Statistical Analysis of an SEIR Epidemic Model

This thesis was focussed on statistical analysis methods and proposes the use of Bayesian inference to extract information contained in experimental data by estimating Ebola model parameters. The model is a system of differential equations expressing the behavior and dynamics of Ebola. Two sets of data (onset and death data) were both used to estimate parameters, which has not been done by previous researchers in (Chowell, 2004). To be able to use both data, a new version of the model has been built. Model parameters have been estimated and then used to calculate the basic reproduction number and to study the disease-free equilibrium. Estimates of the parameters were useful to determine how well the model fits the data and how good estimates were, in terms of the information they provided about the possible relationship between variables. The solution showed that Ebola model fits the observed onset data at 98.95% and the observed death data at 93.6%. Since Bayesian inference can not be performed analytically, the Markov chain Monte Carlo approach has been used to generate samples from the posterior distribution over parameters. Samples have been used to check the accuracy of the model and other characteristics of the target posteriors.

Evolutionary analysis of mitogenomes from parasitic and free-living flatworms

Mitochondrial genomes (mitogenomes) are useful and relatively accessible sources of molecular data to explore and understand the evolutionary history and relationships of eukaryotic organisms across diverse taxonomic levels. The availability of complete mitogenomes from Platyhelminthes is limited; of the 40 or so published most are from parasitic flatworms (Neodermata). Here, we present the mitogenomes of two free-living flatworms (Tricladida): the complete genome of the freshwater species Crenobia alpina (Planariidae) and a nearly complete genome of the land planarian Obama sp. (Geoplanidae). Moreover, we have reanotated the published mitogenome of the species Dugesia japonica (Dugesiidae). This contribution almost doubles the total number of mtDNAs published for Tricladida, a species-rich group including model organisms and economically important invasive species. We took the opportunity to conduct comparative mitogenomic analyses between available free-living and selected parasitic flatworms in order to gain insights into the putative effect of life cycle on nucleotide composition through mutation and natural selection. Unexpectedly, we did not find any molecular hallmark of a selective relaxation in mitogenomes of parasitic flatworms; on the contrary, three out of the four studied free-living triclad mitogenomes exhibit higher A+T content and selective relaxation levels. Additionally, we provide new and valuable molecular data to develop markers for future phylogenetic studies on planariids and geoplanids.

An Interface Damage Model for the Simulation of Delamination Under Variable-Mode Ratio in Composite Materials

A thermodynamically consistent damage model for the simulation of progressive delamination under variable mode ratio is presented. The model is formulated in the context of the Damage Mechanics. The constitutive equation that results from the definition of the free energy as a function of a damage variable is used to model the initiation and propagation of delamination. A new delamination initiation criterion is developed to assure that the formulation can account for changes in the loading mode in a thermodynamically consistent way. The formulation proposed accounts for crack closure effets avoiding interfacial penetration of two adjacent layers aftercomplete decohesion. The model is implemented in a finite element formulation. The numerical predictions given by the model are compared with experimental results

Nutrimetabolomics fingerprinting to identify biomarkers of bread exposure in a free-living population from the PREDIMED study cohort

Bread is one of the most widely consumed foods. Its impact on human health is currently of special interest for researchers. We aimed to identify biomarkers of bread consumption by applying a nutrimetabolomic approach to a free-living population. An untargeted HPLC q-TOF-MS and multivariate analysis was applied to human urine from 155 subjects stratified by habitual bread consumption in three groups: non-consumers of bread (n = 56), white-bread consumers (n = 48) and whole-grain bread consumers (n = 51). The most differential metabolites (variable importance for projection ≥1.5) included compounds originating from cereal plant phytochemicals such as benzoxazinoids and alkylresorcinol metabolites, and compounds produced by gut microbiota (such as enterolactones, hydroxybenzoic and dihydroferulic acid metabolites). Pyrraline, riboflavin, 3-indolecarboxylic acid glucuronide, 2,8-dihydroxyquinoline glucuronide and N-α-acetylcitrulline were also tentatively identified. In order to combine multiple metabolites in a model to predict bread consumption, a stepwise logistic regression analysis was used. Receiver operating curves were constructed to evaluate the global performance of individual metabolites and their combination. The area under the curve values [AUC (95 % CI)] of combined models ranged from 77.8 % (69.1 86.4 %) to 93.7 % (89.4 98.1 %), whereas the AUC for the metabolites included in the models had weak values when they were evaluated individually: from 58.1 % (46.6 69.7 %) to 78.4 % (69.8 87.1 %). Our study showed that a daily bread intake significantly impacted on the urinary metabolome, despite being examined under uncontrolled free-living conditions. We further concluded that a combination of several biomarkers of exposure is better than a single biomarker for the predictive ability of discriminative analysis.

