Towards Prediction of Blood Flow in Coiled Aneurysms Before Treatment: A Porous Media Approach.

Modeling blood flow in aneurysms treated with coils could be used to understand the complete embolization of the aneurysm, through thrombus formation that fills the entire sac. Modeling of the endovascular coil mass as a porous medium is a technique that allows for study of aneurysm hemodynamics, efficiently for patient-specific treatment outcome predictions. Models in the literature use mean porosity of coils in the aneurysmal volume, proving inadequate for outcome prediction. However, models that consider heterogeneous porosity distribution have shown more accurate hemodynamics. We recently published the porous crown model, considering the heterogeneous coil mass distribution, validated on two patients. This study aims (i) to validate the porous crown model for a larger cohort (eight patients), and (ii) to propose a porous medium model translatable to clinical practice in treatment planning. We analyzed the porosity distribution of the endovascular coils deployed inside the cerebral aneurysm phantoms of eight patients using 3D x-ray synchrotron images. The permeability and inertial factor of the porous crown model are calculated using previously published methodology. We propose a new "bilinear" porous model, that uses the same hypothesis, but the permeability and inertial factor can be defined from just basic information available in the neuro-suite, i.e., the aneurysmal sac volume and the coil volume fraction targeted by the neurosurgeon. These two models are compared to the coil-resolved simulations, considered as the gold standard. The results show that both the porous crown model and the bilinear model produce similarly accurate hemodynamics in the aneurysm. The error in the standard (mean porosity) porous model is 66%, whereas the error of the bilinear model is 26%, compared to the coil-resolved. The bilinear model is promising as a means of treatment outcome prediction at time of intervention.

Modeling Flow in Cerebral Aneurysm After Coils Embolization Treatment: A Realistic Patient-Specific Porous Model Approach.

PURPOSE: Computational fluid dynamics (CFD) has been used to evaluate the efficiency of endovascular treatment in coiled cerebral aneurysms. The explicit geometry of the coil mass cannot typically be incorporated into CFD simulations since the coil mass cannot be reconstructed from clinical images due to its small size and beam hardening artifacts. The existing methods use imprecise porous medium representations. We propose a new porous model taking into account the porosity heterogeneity of the coils deployed in the aneurysm. METHODS: The porosity heterogeneity of the coil mass deployed inside two patients' cerebral aneurysm phantoms is first quantified based on 3D X-ray synchrotron images. These images are also used to compute the permeability and the inertial factor arising in porous models. A new homogeneous porous model (porous crowns model), considering the coil's heterogeneity, is proposed to recreate the flow within the coiled aneurysm. Finally, the validity of the model is assessed through comparisons with coil-resolved simulations. RESULTS: The strong porosity gradient of the coil measured close to the aneurysmal wall is well captured by the porous crowns model. The permeability and the inertial factor values involved in this model are closed to the ideal homogeneous porous model leading to a mean velocity in the aneurysmal sac similar as in the coil-resolved model. CONCLUSION: The porous crowns model allows for an accurate description of the mean flow within the coiled cerebral aneurysm.

Investigating the influence of freezing rate and frozen storage conditions on a model sponge cake using synchrotron X-rays micro-computed tomography.

Synchrotron X-rays micro-computed tomography was applied to visualize and quantify 3D ice crystal changes into a model sponge cake after freezing and subsequent frozen storage. Model sponge cake samples were submitted to two different freezing rates (fast: 17.2 °C min-1 and slow: 0.3 °C min-1), then stored at constant and fluctuating temperatures over a two weeks period. 3D images were acquired at frozen state thanks to a thermostated cell (CellStat) and processed using a grey level based segmentation method. Image analysis revealed that the ice volume fraction is conserved during storage but ice crystal size and location change whatever the freezing rate and the storage conditions. Maximum local thicknesses increase both inside (from 20 µm to 50 µm) and outside (from 47 µm to 70 µm) the matrix during the fourteen days storage period. Both specific surface areas between starch and ice (SSAice/starch) and between air and ice (SSAair/ice) also evolve with storage duration: SSAice/starch decreases up to - 30 % while SSAair/ice increases up to + 13 % depending on the freezing rates and the storage conditions. These results highlighted that, during storage, ice crystals evolve according to two different mechanisms depending on the freezing rate: fast freezing leads to a local redistribution of water both within the starch matrix and within the pores, while slow freezing results in both local redistribution within the starch matrix and water migration towards the pores. In addition, stable storage temperatures favor local water redistribution whereas water migration from the starch matrix towards the pores was greater in the case of fluctuating storage temperatures. This study shows that freezing and frozen storage conditions have a synergistic effect on the microstructure evolution of sponge cake due to recrystallization phenomena.

