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Coordinated electrical activation of the heart is essential for the maintenance of a regular cardiac rhythm and effective contractions. Action potentials spread from one cell to the next via gap junction channels. Because of the elongated shape of cardiomyocytes, longitudinal resistivity is lower than transverse resistivity causing electrical anisotropy. Moreover, non-uniformity is created by clustering of gap junction channels at cell poles and by non-excitable structures such as collagenous strands, vessels or fibroblasts. Structural changes in cardiac disease often affect passive electrical properties by increasing non-uniformity and altering anisotropy. This disturbs normal electrical impulse propagation and is, consequently, a substrate for arrhythmia. However, to investigate how these structural changes lead to arrhythmias remains a challenge. One important mechanism, which may both cause and prevent arrhythmia, is the mismatch between current sources and sinks. Propagation of the electrical impulse requires a sufficient source of depolarizing current. In the case of a mismatch, the activated tissue (source) is not able to deliver enough depolarizing current to trigger an action potential in the non-activated tissue (sink). This eventually leads to conduction block. It has been suggested that in this situation a balanced geometrical distribution of gap junctions and reduced gap junction conductance may allow successful propagation. In contrast, source-sink mismatch can prevent spontaneous arrhythmogenic activity in a small number of cells from spreading over the ventricle, especially if gap junction conductance is enhanced. Beside gap junctions, cell geometry and non-cellular structures strongly modulate arrhythmogenic mechanisms. The present review elucidates these and other implications of passive electrical properties for cardiac rhythm and arrhythmogenesis.

Tato disertační práce analyzuje artefakty v NMR obrazech. V lékařské praxi mohou artefakty zabránit diagnostice patologických tkání, a proto je třeba tyto nežádoucí jevy odstranit. Vzhledem k nutnosti vyloučit artefakty způsobené nehomogenitou statického magnetického pole jsou v dané souvislosti diskutovány také nové možnosti měření deformací. Práce popisuje metodu pro měření základního pole i RF pole a jejich nehomogenit na základě měření MR obrazů T2 a T2*. Metoda kombinuje akviziční postupy pro spinové a gradientní echo za účelem rozlišení relaxačních časů T2 a T2*. V této souvislosti také vyvstává potřeba provést exponenciální aproximaci relaxačního procesu. Experimentální výsledky pro plastové i měděné vzorky jsou prezentovány v příslušné části práce. Pokud jde o vlastní členení popisovaných jevů, je třeba uvést, že významný problém představují artefakty způsobené magnetickou susceptibilitou. Různé hodnoty magnetické vodivosti na rozhraní mezi dvěma materiály mohou způsobit deformaci magnetického pole, přičemž může dojít i k úplné ztrátě signálu.

The loss of efficiency and performance of bioprocesses on scale-up is well known, but not fully understood. This work addresses this problem, by studying the effect of some fermentation gradients (pH, glucose and oxygen) at a larger scale in a bench-scale two compartment reactor (PFR + STR) using the cadaverine-producing recombinant bacterium, Corynebacterium glutamicum DM1945 Δact3 Ptuf-ldcC_OPT. The initial scale down strategy increased the magnitude of these gradients by only increasing the mean cell residence time in the plug flow reactor (τ_PFR). The cell growth and product related rate constants were compared as the τ_PFR was increased; differences were significant in some cases, but only up to 2 min residence time. For example, losses in cadaverine productivity when compared to the control fed-batch fermentation on average for the τ_PFR of 1 min, 2 min and 5 min were 25 %, 42 % and 46 % respectively. This indicated that the increasing the τ_PFR alone does not necessarily increase the magnitude of fermentation gradients. The new scale-down strategy developed here, increased the magnitude of fermentation gradients by not only increasing the τ_PFR, but also considering the mean frequency at which the bacterial cells entered the PFR section (f_m). The f_m was kept constant by reducing the broth volume in the STR. Hence, the bacterial cells also spent shorter times in the well mixed STR, as the τ_PFR was increased (hypothesised as giving the bacterial cells less time to recover the non-ideal PFR section of the SDR). On adoption of this strategy cadaverine productivity decreases for the τ_PFR of 1 min, 2 min and 5 min were 25 %, 32 % and 53 % respectively. Thus, highlighting that loss in performance is most likely to occur as the magnitude of heterogeneity within the fermentation environment increases. However, Corynebacterium glutamicum DM1945 Δact3 Ptuf-ldcC_OPT did show some resilience in its biomass productivity. It was only marginally affected in the harshest of conditions simulated here.