Nutrimetabolomics fingerprinting to identify biomarkers of bread exposure in a free-living population from the PREDIMED study cohort

Bread is one of the most widely consumed foods. Its impact on human health is currently of special interest for researchers. We aimed to identify biomarkers of bread consumption by applying a nutrimetabolomic approach to a free-living population. An untargeted HPLC q-TOF-MS and multivariate analysis was applied to human urine from 155 subjects stratified by habitual bread consumption in three groups: non-consumers of bread (n = 56), white-bread consumers (n = 48) and whole-grain bread consumers (n = 51). The most differential metabolites (variable importance for projection ≥1.5) included compounds originating from cereal plant phytochemicals such as benzoxazinoids and alkylresorcinol metabolites, and compounds produced by gut microbiota (such as enterolactones, hydroxybenzoic and dihydroferulic acid metabolites). Pyrraline, riboflavin, 3-indolecarboxylic acid glucuronide, 2,8-dihydroxyquinoline glucuronide and N-α-acetylcitrulline were also tentatively identified. In order to combine multiple metabolites in a model to predict bread consumption, a stepwise logistic regression analysis was used. Receiver operating curves were constructed to evaluate the global performance of individual metabolites and their combination. The area under the curve values [AUC (95 % CI)] of combined models ranged from 77.8 % (69.1 86.4 %) to 93.7 % (89.4 98.1 %), whereas the AUC for the metabolites included in the models had weak values when they were evaluated individually: from 58.1 % (46.6 69.7 %) to 78.4 % (69.8 87.1 %). Our study showed that a daily bread intake significantly impacted on the urinary metabolome, despite being examined under uncontrolled free-living conditions. We further concluded that a combination of several biomarkers of exposure is better than a single biomarker for the predictive ability of discriminative analysis.

Use of multivariate experimental designs for optimizing the reductive degradation of an azo dye in the presence of redox mediators

The optimization of the anaerobic degradation of the azo dye Remazol golden yellow RNL was performed according to multivariate experimental designs: a 2² full-factorial design and a central composite design (CCD). The CCD revealed that the best incubation conditions (90% color removal) for the degradation of the azo dye (50 mg L- 1) were achieved with 350 mg L- 1 of yeast extract and 45 mL of anaerobic supernatant (free cell extract) produced from the incubation of 650 mg L- 1 of anaerobic microorganisms and 250 mg L- 1 of glucose. A first-order kinetics model best fit the experimental data (k = 0.0837 h- 1, R² = 0.9263).

A model for specific interactions of manganese-phthalocyanine in protic media

Extinction coefficients (e) changes of manganese phthalocyanine (Mn-Pc) were studied in different organic solvents and related to solvent polarity scales; (Kosower's values (Z), Dimroth's values (E T), donor numbers (DN) and linear solvation energy relationships (LSER) or linear free energy relationships (LFER));, theoretical molecular orbital calculations and ligand/solvent coordination processes in order to predict molecular interaction with the medium and identification of predominant intermolecular forces.