Individual fibre separation in 3D fibrous materials imaged by X-ray tomography.

Modelling the physical behaviour of fibrous materials still remains a great challenge because it requires to evaluate the inner structure of the different phases at the phase scale (fibre or matrix) and the at constituent scale (fibre). X-ray computed tomography (CT) imaging can help to characterize and to model these structures, since it allows separating the phases, based on the grey level of CT scans. However, once the fibrous phase has been isolated, automatically separating the fibres from each other is still very challenging. This work aims at proposing a method which allows separating the fibres and localizing the fibre-fibre contacts for various fibres geometries, that is: straight or woven fibres, with circular or non-circular cross sections, in a way that is independent of the fibres orientations. This method uses the local orientation of the structure formed by the fibrous phase and then introduces the misorientation angle. The threshold of this angle is the only parameter required to separate the fibres. This paper investigates the efficiency of the proposed algorithm in various conditions, for instance by changing the image resolution or the fibre tortuosity on synthetic images. Finally, the proposed algorithm is applied to real images or samples made up of synthetic solid fibres.

First visualisation of bacterial biofilms in 3D porous media with neutron microtomography without contrast agent.

Characterising bacterial biofilm growth in porous media is important for developing reliable numerical models of biofouling in industrial biofilters. One of the promising imaging methods to do that has been a recent successful application of X-ray microtomography. However, this technique requires a contrast agent (1-chloronaphtalene, for example) to distinguish biofilm from the liquid phase, which raises concern about biofilm disruption and impaired image interpretation. To overcome these drawbacks, we tested a new approach based on neutron tomography (NT), which does not need a contrast agent, by imaging two types of porous media (polytetrafluoroethylene - PTFE - and clay beads of various diameters) in glass or PTFE tubes in which bacterial biofilms were grown for 7 days and by comparing these images with the ones obtained with X-ray microtomography. NT images showed that the biofilm formed preferentially around the beads and at bead/bead interface. Visual comparison of both imaging techniques showed consistent biofilm spatial distributions and that the contrasting agent did not significantly disrupt the biofilm. NT images, on the other hand, were still too noisy to allow quantitative measurements. Therefore, X-ray microtomography (provided it uses non-disruptive contrast agents) seems to provide more reliable microstructural descriptors.

3D Characterization of Sponge Cake as Affected by Freezing Conditions Using Synchrotron X-ray Microtomography at Negative Temperature.

In this study, the microstructural evolution of a non-reactive porous model food (sponge cake) during freezing was investigated. Sponge cake samples were frozen at two different rates: slow freezing (0.3 °C min-1) and fast freezing (17.2 °C min-1). Synchrotron X-ray microtomography (µ-CT) and cryo-scanning electron microscopy (Cryo-SEM) were used to visualize and analyze the microstructure features. The samples were scanned before and after freezing using a specific thermostated cell (CellStat) combined with the synchrotron beamline. Cryo-SEM and 3D µ-CT image visualization allowed a qualitative analysis of the ice formation and location in the porous structure. An image analysis method based on grey level was used to segment the three phases of the frozen samples: air, ice and starch. Volume fractions of each phase, ice local thickness and shape characterization were determined and discussed according to the freezing rates.

Lagrangian Trajectory Simulation of Platelets and Synchrotron Microtomography Augment Hemodynamic Analysis of Intracranial Aneurysms Treated With Embolic Coils.

