A one-dimensional mathematical model of collecting lymphatics coupled with an electro-fluid-mechanical contraction model and valve dynamics

We propose a one-dimensional model for collecting lymphatics coupled with a novel Electro-Fluid-Mechanical Contraction (EFMC) model for dynamical contractions, based on a modified FitzHugh–Nagumo model for action potentials. The one-dimensional model for a deformable lymphatic vessel is a nonlinear system of hyperbolic Partial Differential Equations (PDEs). The EFMC model combines the electrical activity of lymphangions (action potentials) with fluid-mechanical feedback (circumferential stretch of the lymphatic wall and wall shear stress) and lymphatic vessel wall contractions. The EFMC model is governed by four Ordinary Differential Equations (ODEs) and phenomenologically relies on: (1) environmental calcium influx, (2) stretch-activated calcium influx, and (3) contraction inhibitions induced by wall shear stresses. We carried out a stability analysis of the stationary state of the EFMC model. Contractions turn out to be triggered by the instability of the stationary state. Overall, the EFMC model allows emulating the influence of pressure and wall shear stress on the frequency of contractions observed experimentally. Lymphatic valves are modelled by extending an existing lumped-parameter model for blood vessels. Modern numerical methods are employed for the one-dimensional model (PDEs), for the EFMC model and valve dynamics (ODEs). Adopting the geometrical structure of collecting lymphatics from rat mesentery, we apply the full mathematical model to a carefully selected suite of test problems inspired by experiments. We analysed several indices of a single lymphangion for a wide range of upstream and downstream pressure combinations which included both favourable and adverse pressure gradients. The most influential model parameters were identified by performing two sensitivity analyses for favourable and adverse pressure gradients.     

Modeling simultaneous hexavalent chromium reduction and phenol degradation by a defined coculture of bacteria

Based on the kinetics of Cr(VI) reduction by Escherichia coli ATCC 33456 and phenol degradation by Pseudomonas putida DMP-1, a mathematical model is developed to describe simultaneous Cr(VI) reduction and phenol degradation in the coculture of the two species. The developed model incorporates the toxicity effects of Cr(VI) and phenol on phenol degradation and Cr(VI) reduction in the coculture. The model illustrates the inhibitory effects of phenol on Cr(VI) reduction and Cr(VI) toxicity toward phenol degradation. The model also reveals the recoveries of the activities of the repressed bacterial cells with continuous Cr(VI) reduction and phenol degradation in the coculture. The model is capable of predicting simultaneous Cr(VI) reduction and phenol degradation within a broad range of Cr(VI) and phenol concentrations and under an appropriate composition of populations. However, the model simulates lower concentrations of phenol than experimental observations once Cr(VI) is reduced to a low level (<7 mg/L). The model simulation for Cr(VI) also deviates from experimental data when P. putida is outnumbered by E. coli by a ratio of 1:5. (c) 1995 John Wiley & Sons, Inc.     

Mathematical modelling of liver regeneration after intoxication with CCl(4)

Liver regeneration is a complex process, having evolved to protect animals from the consequences of liver loss caused by food toxins. In this study, we established a mathematical spatial-temporal model of the liver lobule regenerating after CCl(4) intoxication. The aim of modelling the regeneration process by matching experimental observations with those from a mathematical model is to gain a better understanding of the process and to recognize which parameters are relevant for specific phenomena. In order to set up a realistic minimal model, we first reconstructed a schematised liver lobule after determination of: (i) the mean number of hepatocytes between the central vein and the periphery of the lobule, (ii) the mean size of the hepatocytes and (iii) the mean number of hepatocyte columns in the inner, midzonal and peripheral ring of the lobule. In a next step, we determined the time course of cell death and BrdU incorporation after intoxication of male Sprague Dawley rats with CCl(4), thereby differentiating between inner, midzonal and peripheral hepatocytes. These parameters were used to construct a model. The basic unit of this model is the individual cell. The detailed behaviour of the cells is studied, controlled by the model parameters: (1) probability of cell division at defined positions of the lobule at a given time, (2) "coordinated cell orientation", i.e., the ability of the cells to align during the regeneration process into columns towards the central vein of a liver lobule, (3) cell cycle duration, (4) the migration activity and (5) the polarity of the hepatocytes resulting in polar cell-cell adhesion between them. In a schematised lobule, the model shows that CCl(4) initially induced cell death of a pericentral ring of hepatocytes, followed by a wave of proliferation that starts in the surviving hepatocytes next to the inner ring of dead cells and continues to the peripheral hepatocytes, finally restoring the characteristic micro-architecture of the lobule in a 7-day process. This model was used to systematically analyze the influence of parameters 1-5. Interestingly, coordinated cell orientation and cell polarity were identified to be the most critical parameters. Elimination led to destruction of the characteristic micro-architecture of the lobule and to a high degree of disorder characterized by hexagonal cell structures. Our model suggests that the ability of hepatocytes to realign after cell division by a process of coordinated cell orientation (model parameter 2) in combination with cell polarity (model parameter 5) may be at least as critical as hepatocyte proliferation (model parameter 1) itself.     

