Exhaled SARS-CoV-2 quantified by face-mask sampling in hospitalised patients with COVID-19.

BACKGROUND: Human to human transmission of SARS-CoV-2 is driven by the respiratory route but little is known about the pattern and quantity of virus output from exhaled breath. We have previously shown that face-mask sampling (FMS) can detect exhaled tubercle bacilli and have adapted its use to quantify exhaled SARS-CoV-2 RNA in patients admitted to hospital with Coronavirus Disease-2019 (COVID-19). METHODS: Between May and December 2020, we took two concomitant FMS and nasopharyngeal samples (NPS) over two days, starting within 24 h of a routine virus positive NPS in patients hospitalised with COVID-19, at University Hospitals of Leicester NHS Trust, UK. Participants were asked to wear a modified duckbilled facemask for 30 min, followed by a nasopharyngeal swab. Demographic, clinical, and radiological data, as well as International Severe Acute Respiratory and emerging Infections Consortium (ISARIC) mortality and deterioration scores were obtained. Exposed masks were processed by removal, dissolution and analysis of sampling matrix strips fixed within the mask by RT-qPCR. Viral genome copy numbers were determined and results classified as Negative; Low: ≤999 copies; Medium: 1000-99,999 copies and High ≥ 100,000 copies per strip for FMS or per 100 µl for NPS. RESULTS: 102 FMS and NPS were collected from 66 routinely positive patients; median age: 61 (IQR 49 - 77), of which FMS was positive in 38% of individuals and concomitant NPS was positive in 50%. Positive FMS viral loads varied over five orders of magnitude (<10-3.3 x 106 genome copies/strip); 21 (32%) patients were asymptomatic at the time of sampling. High FMS viral load was associated with respiratory symptoms at time of sampling and shorter interval between sampling and symptom onset (FMS High: median (IQR) 2 days (2-3) vs FMS Negative: 7 days (7-10), p = 0.002). On multivariable linear regression analysis, higher FMS viral loads were associated with higher ISARIC mortality (Medium FMS vs Negative FMS gave an adjusted coefficient of 15.7, 95% CI 3.7-27.7, p = 0.01) and deterioration scores (High FMS vs Negative FMS gave an adjusted coefficient of 37.6, 95% CI 14.0 to 61.3, p = 0.002), while NPS viral loads showed no significant association. CONCLUSION: We demonstrate a simple and effective method for detecting and quantifying exhaled SARS-CoV-2 in hospitalised patients with COVID-19. Higher FMS viral loads were more likely to be associated with developing severe disease compared to NPS viral loads. Similar to NPS, FMS viral load was highest in early disease and in those with active respiratory symptoms, highlighting the potential role of FMS in understanding infectivity.

Mechanical properties of 3-D printed polyvinyl alcohol matrix for detection of respiratory pathogens.

Polyvinyl alcohol is used to 3D print (fused deposition modelling) sampling matrices for bacterial detection. A specific configuration was designed using Computer-Aided Design software. The mechanical properties of the printed samples were studied using uniaxial tensile testing, and compared to those of the original Polyvinyl alcohol filament, with and without heat treatment. The effects of different factors such as UV treatment, printing speed, infill density and printing direction on the mechanical properties of the printed samples including strength, strain and modulus of elasticity were studied. The results show that the effect of the fused deposition modelling process on the mechanical properties of the printed Polyvinyl alcohol cannot be explained by its exposure to heat. UV treatment reduced the strength, characteristic strains and Young's modulus. It makes Polyvinyl alcohol samples brittle. The effects of printing speed and the infill density on the mechanical properties of printed samples can be no linear. An unexpected relation between printing direction and mechanical properties was demonstrated by the studied specimens that needs further theoretical understanding. There is a huge scatter in strength of PVA samples compared with typical engineering materials, and in the fracture strain of original PVA filament, the 3D printing process can reduce the scatter but only by a limited extent. To summarise, there is a sophisticated relation between printing parameters and the mechanical properties of the printed Polyvinyl alcohol.

3-D printed polyvinyl alcohol matrix for detection of airborne pathogens in respiratory bacterial infections.