Content Based Image Retrieval (CBIR) is an important research area in the field of multimedia information retrieval. The application of CBIR in the medical domain has been attempted before, however the use of CBIR in medical diagnostics is a daunting task. The goal of diagnostic medical image retrieval is to provide diagnostic support by displaying relevant past cases, along with proven pathologies as ground truths. Moreover, medical image retrieval can be extremely useful as a training tool for medical students and residents, follow-up studies, and for research purposes. Despite the presence of an impressive amount of research in the area of CBIR, its acceptance for mainstream and practical applications is quite limited. The research in CBIR has mostly been conducted as an academic pursuit, rather than for providing the solution to a need. For example, many researchers proposed CBIR systems where the image database consists of images belonging to a heterogeneous mixture of man-made objects and natural scenes while ignoring the practical uses of such systems. Furthermore, the intended use of CBIR systems is important in addressing the problem of "Semantic Gap". Indeed, the requirements for the semantics in an image retrieval system for pathological applications are quite different from those intended for training and education. Moreover, many researchers have underestimated the level of accuracy required for a useful and practical image retrieval system. The human eye is extremely dexterous and efficient in visual information processing; consequently, CBIR systems should be highly precise in image retrieval so as to be useful to human users. Unsurprisingly, due to these and other reasons, most of the proposed systems have not found useful real world applications. In this dissertation, an attempt is made to address the challenging problem of developing a retrieval system for medical diagnostics applications. More specifically, a system for semantic retrieval of Magnetic Resonance (MR) images in 3D brain volumes is proposed. The proposed retrieval system has a potential to be useful for clinical experts where the human eye may fail. Previously proposed systems used imprecise segmentation and feature extraction techniques, which are not suitable for precise matching requirements of the image retrieval in this application domain. This dissertation uses multiscale representation for image retrieval, which is robust against noise and MR inhomogeneity. In order to achieve a higher degree of accuracy in the presence of misalignments, an image registration based retrieval framework is developed. Additionally, to speed-up the retrieval system, a fast discrete wavelet based feature space is proposed. Further improvement in speed is achieved by semantically classifying of the human brain into various "Semantic Regions", using an SVM based machine learning approach. A novel and fast identification system is proposed for identifying a 3D volume given a 2D image slice. To this end, we used SVM output probabilities for ranking and identification of patient volumes. The proposed retrieval systems are tested not only for noise conditions but also for healthy and abnormal cases, resulting in promising retrieval performance with respect to multi-modality, accuracy, speed and robustness. This dissertation furnishes medical practitioners with a valuable set of tools for semantic retrieval of 2D images, where the human eye may fail. Specifically, the proposed retrieval algorithms provide medical practitioners with the ability to retrieve 2D MR brain images accurately and monitor the disease progression in various lobes of the human brain, with the capability to monitor the disease progression in multiple patients simultaneously. Additionally, the proposed semantic classification scheme can be extremely useful for semantic based categorization, clustering and annotation of images in MR brain databases. This research framework may evolve in a natural progression towards developing more powerful and robust retrieval systems. It also provides a foundation to researchers in semantic based retrieval systems on how to expand existing toolsets for solving retrieval problems.