A fuzzy-genetic model for estimating forces from electromyographical activity of antagonistic muscles due to planar lower arm movements: the effect of nonlinear muscle properties

The aim of this paper is to create a model for mapping the surface electromyogram (EMG) signals to the force that generated by human arm muscles. Because the parameters of each person's muscle are individual, the model of the muscle must have two characteristics: (1) The model must be adjustable for each subject. (2) The relationship between the input and output of model must be affected by the force-length and the force-velocity behaviors are proven through Hill's experiments. Hill's model is a kinematic mechanistic model with three elements, i.e. one contractile component and two nonlinear spring elements.In this research, fuzzy systems are applied to improve the muscle model. The advantages of using fuzzy system are as follows: they are robust to noise, they prove an adjustable nonlinear mapping, and are able to model the uncertainties of the muscle.Three fuzzy coefficients have been added to the relationships of force-length (active and passive) and force-velocity existing in Hill's model. Then, a genetic algorithm (GA) has been used as a biological search method that can adjust the parameters of the model in order to achieve the optimal possible fit.Finally, the accuracy of the fuzzy genetic implementation Hill-based muscle model (FGIHM) is invested as following: the FGIHM results have 12.4% RMS error (in worse case) in comparison to the experimental data recorded from three healthy male subjects. Moreover, the FGIHM active force-length relationship which is the key characteristics of muscles has been compared to virtual muscle (VM) and Zajac muscle model. The sensitivity of the FGIHM has been evaluated by adding a white noise with zero mean to the input and FGIHM has proved to have lower sensitivity to input noise than the traditional Hill's muscle model.     

Computation of a Stabilizing Set of Feedback Matrices bf a Large-scale Nonlinear Musculoskeletal Dynamic Model

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/ output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.     

Computation of a stabilizing set of feedback matrices of a large-scale nonlinear musculoskeletal dynamic model

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.     

Role of physical properties of resistance vessel wall in regulating peripheral blood flow--II. Structural and mechanical behavior

In order to examine the structural and mechanical properties of the vessel wall resistance when subjected to autoregulatory flow control, a mechanical model for the vascular wall was derived from a mathematical model. The mechanical model was an analogue model which connected in series the Maxwell model (elastic modulus: K3) with the parallel elements of Hill's model (elastic modules: K2) and Hooke's elastic model (elastic modulus: K1); it was also mathematically equivalent to the Spring model (see part I). The structural and mechanical properties of the resistance vessel wall were characterized by the three elastic moduli (K1, alpha K2 and K3) [mmHg]. The parameter alpha was a modification factor of the elastic modulus K2 given by the myogenic mechanism. After a numerical analysis of the experimental data given by the mechanical model, we confirmed that the arterial pressure range for autoregulatory flow controls shifted to the upper region with an increase of the elastic modulus K1 and the flow regulation was reduced.     

Body composition techniques and the four-compartment model in children.

The purpose of this study was to compare the accuracy, precision, and bias of fat mass (FM) as assessed by dual-energy X-ray absorptiometry (DXA), hydrostatic weighing (HW), air-displacement plethysmography (PM) using the BOD POD body composition system and total body water (TBW) against the four-compartment (4C) model in 25 children (11.4 +/- 1.4 yr). The regression between FM by the 4C model and by DXA deviated significantly from the line of identity (FM by 4C model = 0.84 x FM by DXA + 0.95 kg; R(2) = 0.95), as did the regression between FM by 4C model and by TBW (FM by 4C model = 0. 85 x FM by TBW - 0.89 kg; R(2) = 0.98). The regression between FM by the 4C model and by HW did not significantly deviate from the line of identity (FM by 4C model = 1.09 x FM by HW + 0.94 kg; R(2) = 0. 95) and neither did the regression between FM by 4C (using density assessed by PM) and by PM (FM by 4C model = 1.03 x FM by PM + 0.88; R(2) = 0.97). DXA, HW, and TBW all showed a bias in the estimate of FM, but there was no bias for PM. In conclusion, PM was the only technique that could accurately, precisely, and without bias estimate FM in 9- to 14-yr-old children.     

