrix for solving matrix equations. The mass lumping technique is also applied to the matrix equations of auxiliary variables. The newly developed code is applied to simulate Vincent and Briggs(1989)' wave transformation experiments and the results show that the numerical solution is almost wiggle-free and it matches very well with experimental data. Due to improvement of computational efficiency and wiggle reduction, it is plausible to apply this model to a realistic problem such as harbor oscillation problems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.3
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• pp.243-259
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• 2016

The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.21 no.2
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• pp.108-116
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• 2009

The present study introduces a Legendre interpolation function which is capable of analyzing wave transformation effectively in a finite element method. A Lagrangian interpolation function has been mostly used for a finite element method with a higher-order interpolation function. Although this function has an advantage of giving an accurate result with less number of elements, simulation time increases. Calculation time can be reduced by mass lumping, whereas the accuracy of solution is lowered. In this study, we introduce a modified Lagrangian interpolation function, Legendre cardinal interpolation, which can reduce simulation time with keeping up favorable accuracy. Through various numerical simulations using a Boussinesq equations model, the superiority of the Legendre cardinal interpolation function to a Lagrangian interpolation function was shown.

• KSBB Journal
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• v.14 no.5
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• pp.550-560
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• 1999

There have been many research efforts on biofilter modeling including Ottengraf et al. who derived a model equation for the concentration profile of pollutants(e.g., VOCs) in the biolayer and solved their outlet concentration of the waste gas stream through biofilter. However, for most of research works done so far, the effects to explain the effect of adsorption of organic particles to medium(i.e., adsorbent) have been ignored. In this work biofilter modeling accompanying process lumping has been proposed and the theoretical effect of adsorption property of the medium, on the biofilter performance of eliminating organic components in waste gas stream, is intensively discussed.

• Journal of the military operations research society of Korea
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• v.11 no.1
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• pp.111-129
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• 1985

Markov chains with large transition probability matrices occur in many applications such as manpowr models. Under certain conditions the state space of a stationary discrete parameter finite Markov chain may be partitioned into subsets, each of which may be treated as a single state of a smaller chain that retains the Markov property. Such a chain is said to be 'lumpable' and the resulting lumped chain is a special case of more general functions of Markov chains. There are several reasons why one might wish to lump. First, there may be analytical benefits, including relative simplicity of the reduced model and development of a new model which inherits known or assumed strong properties of the original model (the Markov property). Second, there may be statistical benefits, such as increased robustness of the smaller chain as well as improved estimates of transition probabilities. Finally, the identification of lumps may provide new insights about the process under investigation.

• Korean Chemical Engineering Research
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• v.50 no.1
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• pp.155-161
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• 2012

A dynamic biofilter model was suggested to integrate the effect of biofilter-medium adsorption capacity on the removal efficiency of volatile organic compound (VOC) contained in waste air. In particular, the suggested biofilter model is composed of four components such as biofilm, gas phase, sorption volume and adsorption phase and is capable of predicting the unsteady behavior of biofilter-operation. The process-lumping model previously suggested was limited in the application for the treatment of waste air since it was derived under the assumption that the adsorbed amount of VOC equilibrated with biofilter-media would be proportional to the concentration of dissolved VOC in the sorption volume of biofilter-media. Therefore a Freundlich adsorption isotherm was integrated into a robust biofilter process-lumping model applicable to a wide range of VOC concentration. The values of model parameters related to biofilter-medium adsorption were obtained from the dynamic adsorption column experiments in the preceding article and literature survey. Furthermore a separate biofilter experiment was conducted to treat waste air containing ethanol and the experimental result was compared with the model predictions with various values of Thiele modulus (${\phi}$). The obtained value of Thiele modulus (${\phi}$) was close to 0.03.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.2043-2047
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• 2003

The distributions of blood pressure, blood flow, and blow volume in the left common artery (LCCA) were determined using the lumping parameter method. In order to develop a mathematical model for microcirculation in LCCA, the present study adopted preexisted set of measured morphological data on anatomy, mechanical properties of the coronary vessels, viscosity of blood, the basic laws of physics, and the appropriate boundary condition. Pressures and volumes of blood and flow resistance were expressed in terms of electrical voltages, current, and resistances, respectively, in the electrical analog model. The results of two mathematical models, symmetrical and asymmetrical models, were compared with other investigator's data. The present results were in good agreement with previous studies. It was found that the mean pressure profiles were similar in both models.