There is a growing consensus that life-threatening cardiac arrhythmias like ventricular tachycardia (VT) or ventricular fibrillation (VF) arise because of the formation of spiral waves of electrical activation in cardiac tissue; unbroken spiral waves are associated with VT and broken ones with VF. Several experimental studies have shown that inhomogeneities in cardiac tissue can have dramatic effects on such spiral waves. In this thesis we try to understand these experimental results by carrying out detailed and systematic studies of the interaction of spiral waves with different types of inhomogeneities in mathematical models for cardiac tissue. In Chapter 1 we begin with a general introduction to cardiac arrhythmias, the cardiac conduction system, and the connection between electrical activation waves in cardiac tissue and cardiac arrhythmias. As we have noted above, VT and VF are believed to be associated with spiral waves of electrical activation on cardiac tissue; such spiral waves form because cardiac tissue is an excitable medium. Thus we give an overview of excitable media, in which sub-threshold perturbations decay but super-threshold perturbations lead to an action potential that consists of a rapid stage of depolarization of cardiac cells followed by a slow phase of repolarization. During this repolarization phase the cells are refractory. We then give an overview of earlier studies of the effects of inhomogeneities in cardiac tissue; and we end with a brief description of the principal problems we study here. Chapter 2 describes the models we use in our work. We start with a general introduction to the cable equation and then discuss the Hodgkin-Huxley-formalism for the transport of ions across a cell membrane through voltage-gated ion channels. We then describe in detail the three models that we use for cardiac tissue, which are, in order of increasing complexity, the Panfilov model, the Luo Rudy Phase I (LRI) model, and the reduced Priebe Beuckelmann (RPB)model. We then give the numerical schemes we use for solving these model equations and the initial conditions that lead to the formation of spiral waves. For all these models we give representative results from our simulations and compare the states with spiral turbulence. In Chapter 3 we investigate the effects of conduction inhomogeneities (obstacles) in the three models introduced in Chapter 2. We outline first the experimental results that have provided the motivation for our study. We then discuss how we introduce obstacles in our simulations of the Panffilov, LRI, and RPB models for cardiac tissue. Next we present the results of our numerical studies of the effects, on spiral-wave dynamics, of the sizes, shapes, and positions of the obstacles. Our Principal result is that spiral-wave dynamics in these models depends sensitively on the position of the obstacle. We find, in particular, that, merely by changing the position of a conduction inhomogeneity, we may convert spiral turbulence (the analogue in our models of VF) to a single rotating spiral (the analogue of VT) anchored to the obstacle or vice versa; even more exciting is the possibility that, at the boundary between these two types of behaviour, we find a quiescent state Q with no spiral waves. Thus our study obtains all the possible qualitative behaviours found in experiments, namely, (1) VF might persist even in the presence of an obstacle, (2) it might be suppressed partially and become VT, or (3) it might be eliminated completely. In Chapter 4 we extend our work on conduction inhomogeneities (Chapter 3) to ionic inhomogeneities. Unlike conduction inhomogeneities, ionic inhomogeneities allow the conduction of activation waves. We find, nevertheless, that they too can lead to the anchoring of spiral waves or even the complete elimination of spiral-wave turbulence. Since spiral waves can enter the region in which there is an ionic inhomogeneity, their behaviours in the presence of such an inhomogeneity are richer than those with conduction inhomogeneities. We find, in particular, that a single spiral wave anchored at an ionic inhomogeneity can show temporal evolution that may be periodic, quasiperiodic, or even chaotic. In the last case the spiral wave shows a chaotic pattern inside the ionic inhomogeneity and a regular one outside it. Defibrillation is the control of arrhythmias such as VF. Most often defibrillation is effected electrically by administering a shock, either externally or via an internally implanted defibrillator. The development of low-amplitude defibrillation schemes, which minimise the deleterious effects of the applied shock, is a major challenge in the treatment of cardiac arrhythmias. Numerical studies of models for cardiac tissue provide us with convenient means of studying the elimination of spiral-wave turbulence by the application of external electrical stimuli; this is the numerical analogue of defibrillation. Over the years some low-amplitude defibrillation schemes have been suggested on the basis of such numerical studies. In Chapter 5 we discuss two such schemes that have been shown to suppress spiral-wave turbulence in two-dimensional models for cardiac tissue and also scroll-wave turbulence in three-dimensional models. One of these schemes uses local electrical pacing, typically in the centre of the simulation domain; the other applies the external electrical stimuli over a mesh. We study the efficacy of these schemes in the presence of conduction inhomogeneities. We find, in particular, that the local-pacing scheme, though effective in a homogeneous simulation domain, fails to control spiral turbulence in the presence of an obstacle and, indeed, might even facilitate spiral-wave break up. By contrast, the second scheme, which uses a mesh, succeeds in eliminating spiral-wave turbulence even in the presence of an obstacle. We end with some concluding remarks about the possible experimental implications of our study in Chapter 6.