A community-based framework for aquatic ecosystem models

Here, we communicate a point of departure in the development of aquatic ecosystem models, namely a new community-based framework, which supports an enhanced and transparent union between the collective expertise that exists in the communities of traditional ecologists and model developers. Through a literature survey, we document the growing importance of numerical aquatic ecosystem models while also noting the difficulties, up until now, of the aquatic scientific community to make significant advances in these models during the past two decades. Through a common forum for aquatic ecosystem modellers we aim to (i) advance collaboration within the aquatic ecosystem modelling community, (ii) enable increased use of models for research, policy and ecosystem-based management, (iii) facilitate a collective framework using common (standardised) code to ensure that model development is incremental, (iv) increase the transparency of model structure, assumptions and techniques, (v) achieve a greater understanding of aquatic ecosystem functioning, (vi) increase the reliability of predictions by aquatic ecosystem models, (vii) stimulate model inter-comparisons including differing model approaches, and (viii) avoid ??re-inventing the wheel??, thus accelerating improvements to aquatic ecosystem models. We intend to achieve this as a community that fosters interactions amongst ecologists and model developers. Further, we outline scientific topics recently articulated by the scientific community, which lend themselves well to being addressed by integrative modelling approaches and serve to motivate the progress and implementation of an open source model framework.     

Exploration of the specific structural characteristics of thiol-modified single-stranded DNA self-assembled monolayers on gold by a simple model

This paper proposed a simple hexagonal model to explore the specific structural characteristics of thiol-modified single-stranded DNA (ss-DNA) self-assembled monolayers (SAMs) on gold substrate. The calibrated gyration diameter d'(g)(d'(g)=rd(g)) was used to quantify the size of ss-DNA molecules on gold by introducing a calibrating factor r, where d(g) was ss-DNA gyration diameter in solution. Based on the model, the interfacial parameters of ss-DNA-SAMs on gold assembled under different ionic strength were obtained theoretically. The ss-DNA-SAMs were assembled on gold under different concentrations of C(NaCl) and six important electrochemical parameters were used to validate the model experimentally, which include surface coverage (Γ(m)), interfacial capacitance (C), phase angle (Ф(1 Hz)), ions transfer resistance (R(it)(*)), current density difference (Δj) and charge transfer resistance (R(ct)) from chronocoulometry (CC), cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS). Three main aspects were included in this paper: (1) construction of a simple hexagonal model to describe the specific structural characteristics of ss-DNA-SAMs on gold; (2) calculation of the calibrating factor r by CC experiments and several important conclusions from the simple model; and (3) confirmation of the simple model by our experimental results and literature reports. The simple model may provide an important reference for optimizing the design of DNA sensor.     

Boundary-element calculations for dielectric behavior of doublet-shaped cells

In order to simulate dielectric relaxation spectra (DRS) of budding yeast cells (Saccharomyces cerevisiae) in suspension, the complex polarization factor (Clausius-Mossotti factor) beta for a single cell and the complex permittivity of a cell suspension epsilon(sus)* were calculated with a doublet-shaped model (model RD), in which two spheres were connected with a part of a ring torus, using the boundary element method. The beta values were represented by a diagonal tensor consisting of components beta(z) parallel to the rotation axis (z axis) and beta(h) in a plane (h plane) perpendicular to the axis. The epsilon(sus)* values were calculated from the complex permittivity of the suspending medium epsilon(a)* and the components of beta. The calculation was compared with that of a conventional prolate spheroid model (model CP). It was found that model CP could be used as a first approximation to model RD. However, differences existed in beta(z) between models RD and CP; beta(z) showed three relaxation terms in the case of model RD in contrast with two terms in model CP. Narrowing the junction between the two spheres in model RD markedly decreased the characteristic frequency of one of the relaxation terms in beta(z). This suggests that the structure of the junction can be estimated from DRS. Effects of the shape change from model RD to a two-sphere model (model RD without the junction) were also examined. The behavior of beta(z) in the two-sphere model, the relaxation intensity of which was much lower than model RD, was quite similar to that in a single-sphere model. These simulations were consistent with the experimental observations of the dielectric behavior of the yeast cells during cell cycle progression.     