Novel sampling matrices were manufactured using 3D printing for the detection of respiratory pathogens in expired air. A specific configuration of the matrices was designed using Computer-Aided Design software. Polyvinyl alcohol (PVA) was printed using fused deposition modelling to create a multilayer matrix to enhance the capture of bacteria. The performance of these matrices was compared with gelatine filters that have been used for this work to date. PVA matrices (60 mm diameter) were contaminated with bacteria either by direct inoculation, or by aerosol exposure using an Omron A3 nebuliser. Rough and smooth morphotypes of Mycobacterium abscessus, M. smegmatis and M. bovis BCG, were used in this study to contaminate the matrices. PVA matrices and gelatine sampling filters were contaminated to compare recovery rates for quantitative analyses. These were dissolved in water, bacteria pelleted and DNA extracted followed by a Mycobacterium-specific quantitative Polymerase Chain Reaction (qPCR).The results showed that 3D printed PVA matrices are very effective to capture the bacteria. 3D printed PVA matrix and gelatine filters yielded results of the same order of magnitude for mycobacterial analyses, however, PVA matrix offers several advantages over the latter material. 3D printed PVA is considered as an economic and time-effective matrix as it is cheaper than gelatine filters. PVA is sufficiently robust to be handled and loaded into the surgical masks for sampling, compared to the brittle gelatine filters that required supportive frames. PVA is a synthetic material and it is suitable for DNA-based analyses, whilst gelatine is derived from animal collagen, and carries a high bacterial DNA background that interferes with the target DNA analysis. Furthermore, PVA dissolves in distilled water without requiring chemicals or enzymes, such as the case for gelatine hydrolysis. To summarise, 3D printed PVA sampling matrix is considered a promising tool used for microbiological diagnostic purposes.

A model of polymer degradation and erosion for finite element analysis of bioresorbable implants.

Finite element analysis is a powerful tool for the design of bioresorbable medical implants made of aliphatic polyesters such as bioresorbable vascular scaffolds. However polymer erosion has been traditionally modelled using empirical rules rather than differential equations. The rule-based models are difficult to implement in a finite element analysis. Consequently, these models have been limited to simple geometries such as plates or spheres. This paper presents a set of differential equations that govern the hydrolytic chain scission and bulk erosion of bioresorbable implants where polymer erosion is modelled using a differential equation instead of empirical rules. These differential equations can be conveniently solved using a commercial finite element package to calculate the molecular weight and mass loss as functions of time for bioresorbable implant made of aliphatic polyesters. A case study of Absorb bioresorbable vascular scaffolds (BVSs) is presented using data obtained from the literature, where 98 Absorb BVSs were implanted in 40 porcine coronary arteries. It is demonstrated that the finite element model can fit the data of both molecular weight and mass loss as functions of time to an accuracy of approximately 5%. The finite element model and the back-calculated model parameters can be used to design future implants that degrade in a controlled pattern with required mechanical performance.

Exhaled Mycobacterium tuberculosis output and detection of subclinical disease by face-mask sampling: prospective observational studies.

BACKGROUND: Tuberculosis remains a global health challenge, with early diagnosis key to its reduction. Face-mask sampling detects exhaled Mycobacterium tuberculosis. We aimed to investigate bacillary output from patients with pulmonary tuberculosis and to assess the potential of face-mask sampling as a diagnostic method in active case-finding. METHODS: We did a 24-h longitudinal study in patients from three hospitals in Pretoria, South Africa, with microbiologically confirmed pulmonary tuberculosis. Patients underwent 1 h of face-mask sampling eight times over a 24-h period, with contemporaneous sputum sampling. M tuberculosis was detected by quantitative PCR. We also did an active case-finding pilot study in inhabitants of an informal settlement near Pretoria. We enrolled individuals with symptoms of tuberculosis on the WHO screening questionnaire. Participants provided sputum and face-mask samples that were tested with the molecular assay Xpert MTB/RIF Ultra. Sputum-negative and face-mask-positive individuals were followed up prospectively for 20 weeks by bronchoscopy, PET-CT, and further sputum analysis to validate the diagnosis. FINDINGS: Between Sept 22, 2015, and Dec 3, 2015, 78 patients with pulmonary tuberculosis were screened for the longitudinal study, of whom 24 completed the study (20 had HIV co-infection). M tuberculosis was detected in 166 (86%) of 192 face-mask samples and 38 (21%) of 184 assessable sputum samples obtained over a 24-h period. Exhaled M tuberculosis output showed no diurnal pattern and did not associate with cough frequency, sputum bacillary content, or chest radiographic disease severity. On May 16, 2018, 45 individuals were screened for the prospective active case-finding pilot study, of whom 20 had tuberculosis symptoms and were willing to take part. Eight participants were diagnosed prospectively with pulmonary tuberculosis, of whom six were exclusively face-mask positive at screening. Four of these participants (three of whom were HIV-positive) had normal findings on chest radiography but had treatment-responsive early tuberculosis-compatible lesions on PET-CT scans, with Xpert-positive sputum samples after 6 weeks. INTERPRETATION: Face-mask sampling offers a highly efficient and non-invasive method for detecting exhaled M tuberculosis, informing the presence of active infection both with greater consistency and at an earlier disease stage than with sputum samples. The approach shows potential for diagnosis and screening, particularly in difficult-to-reach communities. FUNDING: Wellcome Trust, CARA (Council for At-Risk Academics), University of Leicester, the UK Medical Research Council, and the National Institute for Health Research. VIDEO ABSTRACT.