Content Based Image Retrieval (CBIR) is an important research area in the field of multimedia information retrieval. The application of CBIR in the medical domain has been attempted before, however the use of CBIR in medical diagnostics is a daunting task. The goal of diagnostic medical image retrieval is to provide diagnostic support by displaying relevant past cases, along with proven pathologies as ground truths. Moreover, medical image retrieval can be extremely useful as a training tool for medical students and residents, follow-up studies, and for research purposes. Despite the presence of an impressive amount of research in the area of CBIR, its acceptance for mainstream and practical applications is quite limited. The research in CBIR has mostly been conducted as an academic pursuit, rather than for providing the solution to a need. For example, many researchers proposed CBIR systems where the image database consists of images belonging to a heterogeneous mixture of man-made objects and natural scenes while ignoring the practical uses of such systems. Furthermore, the intended use of CBIR systems is important in addressing the problem of "Semantic Gap". Indeed, the requirements for the semantics in an image retrieval system for pathological applications are quite different from those intended for training and education. Moreover, many researchers have underestimated the level of accuracy required for a useful and practical image retrieval system. The human eye is extremely dexterous and efficient in visual information processing; consequently, CBIR systems should be highly precise in image retrieval so as to be useful to human users. Unsurprisingly, due to these and other reasons, most of the proposed systems have not found useful real world applications. In this dissertation, an attempt is made to address the challenging problem of developing a retrieval system for medical diagnostics applications. More specifically, a system for semantic retrieval of Magnetic Resonance (MR) images in 3D brain volumes is proposed. The proposed retrieval system has a potential to be useful for clinical experts where the human eye may fail. Previously proposed systems used imprecise segmentation and feature extraction techniques, which are not suitable for precise matching requirements of the image retrieval in this application domain. This dissertation uses multiscale representation for image retrieval, which is robust against noise and MR inhomogeneity. In order to achieve a higher degree of accuracy in the presence of misalignments, an image registration based retrieval framework is developed. Additionally, to speed-up the retrieval system, a fast discrete wavelet based feature space is proposed. Further improvement in speed is achieved by semantically classifying of the human brain into various "Semantic Regions", using an SVM based machine learning approach. A novel and fast identification system is proposed for identifying a 3D volume given a 2D image slice. To this end, we used SVM output probabilities for ranking and identification of patient volumes. The proposed retrieval systems are tested not only for noise conditions but also for healthy and abnormal cases, resulting in promising retrieval performance with respect to multi-modality, accuracy, speed and robustness. This dissertation furnishes medical practitioners with a valuable set of tools for semantic retrieval of 2D images, where the human eye may fail. Specifically, the proposed retrieval algorithms provide medical practitioners with the ability to retrieve 2D MR brain images accurately and monitor the disease progression in various lobes of the human brain, with the capability to monitor the disease progression in multiple patients simultaneously. Additionally, the proposed semantic classification scheme can be extremely useful for semantic based categorization, clustering and annotation of images in MR brain databases. This research framework may evolve in a natural progression towards developing more powerful and robust retrieval systems. It also provides a foundation to researchers in semantic based retrieval systems on how to expand existing toolsets for solving retrieval problems.

Λαμβάνοντας υπόψη, ότι η αποδοτική σχεδίαση, αξιολόγηση και εγκατάσταση ενός ασύρματου δικτύου επικοινωνιών, απαιτούν τον ακριβή χαρακτηρισμό του καναλιού διάδοσης και ειδικότερα των διαλείψεων μικρής και μεγάλης κλίμακας, το αντικείμενο μελέτης της παρούσας Διδακτορικής Διατριβής (ΔΔ) εστιάζεται στη μοντελοποίηση των διαλείψεων με νέα γενικότερα στατιστικά μοντέλα και απαρτίζεται από τρεις θεματικές ενότητες που αφορούν α) μοντέλα παρουσία συνιστώσας Οπτικής Επαφής (ΟΕ), β) μοντέλα που χαρακτηρίζονται από απουσία συνιστώσας ΟΕ καθώς και γ) χρήσιμες στατιστικές εκφράσεις για τη περιγραφή του τυχαίου θορύβου FM και της μέσης χωρητικότητας του καναλιού για μερικά από τα νέα κανάλια (α-μ, α-η-μ, α-κ-μ και α-λ-η-μ). Με βάση την υφιστάμενη διεθνή βιβλιογραφία, οι κατανομές που περιγράφουν κανάλια διαλείψεων δεν είναι αρκετά ευέλικτες και πολλές φορές είναι ανεπαρκείς για τη προσαρμογή αυτών σε δεδομένα προερχόμενα από