Affinity analysis of non-steady-state data obtained under mass transport limited conditions using BIAcore technology

Binding data obtained with Biacore instrumentation is often evaluated using a kinetic transport model where reaction rate constants and a mass transport coefficient are used to describe the interaction. Here the use of a simplified model, an affinity transport model, for determination of the affinity (K(D)) but not the kinetics (k(a), k(d)) has been investigated. When binding rates were highly governed by mass transport effects the two models returned the same affinity and gave similar residuals, but k(a) and k(d) values found with the kinetic transport model were unreliable. On the other hand the affinity transport model failed to describe the data when binding curves were less influenced by mass transport effects. Under such circumstances the kinetic transport model returned correct k(a) and k(d) values. Depending on the outcome of the analysis the affinity transport model can therefore be used to reduce uncertainties of the kinetic parameters or as an easy way to determine K(D) values from non-steady-state data. The use of the affinity transport model is illustrated with simulated data and with binding data obtained for the interaction between a 439 Da thrombin inhibitor and immobilized thrombin. Since it is more difficult to resolve high k(a) values for low molecular weight analytes, the affinity transport model may be particularly useful for affinity analysis involving fast reactions between such analytes and immobilized protein targets.     

Signal-induced Ca2+ oscillations: properties of a model based on Ca(2+)-induced Ca2+ release.

We consider a simple, minimal model for signal-induced Ca2+ oscillations based on Ca(2+)-induced Ca2+ release. The model takes into account the existence of two pools of intracellular Ca2+, namely, one sensitive to inositol 1,4,5 trisphosphate (InsP3) whose synthesis is elicited by the stimulus, and one insensitive to InsP3. The discharge of the latter pool into the cytosol is activated by cytosolic Ca2+. Oscillations in cytosolic Ca2+ arise in this model either spontaneously or in an appropriate range of external stimulation; these oscillations do not require the concomitant, periodic variation of InsP3. The following properties of the model are reviewed and compared with experimental observations: (a) Control of the frequency of Ca2+ oscillations by the external stimulus or extracellular Ca2+; (b) correlation of latency with period of Ca2+ oscillations obtained at different levels of stimulation; (c) effect of a transient increase in InsP3; (d) phase shift and transient suppression of Ca2+ oscillations by Ca2+ pulses, and (e) propagation of Ca2+ waves. It is shown that on all these counts the model provides a simple, unified explanation for a number of experimental observations in a variety of cell types. The model based on Ca(2+)-induced Ca2+ release can be extended to incorporate variations in the level of InsP3 as well as desensitization of the InsP3 receptor; besides accounting for the phenomena described by the minimal model, the extended model might also account for the occurrence of complex Ca2+ oscillations.     

On Zeeman's equations for the nerve impulse

A model for the nerve impulse due to Zeeman (1972) and based on catastrophe theory is compared with alternative models and criticisms of Zeeman's model by Sussmann and Zahler (1977, 1978) are assessed. The criticisms of Zeeman's motivation for his model are found to carry some weight. Sussmann and Zahler (1977, 1978) list numerous features of Zeeman's model which, they state, are not in agreement with experiment. These statements as they stand are largely erroneous, and the model still remains to be tested by a critical series of experiments. However, a detailed analysis reveals defects in Zeeman's model, not among those claimed by Sussmann and Zahler, showing that the explicit equations of the model cannot be correct. The possibility of a modified approach along similar lines and its ultimate adoption remains open.     

Mechanobiological model of arterial growth and remodeling

A coupled agent-based model (ABM) and finite element analysis (FEA) computational framework is developed to study the interplay of bio-chemo-mechanical factors in blood vessels and their role in maintaining homeostasis. The agent-based model implements the power of REPAST Simphony libraries and adapts its environment for biological simulations. Coupling a continuum-level model (FEA) to a cellular-level model (ABM) has enabled this computational framework to capture the response of blood vessels to increased or decreased levels of growth factors, proteases and other signaling molecules (on the micro scale) as well as altered blood pressure. Performance of the model is assessed by simulating porcine left anterior descending artery under normotensive conditions and transient increases in blood pressure and by analyzing sensitivity of the model to variations in the rule parameters of the ABM. These simulations proved that the model is stable under normotensive conditions and can recover from transient increases in blood pressure. Sensitivity studies revealed that the model is most sensitive to variations in the concentration of growth factors that affect cellular proliferation and regulate extracellular matrix composition (mainly collagen).     