A model for hydrolytic degradation and erosion of biodegradable polymers.

For aliphatic polyesters such as PLAs and PGAs, there is a strong interplay between the hydrolytic degradation and erosion - degradation leads to a critically low molecular weight at which erosion starts. This paper considers the underlying physical and chemical processes of hydrolytic degradation and erosion. Several kinetic mechanisms are incorporated into a mathematical model in an attempt to explain different behaviours of mass loss observed in experiments. In the combined model, autocatalytic hydrolysis, oligomer production and their diffusion are considered together with surface and interior erosion using a set of differential equations and Monte Carlo technique. Oligomer and drug diffusion are modelled using Fick's law with the diffusion coefficients dependent on porosity. The porosity is due to the formation of cavities which are a result of polymer erosion. The model can follow mass loss and drug release up to 100%, which cannot be explained using a simple reaction-diffusion. The model is applied to two case studies from the literature to demonstrate its validity. The case studies show that a critical molecular weight for the onset of polymer erosion and an incubation period for the polymer dissolution are two critical factors that need to be considered when predicting mass loss and drug release. STATEMENT OF SIGNIFICANCE: In order to design bioresorbable implants, it is important to have a mathematical model to predict polymer degradation and corresponding drug release. However, very different behaviours of polymer degradation have been observed and there is no single model that can capture all these behaviours. For the first time, the model presented in this paper is capable of capture all these observed behaviours by switching on and off different underlying mechanisms. Unlike the existing reaction-diffusion models, the model presented here can follow the degradation and drug release all the way to the full disappearance of an implant.

A Mechanistic Model for Acidic Drug Release Using Microspheres Made of PLGA 50:50.

Polyester microspheres are extensively studied for controlled release drug delivery devices, and many models have been developed to describe drug release from the bulk polymer. However, the interaction between drugs and polymers is ignored in most of the existing mathematical models. This paper presents a mechanistic model which captures the interplay between acidic drugs and bioresorbable polyesters. The model considers the autocatalytic effect on polymer degradation arising from carboxylic acid end groups of oligomers and drug molecules. Hence, the enhancing effect of acidic drug on the rate of degradation was fully considered. On the other hand the drug release from polyester microspheres is controlled by drug diffusion from polymer matrix. The drug diffusion coefficient depends strongly on the level of degradation of the polymer. This effect is also included in the model. It is shown that the model can effectively predict experimental data in the literature for both polymer degradation and drug release. Furthermore, the model is used to design different systems of microspheres which release drugs with either a zero order profile or burst followed by zero order release profile.

Detection of degradation in polyester implants by analysing mode shapes of structure vibration.

This paper presents a numerical study on using vibration analysis to detect degradation in degrading polyesters. A numerical model of a degrading plate sample is considered. The plate is assumed to degrade following the typical behaviour of amorphous copolymers of polylactide and polyglycolide. Due to the well-known autocatalytic effect in the degradation of these polyesters, the inner core of the plate degrades faster than outer surface region, forming layers of materials with varying Young׳s modulus. Firstly the change in molecular weight and corresponding change in Young׳s modulus at different times are calculated using the mathematical models developed in our previous work. Secondly the first four mode shapes of transverse vibration of the plate are calculated using the finite element method. Finally the curvature of the mode shapes are calculated and related to the spatial distribution of the polymer degradation. It is shown that the curvature of the mode shapes can be used to detect the onset and distribution of polymer degradation. The level of measurement accuracy required in an experiment is presented to guide practical applications of the method. At the end of this paper a demonstration case of coronary stent is presented showing how the method can be used to detect degradation in an implant of sophisticated structure.