πειραματικές μετρήσεις της έντασης ανά μονάδα επιφάνειας του ηλεκτρομαγνητικού πεδίου, τόσο για κανάλια εσωτερικών, όσο και για κανάλια υπαίθριων (εξωτερικών) χώρων. Έτσι, αρχικά δίδεται ο φυσικός μηχανισμός για την ερμηνεία κάθε νέου παρουσιαζόμενου μοντέλου. Χρησιμοποιώντας το μαθηματικό φορμαλισμό που προκύπτει από την μοντελοποίηση του ασύρματου καναλιού μέσω διαφόρων μιγαδικών Gaussian διεργασιών με διαφορετικές ιδιότητες, παρέχονται χρήσιμες εκφράσεις για την περιγραφή και αξιολόγηση των ψηφιακών συστημάτων επικοινωνιών που λειτουργούν σε περιβάλλοντα διαλείψεων. Στη συνέχεια, παρουσιάζεται η μελέτη που αφορά μοντέλα που υποθέτουν ότι η συνιστώσα πολυδιόδευσης συνυπάρχει με συνιστώσα. Έπειτα, πραγματοποιείται μελέτη μοντέλων που λειτουργούν σε συνθήκες διαλείψεων, όπου δεν υφίσταται συνιστώσα ΟΕ. Στη συνέχεια της ΔΔ, αναφορικά με κάποια από τα μοντέλα που παρουσιάστηκαν, πραγματοποιείται μελέτη και διερεύνηση του τυχαίου θορύβου FM και της Μέσης Χωρητικότητας του Καναλιού (ΜΧΚ). / The effective design, assessment, and installation of a wireless radio network require an accurate characterization of the propagation channel and, in particular, the small and large scale fading. By taking this into consideration, the subject of this Philosophy Diploma (PhD) dissertation is summarized in the characterization of fading with new more general statistical models and it is composed from three thematic units that concern: a) models under LOS conditions, v) models that are characterized by lack of a LOS component as well as c) useful statistical expressions for the description of random noise FM and average channel capacity for some of the new channels. A important amount of scientific work shows that the existing distributions are not enough flexible and many times are insufficient for the adaptation in data coming from experimental measurements of intensity per unit of surface of the electromagnetic field for both indoor and outdoor channels. Based on this fact, the objective of the Thesis was the production of new more general models with always natural background. Thus, initially, the natural mechanism is given for the interpretation of each new presented model. Using the mathematic formalism that results from the modelling of wireless channel via various complex Gaussian processes with different attributes, useful expressions are provided for the description and evaluation of digital communication systems that operate in fading environments. Consequently, initially, the basic theoretical background is presented that is rendered useful and essential for the study of fading channels. Next, a study is presented that concerns models that assume that the mulitpath part coexists with a LOS component. Then, a study of models, which assume NLOS conditions, takes place. In the next part of the PhD, in regard to some of the presented models, a study of random noise FM and ACC takes place.

La problématique suivie dans ce travail est la détermination des propriétés effectives, élastiques et conductivité, de matériaux poreux hétérogènes tels que des roches, les roches oolithiques en particulier, en relation avec leur microstructure. Le cadre théorique adopté est celui de l’homogénéisation des milieux hétérogènes aléatoires et on suit les approches par tenseurs d’Eshelby. Ces approches sont basées sur la résolution des problèmes d’Eshelby : le problème de l’inclusion (premier problème) et le problème de l’inhomogénéité (second problème) isolées dans un milieu infini. La solution de ces problèmes de référence est analytique, en élasticité linéaire isotrope et en diffusion linéaire stationnaire, dans le cas d’inhomogénéités 2D ou 3D de type ellipsoïde. Elle conduit à la définition de tenseurs caractérisant les interactions entre l’inclusion/inhomogénéité et le milieu environnant. On utilise dans ce travail les tenseurs de contribution relatifs à une inhomogénéité isolée, définis par Kachanov et Sevostianov 2013, contributions à la souplesse (élasticité) et à la résistivité (conductivité). Ces tenseurs au cœur des méthodes d’homogénéisation de type EMA (Effective Medium Approximation), et en particulier les schémas NIA (Non Interaction Approximation), Mori Tanaka et Maxwell. Ce travail est centré sur la caractérisation des paramètres géométriques microstructuraux dont l’influence sur les propriétés effectives est majeure. On étudie en particulier les effets de forme des inhomogénéités, la nouveauté est l’aspect 3D. Les observations microstructurales de roches oolithiques, dont le calcaire de référence de Lavoux, mettent en évidence des hétérogénéités de forme 3D et concave. En particulier les matériaux de remplissage inter-oolithes, pores ou calcite syntaxiale. Ces formes peuvent être observées sur d’autres matériaux hétérogènes et ont été peu étudiées dans le cadre micromécanique. Cela nécessite de considérer des formes non ellipsoïdales et de résoudre numériquement les problèmes d’Eshelby. Le cœur de ce travail est consacré à la détermination des tenseurs de contribution d’inhomogénéités 3D convexes ou concaves de type supersphère (à symétrie cubique) ou supersphéroïde (à symétrie