A practical guide for optimal designs of experiments in the Monod model

The Monod model is a classical microbiological model much used in microbiology, for example to evaluate biodegradation processes. The model describes microbial growth kinetics in batch culture experiments using three parameters: the maximal specific growth rate, the saturation constant and the yield coefficient. However, identification of these parameter values from experimental data is a challenging problem. Recently, it was shown theoretically that the application of optimal design theory in this model is an efficient method for both parameter value identification and economic use of experimental resources (Dette et al., 2003). The purpose of this paper is to provide this method as a computational ?tool? such that it can be used by practitioners-without strong mathematical and statistical backgroundfor the efficient design of experiments in the Monod model. The paper presents careful explanations of the principal theoretical concepts, and a computer program for practical optimal design calculations in Mathematica 5.0 software. In addition, analogous programs in Matlab software will be soon available at www.optimal-design.org. --Monod model,microbial growth,biodegradation kinetics,optimal experimental design,D-optimality

Design of experiments for microbiological models

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A practical guide for optimal designs of experiments in the monod model

The Monod model is a classical microbiological model much used in microbiology, for example to evaluate biodegradation processes. The model describes microbial growth kinetics in batch culture experiments using three parameters: the maximal specific growth rate, the saturation constant and the yield coefficient. However, identification of these parameter values from experimental data is a challenging problem. Recently, it was shown theoretically that the application of optimal design theory in this model is an efficient method for both parameter value identification and economic use of experimental resources (Dette et al., 2003). The purpose of this paper is to provide this method as a computational ”tool” such that it can be used by practitioners -without strong mathematical and statistical background- for the efficient design of experiments in the Monod model. The paper presents careful explanations of the principal theoretical concepts, and a computer program for practical optimal design calculations in Mathematica 5.0 software. In addition, analogous programs in Matlab software will be soon available at www.optimal-design.org

Design of Experiments for the Monod Model - Robust and Efficient Designs

In this paper the problem of designing experiments for a model which is called Monod model and is frequently used in microbiology is studied. The model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, environmental research, pharmacokinetics, and plant physiology. The designs presented so far in the literature are locally optimal designs, which depend sensitively on a preliminary guess of the unknown parameters, and are for this reason in many cases not robust with respect to their misspecification. Uniform designs and maximin optimal designs are considered as a strategy to obtain robust and efficient designs for parameter estimation. In particular standardized maximin D- and E- optimal designs are determined and compared with uniform designs, which are usually applied in these microbiological models. It is shown that standardized maximin optimal designs are always supported on a finite number of points and it is demonstrated that maximin optimal designs are substantially more efficient than uniform designs. Parameter variances can be decreased by a factor two by simply sampling at optimal times during the experiment. Moreover, the maximin optimal designs usually provide the possibility for the experimenter to check the model assumptions, because they have more support points than parameters in the Monod model

Design of experiments for the Monod model : robust and efficient designs

In this paper the problem of designing experiments for a model which is called Monod model and is frequently used in microbiology is studied. The model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, environmental research, pharmacokinetics, and plant physiology. The designs presented so far in the literature are locally optimal designs, which depend sensitively on a preliminary guess of the unknown parameters, and are for this reason in many cases not robust with respect to their misspecification. Uniform designs and maximin optimal designs are considered as a strategy to obtain robust and efficient designs for parameter estimation. In particular standardized maximin D- and E- optimal designs are determined and compared with uniform designs, which are usually applied in these microbiological models. It is shown that standardized maximin optimal designs are always supported on a finite number of points and it is demonstrated that maximin optimal designs are substantially more efficient than uniform designs. Parameter variances can be decreased by a factor two by simply sampling at optimal times during the experiment. Moreover, the maximin optimal designs usually provide the possibility for the experimenter to check the model assumptions, because they have more support points than parameters in the Monod model

Efficient three-dimensional reconstruction of aquatic vegetation geometry: Estimating morphological parameters influencing hydrodynamic drag

Aquatic vegetation can shelter coastlines from energetic waves and tidal currents, sometimes enabling accretion of fine sediments. Simulation of flow and sediment transport within submerged canopies requires quantification of vegetation geometry. However, field surveys used to determine vegetation geometry can be limited by the time required to obtain conventional caliper and ruler measurements. Building on recent progress in photogrammetry and computer vision, we present a method for reconstructing three-dimensional canopy geometry. The method was used to survey a dense canopy of aerial mangrove roots, called pneumatophores, in Vietnam’s Mekong River Delta. Photogrammetric estimation of geometry required 1) taking numerous photographs at low tide from multiple viewpoints around 1 m2 quadrats, 2) computing relative camera locations and orientations by triangulation of key features present in multiple images and reconstructing a dense 3D point cloud, and 3) extracting pneumatophore locations and diameters from the point cloud data. Step 3) was accomplished by a new ‘sector-slice’ algorithm, yielding geometric parameters every 5 mm along a vertical profile. Photogrammetric analysis was compared with manual caliper measurements. In all 5 quadrats considered, agreement was found between manual and photogrammetric estimates of stem number, and of number × mean diameter, which is a key parameter appearing in hydrodynamic models. In two quadrats, pneumatophores were encrusted with numerous barnacles, generating a complex geometry not resolved by hand measurements. In remaining cases, moderate agreement between manual and photogrammetric estimates of stem diameter and solid volume fraction was found. By substantially reducing measurement time in the field while capturing in greater detail the 3D structure, photogrammetry has potential to improve input to hydrodynamic models, particularly for simulations of flow through large-scale, heterogenous canopies