The cost of uniqueness in groundwater model calibration

Calibration of a groundwater model requires that hydraulic properties be estimated throughout a model domain. This generally constitutes an underdetermined inverse problem, for which a Solution can only be found when some kind of regularization device is included in the inversion process. Inclusion of regularization in the calibration process can be implicit, for example through the use of zones of constant parameter value, or explicit, for example through solution of a constrained minimization problem in which parameters are made to respect preferred values, or preferred relationships, to the degree necessary for a unique solution to be obtained. The cost of uniqueness is this: no matter which regularization methodology is employed, the inevitable consequence of its use is a loss of detail in the calibrated field. This, ill turn, can lead to erroneous predictions made by a model that is ostensibly well calibrated. Information made available as a by-product of the regularized inversion process allows the reasons for this loss of detail to be better understood. In particular, it is easily demonstrated that the estimated value for an hydraulic property at any point within a model domain is, in fact, a weighted average of the true hydraulic property over a much larger area. This averaging process causes loss of resolution in the estimated field. Where hydraulic conductivity is the hydraulic property being estimated, high averaging weights exist in areas that are strategically disposed with respect to measurement wells, while other areas may contribute very little to the estimated hydraulic conductivity at any point within the model domain, this possibly making the detection of hydraulic conductivity anomalies in these latter areas almost impossible. A study of the post-calibration parameter field covariance matrix allows further insights into the loss of system detail incurred through the calibration process to be gained. A comparison of pre- and post-calibration parameter covariance matrices shows that the latter often possess a much smaller spectral bandwidth than the former. It is also demonstrated that, as all inevitable consequence of the fact that a calibrated model cannot replicate every detail of the true system, model-to-measurement residuals can show a high degree of spatial correlation, a fact which must be taken into account when assessing these residuals either qualitatively, or quantitatively in the exploration of model predictive uncertainty. These principles are demonstrated using a synthetic case in which spatial parameter definition is based oil pilot points, and calibration is Implemented using both zones of piecewise constancy and constrained minimization regularization. (C) 2005 Elsevier Ltd. All rights reserved.

Adipose tissue engineering based on the controlled release of fibroblast growth factor-2 in a collagen matrix

Adipose tissue forms when basement membrane extract ( Matrigel (TM)) and fibroblast growth factor-2 (FGF-2) are added to our mouse tissue engineering chamber model. A mouse tumor extract, Matrigel is unsuitable for human clinical application, and finding an alternative to Matrigel is essential. In this study we generated adipose tissue in the chamber model without using Matrigel by controlled release of FGF-2 in a type I collagen matrix. FGF-2 was impregnated into biodegradable gelatin microspheres for its slow release. The chambers were filled with these microspheres suspended in 60 mu L collagen gel. Injection of collagen containing free FGF-2 or collagen containing gelatin microspheres with buffer alone served as controls. When chambers were harvested 6 weeks after implantation, the volume and weight of the tissue obtained were higher in the group that received collagen and FGF-2 impregnated microspheres than in controls. Histologic analysis of tissue constructs showed the formation of de novo adipose tissue accompanied by angiogenesis. In contrast, control groups did not show extensive adipose tissue formation. In conclusion, this study has shown that de novo formation of adipose tissue can be achieved through controlled release of FGF-2 in collagen type I in the absence of Matrigel.

Arthritic disease suppression and cartilage protection with glycosaminoglycan polypeptide complexes (Peptacans) derived from the cartilage extracellular matrix: A novel approach to therapy

Molecular fragments of cartilage are antigenic and can stimulate an autoimmune response. Oral administration of type II collagen prevents disease onset in animal models of arthritis but the effects of other matrix components have not been reported. We evaluated glycosaminoglycan polypeptides (GAG-P) and matrix proteins (CaP) from cartilage for a) mitigating disease activity in rats with collagen-induced arthritis (CIA) and adjuvant-induced arthritis (AIA) and b) stimulating proteoglycan (PG) synthesis by chondrocytes in-vitro. CIA and AIA were established in Wistar rats using standard methods. Agents were administered orally (10–200 mg/kg), either for seven days prior to disease induction (toleragenic protocol), or continuously for 15 days after injecting the arthritigen (prophylactic protocol). Joint swelling and arthritis scores were determined on day 15. Histological sections of joint tissues were assessed post-necropsy. In chondrocyte cultures, CaP + / − interleukin-1 stimulated PG biosynthesis. CaP was also active in preventing arthritis onset at 3.3, 10 or 20 mg/kg in the rat CIA model using the toleragenic protocol. It was only active at 20 and 200 mg/kg in the CIA prophylactic protocol. GAG-P was active in the CIA toleragenic protocol at 20 mg/kg but chondroitin sulfate and glucosamine hydrochloride or glucosamine sulfate were all inactive. The efficacy of CaP in the rat AIA model was less than in the CIA model. These findings lead us to suggest that oral CaP could be used as a disease-modifying anti-arthritic drug.

Accounting for management costs in sensitivity analyses of matrix population models

Traditional sensitivity and elasticity analyses of matrix population models have been used to p inform management decisions, but they ignore the economic costs of manipulating vital rates. For exam le, the growth rate of a population is often most sensitive to changes in adult survival rate, but this does not mean that increasing that rate is the best option for managing the population because it may be much more expensive than other options. To explore how managers should optimize their manipulation of vital rates, we incorporated the cost of changing those rates into matrix population models. We derived analytic expressions for locations in parameter space where managers should shift between management of fecundity and survival, for the balance between fecundity and survival management at those boundaries, and for the allocation of management resources to sustain that optimal balance. For simple matrices, the optimal budget allocation can often be expressed as simple functions of vital rates and the relative costs of changing them. We applied our method to management of the Helmeted Honeyeater (Lichenostomus melanops cassidix; an endangered Australian bird) and the koala (Phascolarctos cinereus) as examples. Our method showed that cost-efficient management of the Helmeted Honeyeater should focus on increasing fecundity via nest protection, whereas optimal koala management should focus on manipulating both fecundity and survival simultaneously, These findings are contrary to the cost-negligent recommendations of elasticity analysis, which would suggest focusing on managing survival in both cases. A further investigation of Helmeted Honeyeater management options, based on an individual-based model incorporating density dependence, spatial structure, and environmental stochasticity, confirmed that fecundity management was the most cost-effective strategy. Our results demonstrate that decisions that ignore economic factors will reduce management efficiency.