de révolution). Le premier problème d’Eshelby a été résolu, dans le cas de la supersphère, par intégration numérique de la fonction de Green exacte (solution de Kelvin dans le cas isotrope) sur la surface de l’inclusion. Des modélisations 3D aux éléments finis ont permis de résoudre le second problème d’Eshelby et d’obtenir les tenseurs de contribution à la souplesse et à la résistivité pour les superphère et supersphéroïde. Sur la base des résultats numériques, des relations analytiques simplifiées ont été proposées pour les tenseurs de contribution sous forme de fonctions des paramètres élastiques des constituants et du paramètre adimensionnel p caractérisant la concavité. Un résultat important, dans le cas de la superphère et dans le domaine concave, est l’identification d’un même paramètre géométrique pour les tenseurs de contribution à la souplesse et à la résistivité. Les résultats numériques et théoriques obtenus sont appliqués à deux problèmes : l’estimation de la conductivité thermique effective de roches calcaires oolithiques d’une part et l’étude de l’extension des relations dites de substitution définies par Kachanov et Sevostianov 2007 au cas non ellipsoïdal d’autre part. Pour le premier problème, un modèle micromécanique de type Maxwell, à deux échelles a permis de retrouver les résultats expérimentaux disponibles dans la littérature, en en particulier l’influence de la porosité sur la conductivité thermique effective dans les cas sec et humide. Dans le cas du second problème, les résultats obtenus ont permis de montrer que la validité de relations de substitution est restreinte, dans le cas non ellipsoïdal et en considérant une forme d’inhomogénéité de type supersphère, au domaine convexe seulement / Focusing on the effect of shape factor on the overall effective properties of heterogeneous materials, the 1st and the 2nd Eshelby problem related to 3-D non-ellipsoidal inhomogeneities with a specific application to oolitic rocks have been discussed in the current work. Particular attention is focused on concaves shapes such as supersphere and superspheroid. For rocks, they may represent pores or solid mineral materials embbeded in the surrounding rock matrix. In the 1st Eshelby problem, Eshelby tensor interrelates the resulting strain about inclusion and eigenstrain that would have been experienced inside the inclusion without any external contraire. Calculations of this tensor for superspherical pores– both concave and convex shapes – are performed numerically. Results are given by an integration of derivation of Green’s tensor over volume of the inclusion. Comparisons with the results of Onaka (2001) for convex superspheres show that the performed calculations have an accuracy better than 1%. The current calculations have been done to complete his results. In the 2nd Eshelby problem, property contribution tensors that characterizes the contribution of an individual inhomogeneity on the overall physical properties have been numerically calculated by using Finite Element Method (FEM). Property contribution tensors of 3D non ellipsoidal inhomogeneities, such as supersphere and superspheroid, have been obtained. Simplified analytical relations have been derived for both compliance contribution tensor and resistivity contribution tensor. Property contribution tensors have been used to estimate effective elastic properties and effective conductivity of random heterogeneous materials, in the framework of Non-Interaction Approximation, Mori-Tanaka scheme and Maxwell scheme. Two applications in the field of geomechanics and geophysics have been done. The first application concerns the evaluation of the effective thermal conductivity of oolitic rocks is performed to complete the work of Sevostianov and Giraud (2013) for effective elastic properties. A two step homogenization model has been developed by considering two distinct classes of pores: microporosity (intra oolitic porosity) and meso porosity (inter oolitic porosity). Maxwell homogenization scheme formulated in terms of resistivity contribution tensor has been used for the transition from meso to macroscale. Concave inter oolitic pores of superspherical shape have been taken into account by using resistivity contribution tensor obtained thanks to FEM modelling. Two limiting cases have been considered: ‘dry case’ (air saturated pores) and ‘wet case’ (water liquid saturated pores). Comparisons with experimental data show that variations of effective thermal conductivity with porosity in the most sensitive case of air saturated porosity are correctly reproduced. Applicability of the replacement relations, initially derived by Sevostianov and Kachanov (2007) for ellipsoidal inhomogeneities, to non-ellipsoidal ones has been investigated. It it the second application of newly obtained results on property contribution tensors. We have considered 3D inhomogeneities of superspherical shape. From the results, it has been seen that these relations are valid only in the convex domain, with an accuracy better than 10%. Replacement relations can not be used in the concave domain for such particular 3D shape