Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov Chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient. © 2011 Springer-Verlag.

A cardiovascular occlusion method based on the use of a smart hydrogel

Smart hydrogels for biomedical applications are highly researched materials. However, integrating them into a device for implantation is difficult. This paper investigates an integrated delivery device designed to deliver an electro-responsive hydrogel to a target location inside a blood vessel with the purpose of creating an occlusion. The paper describes the synthesis and characterization of a Pluronic/methacrylic acid sodium salt electro-responsive hydrogel. Application of an electrical bias decelerates the expansion of the hydrogel. An integrated delivery system was manufactured to deliver the hydrogel to the target location in the body. Ex vivo and in vivo experiments in the carotid artery of sheep were used to validate the concept. The hydrogel was able to completely occlude the blood vessel reducing the blood flow from 245 to 0 ml/min after implantation. Ex vivo experiments showed that the hydrogel was able to withstand physiological blood pressures of > 270 mm·Hg without dislodgement. The results showed that the electro-responsive hydrogel used in this paper can be used to create a long-term occlusion in a blood vessel without any apparent side effects. The delivery system developed is a promising device for the delivery of electro-responsive hydrogels.

Select, Link and Rank: Diversified Query Expansion and Entity Ranking using Wikipedia

A search query, being a very concise grounding of user intent, could potentially have many possible interpretations. Search engines hedge their bets by diversifying top results to cover multiple such possibilities so that the user is likely to be satisfied, whatever be her intended interpretation. Diversified Query Expansion is the problem of diversifying query expansion suggestions, so that the user can specialize the query to better suit her intent, even before perusing search results. We propose a method, Select-Link-Rank, that exploits semantic information from Wikipedia to generate diversified query expansions. SLR does collective processing of terms and Wikipedia entities in an integrated framework, simultaneously diversifying query expansions and entity recommendations. SLR starts with selecting informative terms from search results of the initial query, links them to Wikipedia entities, performs a diversity-conscious entity scoring and transfers such scoring to the term space to arrive at query expansion suggestions. Through an extensive empirical analysis and user study, we show that our method outperforms the state-of-the-art diversified query expansion and diversified entity recommendation techniques.

Improved electrochemical performance of Sr2Fe1.5Mo0.4Nb0.1O6-δ -Sm0.2Ce0.8O2-δ composite cathodes by a one-pot method for intermediate temperature solid oxide fuel cells

In this paper, Sr₂Fe_1.5Mo_0.4Nb_0.1O_6-δ (SFMNb)-xSm_0.2Ce_0.8O_2-δ (SDC) (x = 0, 20, 30, 40, 50 wt%) composite cathode materials were synthesized by a one-pot combustion method to improve the electrochemical performance of SFMNb cathode for intermediate temperature solid oxide fuel cells (IT-SOFCs). The fabrication of composite cathodes by adding SDC to SFMNb is conducive to providing extended electrochemical reaction zones for oxygen reduction reactions (ORR). X-ray diffraction (XRD) demonstrates that SFMNb is chemically compatible with SDC electrolytes at temperature up to 1100 °C. Scanning electron microscope (SEM) indicates that the SFMNb-SDC composite cathodes have a porous network nanostructure as well as the single phase SFMNb. The conductivity and thermal expansion coefficient of the composite cathodes decrease with the increased content of SDC, while the electrochemical impedance spectra (EIS) exhibits that SFMNb-40SDC composite cathode has optimal electrochemical performance with low polarization resistance (R_p) on the La_0.9Sr_0.1Ga_0.8Mg_0.2O₃ electrolyte. The R_p of the SFMNb-40SDC composite cathode is about 0.047 Ω cm² at 800 °C in air. A single cell with SFMNb-40SDC cathode also displays favorable discharge performance, whose maximum power density is 1.22 W cm^-2 at 800 °C. All results indicate that SFMNb-40SDC composite material is a promising cathode candidate for IT-SOFCs.