Photoinhibition of Photosystem II. Kinetics, Photoprotection and Mechanism

Photosystem II (PSII) is susceptible to light-induced damage defined as photoinhibition. In natural conditions, plants are capable of repairing the photoinhibited PSII by on-going degradation and re-synthesis of the D1 reaction centre protein of PSII. Photoinhibition is induced by both visible and ultraviolet light and photoinhibition occurs under all light intensities with the same efficiency per photon. In my thesis work, I studied the reaction kinetics and mechanism of photoinhibition of PSII, as well as photoprotection in leaves of higher plants. Action spectroscopy was used to identify photoreceptors of photoinhibition. I found that the action spectrum of photoinhibition in vivo shows resemblance to the absorption spectra of manganese model compounds of the oxygen evolving complex (OEC) suggesting a role for manganese as a photoreceptor of photoinhibition under UV and visible light. In order to study the protective effect of non-photochemical quenching, the action spectrum was measured from leaves of wild type Arabidopsis thaliana and two mutants impaired in nonphotochemical quenching of chlorophyll a excitations. The findings of action spectroscopy and simulations of chlorophyll-based photoinhibition mechanisms suggested that quenching of antenna excitations protects less efficiently than would be expected if antenna chlorophylls were the only photoreceptors of photoinhibition. The reaction kinetics of prolonged photoinhibition was studied in leaves of Cucurbita maxima and Capsicum annuum. The results indicated that photoinhibitory decrease in both the oxygen evolution activity and ratio of variable to maximum fluorescence follows firstorder kinetics in vivo. The persistence of first-order kinetics suggests that already photoinhibited reaction centres do not protect against photoinhibition and that the mechanism of photoinhibition does not have a reversible intermediate. When Cucurbita maxima leaves were photoinhibited with saturating single-turnover flashes and continuous light, the light response curve of photoinhibition was found to be essentially a straight line with both types of illumination, suggesting that similar photoinhibition mechanisms might function during illumination with continuous light and during illumination with short flashes.

Prediction of free-stall occupancy rate in dairycattle barns through fuzzy sets

The goal of this study was to develop a fuzzy model to predict the occupancy rate of free-stalls facilities of dairy cattle, aiding to optimize the design of projects. The following input variables were defined for the development of the fuzzy system: dry bulb temperature (Tdb, °C), wet bulb temperature (Twb, °C) and black globe temperature (Tbg, °C). Based on the input variables, the fuzzy system predicts the occupancy rate (OR, %) of dairy cattle in free-stall barns. For the model validation, data collecting were conducted on the facilities of the Intensive System of Milk Production (SIPL), in the Dairy Cattle National Research Center (CNPGL) of Embrapa. The OR values, estimated by the fuzzy system, presented values of average standard deviation of 3.93%, indicating low rate of errors in the simulation. Simulated and measured results were statistically equal (P>0.05, t Test). After validating the proposed model, the average percentage of correct answers for the simulated data was 89.7%. Therefore, the fuzzy system developed for the occupancy rate prediction of free-stalls facilities for dairy cattle allowed a realistic prediction of stalls occupancy rate, allowing the planning and design of free-stall barns.

Determination of total accumulated rainfall, global radiation, evapotranspiration and degree-days originated from the ECMWF model to sugar cane crop

The climate variability between the growth and harvesting of sugar cane is very important because it directly affects yield. The MODIS sensor has characteristics like spatial and temporal resolution that can be applied to monitoring of vegetative vigor variability in the land surface and then, temporal profiles generation. Agro meteorological data from ECMWF model are free and easy to access and have a good representation of reality. In this study, we used the period between sugar cane growth and harvest in the state of Sao Paulo, Brazil, from temporal profiles selecting of NDVI behavior. For each period the precipitation, evapotranspiration, global radiation, length (days) and degree-days were accumulated. The periods were presented in a map format on MODIS spatial resolution of 250 meters. The results showed the spatial variability of climate variables and the relationship to the reality presented by official data.

KINETICS OF MASS LOSS OF ARABICA COFFEE DURING ROASTING PROCESS

ABSTRACT Roasting is one of the most complex coffee processing steps due to simultaneous transfers of heat and mass. During this process, beans lose mass because of fast physical and chemical changes that will set color and flavor of the commercial coffee beverage. Therefore, we aimed at assessing the kinetics of mass loss in commercially roasted coffee beans according to heating throughout the processing. For that, we used samples of 350-g Arabica coffee processed grains with water content of 0.1217 kga kg-1, in addition to a continuous roaster with firing gas. The roaster had initial temperatures of 285, 325, 345 and 380 °C, decreasing during the process up to 255, 285, 305 and 335 °C respectively. Mass loss was calculated by the difference between grain weight before and after roasting. We observed a linear variation directly dependent on roaster temperature. For each temperature during the process was obtained a constant mass loss rate, which was reported by the Arrhenius model with r2 above 0.98. In a roaster in non-isothermal conditions, the required activation energy to start the mass loss in a commercial coffee roasting index was 52.27 kJ mol -1.