A constitutive law for degrading bioresorbable polymers.

This paper presents a constitutive law that predicts the changes in elastic moduli, Poisson's ratio and ultimate tensile strength of bioresorbable polymers due to biodegradation. During biodegradation, long polymer chains are cleaved by hydrolysis reaction. For semi-crystalline polymers, the chain scissions also lead to crystallisation. Treating each scission as a cavity and each new crystal as a solid inclusion, a degrading semi-crystalline polymer can be modelled as a continuum solid containing randomly distributed cavities and crystal inclusions. The effective elastic properties of a degrading polymer are calculated using existing theories for such solid and the tensile strength of the degrading polymer is predicted using scaling relations that were developed for porous materials. The theoretical model for elastic properties and the scaling law for strength form a complete constitutive relation for the degrading polymers. It is shown that the constitutive law can capture the trend of the experimental data in the literature for a range of biodegradable polymers fairly well.

An atomic finite element model for biodegradable polymers. Part 1. Formulation of the finite elements.

Molecular dynamics (MD) simulations are widely used to analyse materials at the atomic scale. However, MD has high computational demands, which may inhibit its use for simulations of structures involving large numbers of atoms such as amorphous polymer structures. An atomic-scale finite element method (AFEM) is presented in this study with significantly lower computational demands than MD. Due to the reduced computational demands, AFEM is suitable for the analysis of Young's modulus of amorphous polymer structures. This is of particular interest when studying the degradation of bioresorbable polymers, which is the topic of an accompanying paper. AFEM is derived from the inter-atomic potential energy functions of an MD force field. The nonlinear MD functions were adapted to enable static linear analysis. Finite element formulations were derived to represent interatomic potential energy functions between two, three and four atoms. Validation of the AFEM was conducted through its application to atomic structures for crystalline and amorphous poly(lactide).

An atomic finite element model for biodegradable polymers. Part 2. A model for change in Young's modulus due to polymer chain scission.

Atomic simulations were undertaken to analyse the effect of polymer chain scission on amorphous poly(lactide) during degradation. Many experimental studies have analysed mechanical properties degradation but relatively few computation studies have been conducted. Such studies are valuable for supporting the design of bioresorbable medical devices. Hence in this paper, an Effective Cavity Theory for the degradation of Young's modulus was developed. Atomic simulations indicated that a volume of reduced-stiffness polymer may exist around chain scissions. In the Effective Cavity Theory, each chain scission is considered to instantiate an effective cavity. Finite Element Analysis simulations were conducted to model the effect of the cavities on Young's modulus. Since polymer crystallinity affects mechanical properties, the effect of increases in crystallinity during degradation on Young's modulus is also considered. To demonstrate the ability of the Effective Cavity Theory, it was fitted to several sets of experimental data for Young's modulus in the literature.

Degradation mechanisms of bioresorbable polyesters. Part 2. Effects of initial molecular weight and residual monomer.

This paper presents an understanding of how initial molecular weight and initial monomer fraction affect the degradation of bioresorbable polymers in terms of the underlying hydrolysis mechanisms. A mathematical model was used to analyse the effects of initial molecular weight for various hydrolysis mechanisms including noncatalytic random scission, autocatalytic random scission, noncatalytic end scission or autocatalytic end scission. Different behaviours were identified to relate initial molecular weight to the molecular weight half-life and to the time until the onset of mass loss. The behaviours were validated by fitting the model to experimental data for molecular weight reduction and mass loss of samples with different initial molecular weights. Several publications that consider initial molecular weight were reviewed. The effect of residual monomer on degradation was also analysed, and shown to accelerate the reduction of molecular weight and mass loss. An inverse square root law relationship was found between molecular weight half-life and initial monomer fraction for autocatalytic hydrolysis. The relationship was tested by fitting the model to experimental data with various residual monomer contents.

Degradation mechanisms of bioresorbable polyesters. Part 1. Effects of random scission, end scission and autocatalysis.