Synthesis of Pr0.6Sr0.4FeO 3-δ -xCe0.9Pr0.1O 2-δ cobalt-free composite cathodes by a one-pot method for intermediate-temperature solid oxide fuel cells

Cobalt-free composite cathodes consisting of Pr_0.6Sr_0.4FeO _3-δ -xCe_0.9Pr_0.1O _2-δ (PSFO-xCPO, x = 0-50 wt%) have been synthesized using a one-pot method. X-ray diffraction, scanning electron microscopy, thermal expansion coefficient, conductivity, and polarization resistance (R _P ) have been used to characterize the PSFO-xCPO cathodes. Furthermore the discharge performance of the Ni-SSZ/SSZ/GDC/PSFO-xCPO cells has been measured. The experimental results indicate that the PSFO-xCPO composite materials fully consist of PSFO and CPO phases and posses a porous microstructure. The conductivity of PSFO-xCPO decreases with the increase of CPO content, but R _P of PSFO-40CPO shows the smallest value amongst all the samples. The power density of single cells with a PSFO-40CPO composite cathode is significantly improved compared with that of the PSFO cathode, exhibiting 0.43, 0.75, 1.08 and 1.30 W cm^-2 at 650, 700, 750 and 800 °C, respectively. In addition, single cells with the PSFO-40CPO composite cathode show a stable performance with no obvious degradation over 100 h when operating at 750 °C.

Analyzing Gene Centres with the Help of the Checklist Method – the Case of Syria

The present survey of species diversity of cultivated plants is the first for Syria. Some cultivated species will be added in the future, because due to the civil war in Syria, it was not possible to visit the country in the frame of the present work, as initially planned. Checklists proved to be a useful tool for overviewing the cultivated plants of selected areas and allow a characterization of the state of plant genetic resources of Syria. Syria has experienced several civilizations. Man settled in this productive land since ancient times and used its resources. However, such use has led to changes in vegetation and decline of wildlife through the country, in seashore areas, interior, mountains, and grassland. Plant domestication and growing started more than 10,000 years ago in West Asia. Since then, plentiful of economic plant species were present and used by man and his domesticated animals. Forming a part of the Fertile Crescent, where many of the world’s agricultural plants have evolved, Syria is extremely rich in agrobiodiversity. Wild progenitors of wheat and barley and wild relatives of many fruit trees such as almonds and pistachio as well as forage species are still found in marginal lands and less disturbed areas. These are threatened by a wide range of human activities, notably modern, extensive agriculture, overgrazing, overcutting and urban expansion. Syria is also considered as part of one of the main centres of origin, according to Vavilov, who had collected in Syria in 1926. The first expeditions to crop fields showed the exclusive nature of cultivated plants in Syria with a high number of endemic forms. Furthermore, Syria is a part of a biodiversity hotspot. Several studies have been performed to study agrobiodiversity in different parts of Syria, but usually on wild species. Many collections have been carried out; however, they focussed preferably on cereals and pulses, and particularly on wheat, like Vavilov’s expedition. Only 30 crops make up the major part of the conserved Syrian crop plant material in the genebank, indicating that most of the remaining 7,000 species of cultivated plants and many other valuable genetic resources species have only been included on a limited scale in the genebank collections. Although a small country (185,180 km2), Syria accommodates numerous ecosystems that allow for a large diversity of plant genetic resources for agriculture ranging from cold-requiring to subtropical crops to live and thrive. Only few references are available in this respect. The aim of the present study was to complete a checklist of Syria’s cultivated plants of agriculture and horticulture excluding plants only grown as ornamental or for forestry. Furthermore, plants taken for reforestation have not been included, if they do not have also agricultural or horticultural uses. Therefore, the inclusion of plants into the checklist follows the same principles as “Mansfeld’s Encyclopedia”. Main sources of information were published literature, floras of Syria, Lebanon and the Mediterranean, as well as Syrian printed sources in Arabic and/or English, reports from FAO on agricultural statistics in Syria, and data from ICARDA and Bioversity International. In addition, personal observations gathered during professional work in the General Commission for Scientific Agricultural Research (GCSAR) in Syria (since 1989) and participation in projects were taken into account. These were: (1) A project on “Conservation and Sustainable Use of Dry Land Agrobiodiversity in the Near East” with participation of Jordan, Lebanon, Syria, and the Palestinian Authority, focussing on landraces and wild relatives of barley, wheat, lentil, alliums, feed legumes, and fruit trees (1999–2005). (2) A project for vegetable landraces (1993–1995) in collaboration with the former International Plant Genetic Resources Institute and the UN Development Programme, in which 380 local vegetable accessions were evaluated. For medicinal plants and fruit trees I was in personal contact with departments of GCSAR and the Ministry of Agriculture and Agrarian Reform, as well as with private organizations. The resulting checklist was compared with the catalogues of crop plants of Italy and a checklist of cultivated plants of Iraq. The cultivated plant species are presented in alphabetical order according to their accepted scientific names. Each entry consists of a nomenclatural part, folk names, details of plant uses, the distribution in Syria (by provinces), a textual description, and references to literature. In total, 262 species belonging to 146 genera and 57 families were identified. Within-species (intraspecific) diversity is a significant measure of the biodiversity. Intraspecific diversity for wild plants has been and remains to be well studied, but for crop plants there are only few results. Mansfeld’s method is an actual logical contribution to such studies. Among the families, the following have the highest number of crop species: Leguminosae (34 spp.), Rosaceae (24), Gramineae (18), Labiatae (18), Compositae (14), Cruciferae (14), Cucurbitaceae (11), Rutaceae (10), Malvaceae (9), Alliaceae (7), and Anacardiaceae (7). The establishment of an effective programme for the maintenance of plant genetic resources in Syria started in the mid-1970s. This programme considered ex situ and in situ collection of the genetic resources of various field crops, fruit trees and vegetables. From a plant genetic resources viewpoint, it is clear that the homegarden is an important location for the cultivation of so-called neglected and underutilized species (neglected from a research side and underutilized from a larger economic side). Such species have so far not received much care from ecologists, botanists and agronomists, and they are considerably under-represented in genebanks.