Free Prostate-specific Antigen Forms and Kallikrein-related Peptidase 2: Tools for Prostate Cancer Diagnostics

Prostate-specific antigen (PSA) is a marker that is commonly used in estimating prostate cancer risk. Prostate cancer is usually a slowly progressing disease, which might not cause any symptoms whatsoever. Nevertheless, some cases of cancer are aggressive and need to be treated before they become life-threatening. However, the blood PSA concentration may rise also in benign prostate diseases and using a single total PSA (tPSA) measurement to guide the decision on further examinations leads to many unnecessary biopsies, over-detection, and overtreatment of indolent cancers which would not require treatment. Therefore, there is a need for markers that would better separate cancer from benign disorders, and would also predict cancer aggressiveness. The aim of this study was to evaluate whether intact and nicked forms of free PSA (fPSA-I and fPSA-N) or human kallikrein-related peptidase 2 (hK2) could serve as new tools in estimating prostate cancer risk. First, the immunoassays for fPSA-I and free and total hK2 were optimized so that they would be less prone to assay interference caused by interfering factors present in some blood samples. The optimized assays were shown to work well and were used to study the marker concentrations in the clinical sample panels. The marker levels were measured from preoperative blood samples of prostate cancer patients scheduled for radical prostatectomy. The association of the markers with the cancer stage and grade was studied. It was found that among all tested markers and their combinations especially the ratio of fPSA-N to tPSA and ratio of free PSA (fPSA) to tPSA were associated with both cancer stage and grade. They might be useful in predicting the cancer aggressiveness, but further follow-up studies are necessary to fully evaluate the significance of the markers in this clinical setting. The markers tPSA, fPSA, fPSA-I and hK2 were combined in a statistical model which was previously shown to be able to reduce unnecessary biopsies when applied to large screening cohorts of men with elevated tPSA. The discriminative accuracy of this model was compared to models based on established clinical predictors in reference to biopsy outcome. The kallikrein model and the calculated fPSA-N concentrations (fPSA minus fPSA-I) correlated with the prostate volume and the model, when compared to the clinical models, predicted prostate cancer in biopsy equally well. Hence, the measurement of kallikreins in a blood sample could be used to replace the volume measurement which is time-consuming, needs instrumentation and skilled personnel and is an uncomfortable procedure. Overall, the model could simplify the estimation of prostate cancer risk. Finally, as the fPSA-N seems to be an interesting new marker, a direct immunoassay for measuring fPSA-N concentrations was developed. The analytical performance was acceptable, but the rather complicated assay protocol needs to be improved until it can be used for measuring large sample panels.

Drivers and barriers of mobile travel and tourism service adoption : a study of individual perceptions and business model development in a travel and tourism context