The two-sex problem with persistent unions: a generalization of the birth matrix-mating rule model

The birth matrix-mating rule (BMMR) model solves the two-sex problem of classical stable population theory by allowing births to adjust to changes in a population's age-sex composition. To avoid complications the BMMR model assumes that unions last for only a single period. This paper drops that assumption and presents the BMMRPU (BMMR persistent unions) model. To establish the existence of equilibrium in the BMMRPU model, the existence proof used in the BMMR model is supplemented by a fixed-point argument.     

Oxidative transformation of 2-acetylaminofluorene by a chemical model for cytochrome P450: A water-insoluble porphyrin and tert-butyl hydroperoxide

Oxidation of 2-acetylaminofluorene (AAF), a carcinogen, by a chemical model for cytochrome P450 was investigated to identify an active mutagen and elucidate the oxidation pathway. The oxidation system consisted of a water-insoluble tetrakis(pentafluorophenyl)porphyrinatoiron(III) chloride and tert-butyl hydroperoxide. The mutagen derived from AAF by the chemical model was 2-nitro-9-fluorenone (NO(2)=FO), which was mutagenic in Salmonella typhimurium TA1538. AAF was oxidized initially at position 9 of the fluorene carbon by the chemical model forming 2-acetylamino-9-fluorenol (AAF-OH), and then oxidized further to 2-acetylamino-9-fluorenone (AAF=O) as a major product. Initial oxidation of the nitrogen formed 2-nitrofluorene (NO(2)F), and further oxidation yielded 2-nitro-9-fluorenol (NO(2)F-OH) as a minor product. These products, AAF-OH, AAF=O, NO(2)F, and NO(2)F-OH, and their presumable common intermediate, N-hydroxy-2-acetylaminofluorene, were oxidized by the chemical model, and the formation of NO(2)F=O was determined. These results showed that NO(2)F=O was the mutagen derived from AAF in the presence of the chemical model and was formed via oxidation of N-OH-AAF, NO(2)F, and NO(2)F-OH. These results may lead to a new metabolic pathway of AAF.     

Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?

What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.     

极端干旱区多枝柽柳叶片气孔导度的环境响应模拟

气孔通过调节植物体水分散失和CO₂吸收在植物适应环境变化和环境胁迫中发挥重要作用。该文在对极端干旱区多枝柽柳(Tamarix ramosissma)叶片气体交换参数观测的基础上, 引入诊断函数f(H)对BWB模型和BBL模型提出的气孔导度(g_s)模型中的空气湿度(h_s或D_s)进行了评价, 并将评价结果引入叶子飘和于强推导出的g_s机理模型。结果表明: (1) BWB和BBL模型对h_s (或D_s)的模拟效果存在很大差异: BWB模型拟合效果较好(R² = 0.5354), BBL模型的结果显著但效果较差(R² = 0.1103)。试验结果显示: 随h_s(或D_s)的增大, g_s呈先增大后减小的趋势, 可用Gauss模型进行拟合, R²分别为0.593和0.258, 说明g_s与h_s的关系要比D_s更密切; (2)叶子飘和于强给出的简化模型(Simple模型)和该文给出的指数模型(Gauss-h模型)均具有较好的模拟效果(R²分别为0.8707和0.8286), η值分别为0.1245和0.0171, 其值均介于0-1之间; (3)模型验证中Gauss-h模型较Simple模型明显低估了观测值, 当观测条件无限趋近于Simple模型的假设时, Simple模型的拟合效果可得到显著提高(R² = 0.9606)。     

Exploration of the intercellular heterogeneity of topotecan uptake into human breast cancer cells through compartmental modelling

A mathematical multi-cell model for the in vitro kinetics of the anti-cancer agent topotecan (TPT) following administration into a culture medium containing a population of human breast cancer cells (MCF-7 cell line) is described. This non-linear compartmental model is an extension of an earlier single-cell type model and has been validated using experimental data obtained using two-photon laser scanning microscopy (TPLSM). A structural identifiability analysis is performed prior to parameter estimation to test whether the unknown parameters within the model are uniquely determined by the model outputs. The full model has 43 compartments, with 107 unknown parameters, and it was found that the structural identifiability result could not be established even when using the latest version of the symbolic computation software Mathematica. However, by assuming that a priori knowledge is available for certain parameters, it was possible to reduce the number of parameters to 81, and it was found that this (Stage Two) model was globally (uniquely) structurally identifiable. The identifiability analysis demonstrated how valuable symbolic computation is in this context, as the analysis is far too lengthy and difficult to be performed by hand.