Simplified design method for energy dissipating devices in retrofitting of seismically isolated bridges

Abstract: Highway bridges have great values in a country because in case of any natural disaster they may serve as lines to save people’s lives. Being vulnerable under significant seismic loads, different methods can be considered to design resistant highway bridges and rehabilitate the existing ones. In this study, base isolation has been considered as one efficient method in this regards which in some cases reduces significantly the seismic load effects on the structure. By reducing the ductility demand on the structure without a notable increase of strength, the structure is designed to remain elastic under seismic loads. The problem associated with the isolated bridges, especially with elastomeric bearings, can be their excessive displacements under service and seismic loads. This can defy the purpose of using elastomeric bearings for small to medium span typical bridges where expansion joints and clearances may result in significant increase of initial and maintenance cost. Thus, supplementing the structure with dampers with some stiffness can serve as a solution which in turn, however, may increase the structure base shear. The main objective of this thesis is to provide a simplified method for the evaluation of optimal parameters for dampers in isolated bridges. Firstly, performing a parametric study, some directions are given for the use of simple isolation devices such as elastomeric bearings to rehabilitate existing bridges with high importance. Parameters like geometry of the bridge, code provisions and the type of soil on which the structure is constructed have been introduced to a typical two span bridge. It is concluded that the stiffness of the substructure, soil type and special provisions in the code can determine the employment of base isolation for retrofitting of bridges. Secondly, based on the elastic response coefficient of isolated bridges, a simplified design method of dampers for seismically isolated regular highway bridges has been presented in this study. By setting objectives for reduction of displacement and base shear variation, the required stiffness and damping of a hysteretic damper can be determined. By modelling a typical two span bridge, numerical analyses have followed to verify the effectiveness of the method. The method has been used to identify equivalent linear parameters and subsequently, nonlinear parameters of hysteretic damper for various designated scenarios of displacement and base shear requirements. Comparison of the results of the nonlinear numerical model without damper and with damper has shown that the method is sufficiently accurate. Finally, an innovative and simple hysteretic steel damper was designed. Five specimens were fabricated from two steel grades and were tested accompanying a real scale elastomeric isolator in the structural laboratory of the Université de Sherbrooke. The test procedure was to characterize the specimens by cyclic displacement controlled tests and subsequently to test them by real-time dynamic substructuring (RTDS) method. The test results were then used to establish a numerical model of the system which went through nonlinear time history analyses under several earthquakes. The outcome of the experimental and numerical showed an acceptable conformity with the simplified method.