The Travel and Tourism field is undergoing changes due to the rapid development of information technology and digital services. Online travel has profoundly changed the way travel and tourism organizations interact with their customers. Mobile technology such as mobile services for pocket devices (e.g. mobile phones) has the potential to take this development even further. Nevertheless, many issues have been highlighted since the early days of mobile services development (e.g. the lack of relevance, ease of use of many services). However, the wide adoption of smartphones and the mobile Internet in many countries as well as the formation of so-called ecosystems between vendors of mobile technology indicate that many of these issues have been overcome. Also when looking at the numbers of downloaded applications related to travel in application stores like Google Play, it seems obvious that mobile travel and tourism services are adopted and used by many individuals. However, as business is expected to start booming in the mobile era, many issues have a tendency to be overlooked. Travelers are generally on the go and thus services that work effectively in mobile settings (e.g. during a trip) are essential. Hence, the individuals’ perceived drivers and barriers to use mobile travel and tourism services in on-site or during trip settings seem particularly valuable to understand; thus this is one primary aim of the thesis. We are, however, also interested in understanding different types of mobile travel service users. Individuals may indeed be very different in their propensity to adopt and use technology based innovations (services). Research is also switching more from investigating issues of mobile service development to understanding individuals’ usage patterns of mobile services. But designing new mobile services may be a complex matter from a service provider perspective. Hence, our secondary aim is to provide insights into drivers and barriers of mobile travel and tourism service development from a holistic business model perspective. To accomplish the research objectives seven different studies have been conducted over a time period from 2002 – 2013. The studies are founded on and contribute to theories within diffusion of innovations, technology acceptance, value creation, user experience and business model development. Several different research methods are utilized: surveys, field and laboratory experiments and action research. The findings suggest that a successful mobile travel and tourism service is a service which supports one or several mobile motives (needs) of individuals such as spontaneous needs, time-critical arrangements, efficiency ambitions, mobility related needs (location features) and entertainment needs. The service could be customized to support travelers’ style of traveling (e.g. organized travel or independent travel) and should be easy to use, especially easy to take into use (access, install and learn) during a trip, without causing security concerns and/or financial risks for the user. In fact, the findings suggest that the most prominent barrier to the use of mobile travel and tourism services during a trip is an individual’s perceived financial cost (entry costs and usage costs). It should, however, be noted that regulations are put in place in the EU regarding data roaming prices between European countries and national telecom operators are starting to see ‘international data subscriptions’ as a sales advantage (e.g. Finnish Sonera provides a data subscription in the Baltic and Nordic region at the same price as in Finland), which will enhance the adoption of mobile travel and tourism services also in international contexts. In order to speed up the adoption rate travel service providers could consider e.g. more local initiatives of free Wi-Fi networks, development of services that can be used, at least to some extent, in an offline mode (do not require costly network access during a trip) and cooperation with telecom operators (e.g. lower usage costs for travelers who use specific mobile services or travel with specific vendors). Furthermore, based on a developed framework for user experience of mobile trip arrangements, the results show that a well-designed mobile site and/or native application, which preferably supports integration with other mobile services, is a must for true mobile presence. In fact, travel service providers who want to build a relationship with their customers need to consider a downloadable native application, but in order to be found through the mobile channel and make contact with potential new customers, a mobile website should be available. Moreover, we have made a first attempt with cluster analysis to identify user categories of mobile services in a travel and tourism context. The following four categories were identified: info-seekers, checkers, bookers and all-rounders. For example “all-rounders”, represented primarily by individuals who use their pocket device for almost any of the investigated mobile travel services, constituted primarily of 23 to 50 year old males with high travel frequency and great online experience. The results also indicate that travel service providers will increasingly become multi-channel providers. To manage multiple online channels, closely integrated and hybrid online platforms for different devices, supporting all steps in a traveler process should be considered. It could be useful for travel service providers to focus more on developing browser-based mobile services (HTML5-solutions) than native applications that work only with specific operating systems and for specific devices. Based on an action research study and utilizing a holistic business model framework called STOF we found that HTML5 as an emerging platform, at least for now, has some limitations regarding the development of the user experience and monetizing the application. In fact, a native application store (e.g. Google Play) may be a key mediator in the adoption of mobile travel and tourism services both from a traveler and a service provider perspective. Moreover, it must be remembered that many device and mobile operating system developers want service providers to specifically create services for their platforms and see native applications as a strategic advantage to sell more devices of a certain kind. The mobile telecom industry has moved into a battle of ecosystems where device makers, developers of operating systems and service developers are to some extent forced to choose their development platforms.