As frequency of endovascular treatments for intracranial aneurysms increases, there is a growing need to understand the mechanisms for coil embolization failure. Computational fluid dynamics (CFD) modeling often simplifies modeling the endovascular coils as a homogeneous porous medium (PM), and focuses on the vascular wall endothelium, not considering the biomechanical environment of platelets. These assumptions limit the accuracy of computations for treatment predictions. We present a rigorous analysis using X-ray microtomographic imaging of the coils and a combination of Lagrangian (platelet) and Eulerian (endothelium) metrics. Four patient-specific, anatomically accurate in vitro flow phantoms of aneurysms are treated with the same patient-specific endovascular coils. Synchrotron tomography scans of the coil mass morphology are obtained. Aneurysmal hemodynamics are computationally simulated before and after coiling, using patient-specific velocity/pressure measurements. For each patient, we analyze the trajectories of thousands of platelets during several cardiac cycles, and calculate residence times (RTs) and shear exposure, relevant to thrombus formation. We quantify the inconsistencies of the PM approach, comparing them with coil-resolved (CR) simulations, showing the under- or overestimation of key hemodynamic metrics used to predict treatment outcomes. We fully characterize aneurysmal hemodynamics with converged statistics of platelet RT and shear stress history (SH), to augment the traditional wall shear stress (WSS) on the vascular endothelium. Incorporating microtomographic scans of coil morphology into hemodynamic analysis of coiled intracranial aneurysms, and augmenting traditional analysis with Lagrangian platelet metrics improves CFD predictions, and raises the potential for understanding and clinical translation of computational hemodynamics for intracranial aneurysm treatment outcomes.

Reconstructing patient-specific cerebral aneurysm vasculature for in vitro investigations and treatment efficacy assessments.

Perianeurysmal hemodynamics play a vital role in the initiation, growth and rupture of intracranial aneurysms. In vitro investigations of aneurysmal hemodynamics are helpful to visualize and measure blood flow, and aiding surgical planning approaches. Improving in vitro model creation can improve the feasibility and accuracy of hemodynamic investigations and surgical planning, improving clinical value. In this study, in vitro models were created from three-dimensional rotational angiography (3DRA) of six patients harboring intracranial aneurysms using a multi-step process involving 3D printing, index of refraction matching and silicone casting that renders the models transparent for flow visualization. Each model was treated with the same commercially-available, patient-specific, endovascular devices (coils and/or stents). All models were scanned by synchrotron X-ray microtomography to obtain high-resolution imaging of the vessel lumen, aneurysmal sac and endovascular devices. Dimensional accuracy was compared by quantifying the differences between the microtomographic reconstructions of the fabricated phantoms and the original 3DRA obtained during patient treatment. True-scale in vitro flow phantoms were successfully created for all six patients. Optical transparency was verified by using an index of refraction matched working fluid that replicated the mechanical behavior of blood. Synchrotron imaging of vessel lumen, aneurysmal sac and endovascular devices was successfully obtained, and dimensional errors were found to be O(100 µm). The creation of dimensionally-accurate, optically-transparent flow phantoms of patient-specific intracranial aneurysms is feasible using 3D printing technology. Such models may enable in vitro investigations of aneurysmal hemodynamics to aid in treatment planning and outcome prediction to devise optimal patient-specific neurointerventional strategies.

Computational fluid dynamics of cerebral aneurysm coiling using high-resolution and high-energy synchrotron X-ray microtomography: comparison with the homogeneous porous medium approach.