Variational ensemble Kalman filtering applied to data assimilation problems in computational fluid dynamics

One challenge on data assimilation (DA) methods is how the error covariance for the model state is computed. Ensemble methods have been proposed for producing error covariance estimates, as error is propagated in time using the non-linear model. Variational methods, on the other hand, use the concepts of control theory, whereby the state estimate is optimized from both the background and the measurements. Numerical optimization schemes are applied which solve the problem of memory storage and huge matrix inversion needed by classical Kalman filter methods. Variational Ensemble Kalman filter (VEnKF), as a method inspired the Variational Kalman Filter (VKF), enjoys the benefits from both ensemble methods and variational methods. It avoids filter inbreeding problems which emerge when the ensemble spread underestimates the true error covariance. In VEnKF this is tackled by resampling the ensemble every time measurements are available. One advantage of VEnKF over VKF is that it needs neither tangent linear code nor adjoint code. In this thesis, VEnKF has been applied to a two-dimensional shallow water model simulating a dam-break experiment. The model is a public code with water height measurements recorded in seven stations along the 21:2 m long 1:4 m wide flume’s mid-line. Because the data were too sparse to assimilate the 30 171 model state vector, we chose to interpolate the data both in time and in space. The results of the assimilation were compared with that of a pure simulation. We have found that the results revealed by the VEnKF were more realistic, without numerical artifacts present in the pure simulation. Creating a wrapper code for a model and DA scheme might be challenging, especially when the two were designed independently or are poorly documented. In this thesis we have presented a non-intrusive approach of coupling the model and a DA scheme. An external program is used to send and receive information between the model and DA procedure using files. The advantage of this method is that the model code changes needed are minimal, only a few lines which facilitate input and output. Apart from being simple to coupling, the approach can be employed even if the two were written in different programming languages, because the communication is not through code. The non-intrusive approach is made to accommodate parallel computing by just telling the control program to wait until all the processes have ended before the DA procedure is invoked. It is worth mentioning the overhead increase caused by the approach, as at every assimilation cycle both the model and the DA procedure have to be initialized. Nonetheless, the method can be an ideal approach for a benchmark platform in testing DA methods. The non-intrusive VEnKF has been applied to a multi-purpose hydrodynamic model COHERENS to assimilate Total Suspended Matter (TSM) in lake Säkylän Pyhäjärvi. The lake has an area of 154 km2 with an average depth of 5:4 m. Turbidity and chlorophyll-a concentrations from MERIS satellite images for 7 days between May 16 and July 6 2009 were available. The effect of the organic matter has been computationally eliminated to obtain TSM data. Because of computational demands from both COHERENS and VEnKF, we have chosen to use 1 km grid resolution. The results of the VEnKF have been compared with the measurements recorded at an automatic station located at the North-Western part of the lake. However, due to TSM data sparsity in both time and space, it could not be well matched. The use of multiple automatic stations with real time data is important to elude the time sparsity problem. With DA, this will help in better understanding the environmental hazard variables for instance. We have found that using a very high ensemble size does not necessarily improve the results, because there is a limit whereby additional ensemble members add very little to the performance. Successful implementation of the non-intrusive VEnKF and the ensemble size limit for performance leads to an emerging area of Reduced Order Modeling (ROM). To save computational resources, running full-blown model in ROM is avoided. When the ROM is applied with the non-intrusive DA approach, it might result in a cheaper algorithm that will relax computation challenges existing in the field of modelling and DA.