A mathematical model was developed to relate the degradation trend of bioresorbable polymers to different underlying hydrolysis mechanisms, including noncatalytic random scission, autocatalytic random scission, noncatalytic end scission or autocatalytic end scission. The effect of each mechanism on molecular weight degradation and potential mass loss was analysed. A simple scheme was developed to identify the most likely hydrolysis mechanism based on experimental data. The scheme was first demonstrated using case studies, then used to evaluate data collected from 31 publications in the literature to identify the dominant hydrolysis mechanisms for typical biodegradable polymers. The analysis showed that most of the experimental data indicates autocatalytic hydrolysis, as expected. However, the study shows that the existing understanding on whether random or end scission controls degradation is inappropriate. It was revealed that pure end scission cannot explain the observed trend in molecular weight reduction because end scission would be too slow to reduce the average molecular weight. On the other hand, pure random scission cannot explain the observed trend in mass loss because too few oligomers would be available to diffuse out of a device. It is concluded that the chain ends are more susceptible to cleavage, which produces most of the oligomers leading to mass loss. However, it is random scission that dominates the reduction in molecular weight.

A finite element analysis of bone plates available for prophylactic internal fixation of the radial osteocutaneous donor site using the sheep tibia model.

INTRODUCTION: The strengthening effect of prophylactic internal fixation (PIF) with a bone plate at the radial osteocutaneous flap donor site has previously been demonstrated using the sheep tibia model of the human radius. This study investigated whether a finite element (FE) model could accurately represent this biomechanical model and whether stress or strain based failure criteria are most appropriate. METHODS: An FE model of an osteotomised sheep tibia bone was strengthened using 4 types of plates with unilocking or bicortical screw fixation. Torsion and 4-point bending simulations were performed. The maximum von Mises stresses and strain failure criteria were studied. RESULTS: The strengthening effects when applying stress failure criteria [factor 1.76-4.57 bending and 1.33-1.80 torsion] were comparable to the sheep biomechanical model [factor 1.73-2.43 bending and 1.54-2.63 torsion]. The strongest construct was the straight 3.5mm stainless steel unilocking plate. Applying strain criteria the strongest construct was the straight 3.5mm stainless DCP plate with bicortical screw fixation. CONCLUSIONS: The FE model was validated by comparison with the sheep tibia model. The complex biomechanics at the bone-screw interface require further investigation. This FE modelling technique may be applied to a model of the human radius and other sites.

Refinements in osteotomy design to improve structural integrity: a finite element analysis study.

Osteotomy cuts are typically made using a saw, and the meeting point acts as a focus for the concentration of stress and failure. We have studied the impact of different designs of osteotomy cut. Cadaver sheep tibias were scanned by computed tomography (CT) and transformed into a computer-aided design (CAD) model. A standard marginal resection defect was created and then modified, and a finite element analysis made. The relative stress concentrations at the intersection of osteotomy cuts were recorded using principal stresses S1, S3, and von Mises stress, von Mises under both 4-point bending and torsion testing. The osteotomy designs studied were: right-angled and bevelled osteotomy end cuts, overcutting, and a stop drill hole. Peak stress values for 4-point bending and torsion were 24-30% greater at the right-angled osteotomy than the bevelled end cut. Overcutting dramatically increased peak stress values caused by bending and torsion by 48% and 71%, respectively. Substantially lower concentrations of stress were noted with a stop hole using both a 90° (bending 38% and torsion 56%), and a tangential (bending 58% and torsion 60%) cut. A bevelled osteotomy has substantially lower concentrations of stress than a right-angled osteotomy. It is important to avoid creating an overcut as this causes an appreciable increase in the concentration of stress, while a stop drill hole substantially reduces the stress. The creation of a stop hole and the use of judicious bevelling techniques are modifications in the design of an osteotomy that are readily applicable to surgical practice.

A molecular dynamics study of Young's modulus change of semi-crystalline polymers during degradation by chain scissions.