Methyl and ethyl chloride synthesis in microreactors

Methyl chloride is an important chemical intermediate with a variety of applications. It is produced today in large units and shipped to the endusers. Most of the derived products are harmless, as silicones, butyl rubber and methyl cellulose. However, methyl chloride is highly toxic and flammable. On-site production in the required quantities is desirable to reduce the risks involved in transportation and storage. Ethyl chloride is a smaller-scale chemical intermediate that is mainly used in the production of cellulose derivatives. Thus, the combination of onsite production of methyl and ethyl chloride is attractive for the cellulose processing industry, e.g. current and future biorefineries. Both alkyl chlorides can be produced by hydrochlorination of the corresponding alcohol, ethanol or methanol. Microreactors are attractive for the on-site production as the reactions are very fast and involve toxic chemicals. In microreactors, the diffusion limitations can be suppressed and the process safety can be improved. The modular setup of microreactors is flexible to adjust the production capacity as needed. Although methyl and ethyl chloride are important chemical intermediates, the literature available on potential catalysts and reaction kinetics is limited. Thus the thesis includes an extensive catalyst screening and characterization, along with kinetic studies and engineering the hydrochlorination process in microreactors. A range of zeolite and alumina based catalysts, neat and impregnated with ZnCl2, were screened for the methanol hydrochlorination. The influence of zinc loading, support, zinc precursor and pH was investigated. The catalysts were characterized with FTIR, TEM, XPS, nitrogen physisorption, XRD and EDX to identify the relationship between the catalyst characteristics and the activity and selectivity in the methyl chloride synthesis. The acidic properties of the catalyst were strongly influenced upon the ZnCl2 modification. In both cases, alumina and zeolite supports, zinc reacted to a certain amount with specific surface sites, which resulted in a decrease of strong and medium Brønsted and Lewis acid sites and the formation of zinc-based weak Lewis acid sites. The latter are highly active and selective in methanol hydrochlorination. Along with the molecular zinc sites, bulk zinc species are present on the support material. Zinc modified zeolite catalysts exhibited the highest activity also at low temperatures (ca 200 °C), however, showing deactivation with time-onstream. Zn/H-ZSM-5 zeolite catalysts had a higher stability than ZnCl2 modified H-Beta and they could be regenerated by burning the coke in air at 400 °C. Neat alumina and zinc modified alumina catalysts were active and selective at 300 °C and higher temperatures. However, zeolite catalysts can be suitable for methyl chloride synthesis at lower temperatures, i.e. 200 °C. Neat γ-alumina was found to be the most stable catalyst when coated in a microreactor channel and it was thus used as the catalyst for systematic kinetic studies in the microreactor. A binder-free and reproducible catalyst coating technique was developed. The uniformity, thickness and stability of the coatings were extensively characterized by SEM, confocal microscopy and EDX analysis. A stable coating could be obtained by thermally pretreating the microreactor platelets and ball milling the alumina to obtain a small particle size. Slurry aging and slow drying improved the coating uniformity. Methyl chloride synthesis from methanol and hydrochloric acid was performed in an alumina-coated microreactor. Conversions from 4% to 83% were achieved in the investigated temperature range of 280-340 °C. This demonstrated that the reaction is fast enough to be successfully performed in a microreactor system. The performance of the microreactor was compared with a tubular fixed bed reactor. The results obtained with both reactors were comparable, but the microreactor allows a rapid catalytic screening with low consumption of chemicals. As a complete conversion of methanol could not be reached in a single microreactor, a second microreactor was coupled in series. A maximum conversion of 97.6 % and a selectivity of 98.8 % were reached at 340°C, which is close to the calculated values at a thermodynamic equilibrium. A kinetic model based on kinetic experiments and thermodynamic calculations was developed. The model was based on a Langmuir Hinshelwood-type mechanism and a plug flow model for the microreactor. The influence of the reactant adsorption on the catalyst surface was investigated by performing transient experiments and comparing different kinetic models. The obtained activation energy for methyl chloride was ca. two fold higher than the previously published, indicating diffusion limitations in the previous studies. A detailed modeling of the diffusion in the porous catalyst layer revealed that severe diffusion limitations occur starting from catalyst coating thicknesses of 50 μm. At a catalyst coating thickness of ca 15 μm as in the microreactor, the conditions of intrinsic kinetics prevail. Ethanol hydrochlorination was performed successfully in the microreactor system. The reaction temperature was 240-340°C. An almost complete conversion of ethanol was achieved at 340°C. The product distribution was broader than for methanol hydrochlorination. Ethylene, diethyl ether and acetaldehyde were detected as by-products, ethylene being the most dominant by-product. A kinetic model including a thorough thermodynamic analysis was developed and the influence of adsorbed HCl on the reaction rate of ethanol dehydration reactions was demonstrated. The separation of methyl chloride using condensers was investigated. The proposed microreactor-condenser concept enables the production of methyl chloride with a high purity of 99%.

Simulation of the Interaction Mean Free Path between Neutrons and TRISO Particles

The interaction mean free path between neutrons and TRISO particles is simulated using scripts written in MATLAB to solve the increasing error present with an increase in the packing factor in the reactor physics code Serpent. Their movement is tracked both in an unbounded and in a bounded space. Their track is calculated, depending on the program, linearly directly using the position vectors of the neutrons and the surface equations of all the fuel particles; by dividing the space in multiple subspaces, each of which contain a fraction of the total number of particles, and choosing the particles from those subspaces through which the neutron passes through; or by choosing the particles that lie within an infinite cylinder formed on the movement axis of the neutron. The estimate from the current analytical model, based on an exponential distribution, for the mean free path, utilized by Serpent, is used as a reference result. The results from the implicit model in Serpent imply a too long mean free path with high packing factors. The received results support this observation by producing, with a packing factor of 17 %, approximately 2.46 % shorter mean free path compared to the reference model. This is supported by the packing factor experienced by the neutron, the simulation of which resulted in a 17.29 % packing factor. It was also observed that the neutrons leaving from the surfaces of the fuel particles, in contrast to those starting inside the moderator, do not follow the exponential distribution. The current model, as it is, is thus not valid in the determination of the free path lengths of the neutrons.