Study the methods of connecting jacket to the seabed and choosing the best method for Persian Gulf according to soil characteristics

Offshore structures with numerous applications in different environments throughout the world and used at different depths. Due to the expansion of marine industries, including offshore oil industry in Iran , particularly in the Persian Gulf region, in order to more accurately model these structures and to prevent incidents such as the Overturning of the platform serious damage to the South Pars Phase ١٣ was platforms, the use New Technic is essential technologies. One of the methods that are used in the construction of offshore wind turbines, using a pre-pile. In this method, a template is constructed with the dimensions specified in the workshop. After making templates using special vessels for placement in the desired location on the sea bed is carried, then the template is placed on the sea bed, Then, using a hammer for Pile Driving Operation Started Vibration hammer and fit the template of 3 or 4 piles of crushed within this template on the seabed . The next step piling, templates have been removed from the site And Jacket placed on piles. The system was installed on the deck on piles and Consequently Deck Load pile inserted on .It should be noted that the design of these types of platforms, base diameter of the pile diameter independent of the choice as one of the major advantages of this system is. This thesis examines a Template Fixed Platform in the oil Soroush Using the Pre-Piling and the Common Piling systems in the Persian Gulf were studied and the effect of different design compared to the Pre-Piling Platforms Persian Gulf were evaluated. The results suggest that Pre-Piling system compared with conventional systems piling in the Persian Gulf, as a more appropriate model structure and behavior Top Model economic efficiency is selected. It should be noted that all calculations and analyzes were performed using Software Abaqus.

An Information Theoretic Approach to Automatic Query Expansion

International audience

POSITIVE FILTERED P_N METHOD FOR LINEAR TRANSPORT EQUATIONS AND THE ASSOCIATED OPTIMIZATION ALGORITHM

We propose a positive, accurate moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FP_N) expansion in the angular variable. The FP_N moment equations are accurate approximations to linear kinetic equations, but they are known to suffer from the occurrence of unphysical, negative particle concentrations. The new positive filtered P_N (FP_N+) closure is developed to address this issue. The FP_N+ closure approximates the kinetic distribution by a spherical harmonic expansion that is non-negative on a finite, predetermined set of quadrature points. With an appropriate numerical PDE solver, the FP_N+ closure generates particle concentrations that are guaranteed to be non-negative. Under an additional, mild regularity assumption, we prove that as the moment order tends to infinity, the FP_N+ approximation converges, in the L2 sense, at the same rate as the FP_N approximation; numerical tests suggest that this assumption may not be necessary. By numerical experiments on the challenging line source benchmark problem, we confirm that the FP_N+ method indeed produces accurate and non-negative solutions. To apply the FP_N+ closure on problems at large temporal-spatial scales, we develop a positive asymptotic preserving (AP) numerical PDE solver. We prove that the propose AP scheme maintains stability and accuracy with standard mesh sizes at large temporal-spatial scales, while, for generic numerical schemes, excessive refinements on temporal-spatial meshes are required. We also show that the proposed scheme preserves positivity of the particle concentration, under some time step restriction. Numerical results confirm that the proposed AP scheme is capable for solving linear transport equations at large temporal-spatial scales, for which a generic scheme could fail. Constrained optimization problems are involved in the formulation of the FP_N+ closure to enforce non-negativity of the FP_N+ approximation on the set of quadrature points. These optimization problems can be written as strictly convex quadratic programs (CQPs) with a large number of inequality constraints. To efficiently solve the CQPs, we propose a constraint-reduced variant of a Mehrotra-predictor-corrector algorithm, with a novel constraint selection rule. We prove that, under appropriate assumptions, the proposed optimization algorithm converges globally to the solution at a locally q-quadratic rate. We test the algorithm on randomly generated problems, and the numerical results indicate that the combination of the proposed algorithm and the constraint selection rule outperforms other compared constraint-reduced algorithms, especially for problems with many more inequality constraints than variables.

A Highly Improved Method For Sensitive Determination Of Amitriptyline In Pharmaceutical Formulations Using An Unmodified Carbon Nanotube Electrode In The Presence Of Sulfuric Acid.