This paper presents a molecular dynamics study on the change in Young's modulus of semi-crystalline polymers during degradation by chain scissions, which is relevant to the study of mechanical properties of biodegrading polymers. Using a simple polymer model whose structural and mechanical properties are similar to that of a commonly used biodegrading polymer poly(glycolic acid), we combine molecular dynamics and Monte Carlo to model a system of two polymer crystals separated by an amorphous region between them. The polymer chains in the amorphous region are cut randomly to mimic hydrolysis chain scissions. In a series of virtual tensile tests, the systems with various numbers of chain scissions are subjected to a unidirectional deformation. We find that at temperatures below the glass transition temperature of the model polymer, the Young's modulus of the system reduces quickly with the number of chain scissions, while at temperatures above the glass transition temperature, the Young's modulus reduction lags behind the polymer chain scissions. This observation supports the entropy-spring model of amorphous polymers proposed by Wang et al., which suggests that Young's modulus above the glass transition temperature is dominated by the internal energy of the system, while below the glass transition temperature it is dominated by the entropy of the amorphous phase. The numerical study therefore provides a molecular understanding of the widely observed behaviours of semi-crystalline biodegradable polymers.

Polymer chain scission, oligomer production and diffusion: a two-scale model for degradation of bioresorbable polyesters.

This paper presents a computer model for the biodegradation of polyesters such as poly(lactic acid), poly(glycolic acid) and their copolymers. The model can take polymer details such as molecular weight distribution, different end and random scission rates and copolymer ratio as input data. A multi-scale approach is developed: polymer chain scission and oligomer production which occur at the molecular scale are modelled using a kinetic Monte Carlo scheme, oligomer diffusion which occurs at the device scale is modelled using a diffusion equation, and the two are connected at the finite difference nodes of the diffusion equation. The two-scale model can be used to predict the temporal evolution and spatial distribution of molecular weight distribution in a device as well as the weight loss as a function of time. It is shown that the kinetic Monte Carlo scheme can accurately predict the effect of copolymer ratio on the degradation rate. Grizzi and co-workers observed in their experiments that a PLA film 0.3mm thick degrades much more slowly than one that is 2mm thick. The numerical study shows that the conceptional reaction diffusion model suggested by Grizzi et al. needs to be extended in order to explain the size effect fully.

A model for biodegradation of composite materials made of polyesters and tricalcium phosphates.

A saturation behaviour has been observed when incorporating tricalcium phosphate (TCP) in various polyesters to control the degradation rate. This paper presents an understanding of this behaviour using a mathematical model. The coupled process of hydrolysis reaction of the ester bonds, acid dissociation of the carboxylic end groups, dissolution of the calcium phosphates and buffering reactions by the dissolved phosphate ions is modelled together using a set of differential equations. Two non-dimensional groups of the material and chemical parameters are identified which control the degradation rate of the composites. An effectiveness map is established to show the conditions under which incorporating TCP into polyesters is effective, saturated or ineffective. Comparisons are made between the model predictions and existing experimental data in the literature. The map provides a useful tool to guide the design of polyester/TCP composites for tissue engineering and orthopaedic fixation applications.

Analysis of degradation data of poly(l-lactide-co-l,d-lactide) and poly(l-lactide) obtained at elevated and physiological temperatures using mathematical models.

The degradation of resorbable polymeric devices often takes months to years. Accelerated testing at elevated temperatures is an attractive but controversial technique. The purposes of this paper include: (a) to provide a summary of the mathematical models required to analyse accelerated degradation data and to indicate the pitfalls of using these models; (b) to improve the model previously developed by Han and Pan; (c) to provide a simple version of the model of Han and Pan with an analytical solution that is convenient to use; (d) to demonstrate the application of the improved model in two different poly(lactic acid) systems. It is shown that the simple analytical relations between molecular weight and degradation time widely used in the literature can lead to inadequate conclusions. In more general situations the rate equations are only part of a complete degradation model. Together with previous works in the literature, our study calls for care in using the accelerated testing technique.

Inverse engineering of medical devices made of bioresorbable polymers.

The degradation of medical devices made of bioresorbable polymers such as fixation devices in orthopaedic surgeries and scaffolds for tissue engineering can take from months to years. The trial and error approach of device development is therefore problematic and mathematical modelling of the biodegradation can help to accelerate the device development. This paper presents an inverse scheme to obtain the material parameters in a biodegradation model developed by Pan and his co-workers from existing experimental data of bioresorbable devices. The parameters can then be used to predict the degradation rate of new devices made of the same polymer. Firstly, the previously developed model is briefly outlined. Secondly, a finite element scheme and a time integration algorithm are developed for the direct analysis using the biodegradation model. Thirdly, an inverse analysis scheme is presented in combination with the direct analysis. Finally, several case studies of existing degradation data are presented to demonstrate the effectiveness of the inverse engineering approach.