The present paper describes a novel, simple and reliable differential pulse voltammetric method for determining amitriptyline (AMT) in pharmaceutical formulations. It has been described for many authors that this antidepressant is electrochemically inactive at carbon electrodes. However, the procedure proposed herein consisted in electrochemically oxidizing AMT at an unmodified carbon nanotube paste electrode in the presence of 0.1 mol L(-1) sulfuric acid used as electrolyte. At such concentration, the acid facilitated the AMT electroxidation through one-electron transfer at 1.33 V vs. Ag/AgCl, as observed by the augmentation of peak current. Concerning optimized conditions (modulation time 5 ms, scan rate 90 mV s(-1), and pulse amplitude 120 mV) a linear calibration curve was constructed in the range of 0.0-30.0 μmol L(-1), with a correlation coefficient of 0.9991 and a limit of detection of 1.61 μmol L(-1). The procedure was successfully validated for intra- and inter-day precision and accuracy. Moreover, its feasibility was assessed through analysis of commercial pharmaceutical formulations and it has been compared to the UV-vis spectrophotometric method used as standard analytical technique recommended by the Brazilian Pharmacopoeia.

Influence Of Delivery Method On Neuroprotection By Bone Marrow Mononuclear Cell Therapy Following Ventral Root Reimplantation With Fibrin Sealant.

The present work compared the local injection of mononuclear cells to the spinal cord lateral funiculus with the alternative approach of local delivery with fibrin sealant after ventral root avulsion (VRA) and reimplantation. For that, female adult Lewis rats were divided into the following groups: avulsion only, reimplantation with fibrin sealant; root repair with fibrin sealant associated with mononuclear cells; and repair with fibrin sealant and injected mononuclear cells. Cell therapy resulted in greater survival of spinal motoneurons up to four weeks post-surgery, especially when mononuclear cells were added to the fibrin glue. Injection of mononuclear cells to the lateral funiculus yield similar results to the reimplantation alone. Additionally, mononuclear cells added to the fibrin glue increased neurotrophic factor gene transcript levels in the spinal cord ventral horn. Regarding the motor recovery, evaluated by the functional peroneal index, as well as the paw print pressure, cell treated rats performed equally well as compared to reimplanted only animals, and significantly better than the avulsion only subjects. The results herein demonstrate that mononuclear cells therapy is neuroprotective by increasing levels of brain derived neurotrophic factor (BDNF) and glial derived neurotrophic factor (GDNF). Moreover, the use of fibrin sealant mononuclear cells delivery approach gave the best and more long lasting results.

Uv-vis Spectra As An Alternative To The Lowry Method For Quantify Hair Damage Induced By Surfactants.

It is well known that long term use of shampoo causes damage to human hair. Although the Lowry method has been widely used to quantify hair damage, it is unsuitable to determine this in the presence of some surfactants and there is no other method proposed in literature. In this work, a different method is used to investigate and compare the hair damage induced by four types of surfactants (including three commercial-grade surfactants) and water. Hair samples were immersed in aqueous solution of surfactants under conditions that resemble a shower (38 °C, constant shaking). These solutions become colored with time of contact with hair and its UV-vis spectra were recorded. For comparison, the amount of extracted proteins from hair by sodium dodecyl sulfate (SDS) and by water were estimated by the Lowry method. Additionally, non-pigmented vs. pigmented hair and also sepia melanin were used to understand the washing solution color and their spectra. The results presented herein show that hair degradation is mostly caused by the extraction of proteins, cuticle fragments and melanin granules from hair fiber. It was found that the intensity of solution color varies with the charge density of the surfactants. Furthermore, the intensity of solution color can be correlated to the amount of proteins quantified by the Lowry method as well as to the degree of hair damage. UV-vis spectrum of hair washing solutions is a simple and straightforward method to quantify and compare hair damages induced by different commercial surfactants.

Graded Meshes In Bio-thermal Problems With Transmission-line Modeling Method.

In this study, the transmission-line modeling (TLM) applied to bio-thermal problems was improved by incorporating several novel computational techniques, which include application of graded meshes which resulted in 9 times faster in computational time and uses only a fraction (16%) of the computational resources used by regular meshes in analyzing heat flow through heterogeneous media. Graded meshes, unlike regular meshes, allow heat sources to be modeled in all segments of the mesh. A new boundary condition that considers thermal properties and thus resulting in a more realistic modeling of complex problems is introduced. Also, a new way of calculating an error parameter is introduced. The calculated temperatures between nodes were compared against the results obtained from the literature and agreed within less than 1% difference. It is reasonable, therefore, to conclude that the improved TLM model described herein has great potential in heat transfer of biological systems.