BACKGROUND: Computational modeling of intracranial aneurysms provides insights into the influence of hemodynamics on aneurysm growth, rupture, and treatment outcome. Standard modeling of coiled aneurysms simplifies the complex geometry of the coil mass into a homogeneous porous medium that fills the aneurysmal sac. We compare hemodynamics of coiled aneurysms modeled from high-resolution imaging with those from the same aneurysms modeled following the standard technique, in an effort to characterize sources of error from the simplified model. MATERIALS: Physical models of two unruptured aneurysms were created using three-dimensional printing. The models were treated with coil embolization using the same coils as those used in actual patient treatment and then scanned by synchrotron X-ray microtomography to obtain high-resolution imaging of the coil mass. Computational modeling of each aneurysm was performed using patient-specific boundary conditions. The coils were modeled using the simplified porous medium or by incorporating the X-ray imaged coil surface, and the differences in hemodynamic variables were assessed. RESULTS: X-ray microtomographic imaging of coils and incorporation into computational models were successful for both aneurysms. Porous medium calculations of coiled aneurysm hemodynamics overestimated intra-aneurysmal flow, underestimated oscillatory shear index and viscous dissipation, and over- or underpredicted wall shear stress (WSS) and WSS gradient compared with X-ray-based coiled computational fluid dynamics models. CONCLUSIONS: Computational modeling of coiled intracranial aneurysms using the porous medium approach may inaccurately estimate key hemodynamic variables compared with models incorporating high-resolution synchrotron X-ray microtomographic imaging of complex aneurysm coil geometry.

Development and evaluation of an experimental protocol for 3-D visualization and characterization of the structure of bacterial biofilms in porous media using laboratory X-ray tomography.

The development of a reliable model allowing accurate predictions of biofilm growth in porous media relies on a good knowledge of the temporal evolution of biofilm structure within the porous network. Since little is known about the real 3-D structure of biofilms in porous media, this work was aimed at developing a new experimental protocol to visualize the 3-D microstructure of the inside of a porous medium using laboratory X-ray microtomography. A reliable and reproducible methodology is proposed for (1) growing a biofilm inside a porous medium, and (2) X-ray tomography-based characterization of the temporal development of the biofilm at the inlet of the biofilter. The statistical analysis proposed here also validates the results presented in the literature based on a biofilm structure single measurement.

Patient-specific simulation of endovascular repair surgery with tortuous aneurysms requiring flexible stent-grafts.

The rate of post-operative complications is the main drawback of endovascular repair, a technique used to treat abdominal aortic aneurysms. Complex anatomies, featuring short aortic necks and high vessel tortuosity for instance, have been proved likely prone to these complications. In this context, practitioners could benefit, at the preoperative planning stage, from a tool able to predict the post-operative position of the stent-graft, to validate their stent-graft sizing and anticipate potential complications. In consequence, the aim of this work is to prove the ability of a numerical simulation methodology to reproduce accurately the shapes of stent-grafts, with a challenging design, deployed inside tortuous aortic aneurysms. Stent-graft module samples were scanned by X-ray microtomography and subjected to mechanical tests to generate finite-element models. Two EVAR clinical cases were numerically reproduced by simulating stent-graft models deployment inside the tortuous arterial model generated from patient pre-operative scan. In the same manner, an in vitro stent-graft deployment in a rigid polymer phantom, generated by extracting the arterial geometry from the preoperative scan of a patient, was simulated to assess the influence of biomechanical environment unknowns in the in vivo case. Results were validated by comparing stent positions on simulations and post-operative scans. In all cases, simulation predicted stents deployed locations and shapes with an accuracy of a few millimetres. The good results obtained in the in vitro case validated the ability of the methodology to simulate stent-graft deployment in very tortuous arteries and led to think proper modelling of biomechanical environment could reduce the few local discrepancies found in the in vivo case. In conclusion, this study proved that our methodology can achieve accurate simulation of stent-graft deployed shape even in tortuous patient specific aortic aneurysms and may be potentially helpful to help practitioners plan their intervention.

Patient-specific numerical simulation of stent-graft deployment: Validation on three clinical cases.

Endovascular repair of abdominal aortic aneurysms faces some adverse outcomes, such as kinks or endoleaks related to incomplete stent apposition, which are difficult to predict and which restrain its use although it is less invasive than open surgery. Finite element simulations could help to predict and anticipate possible complications biomechanically induced, thus enhancing practitioners' stent-graft sizing and surgery planning, and giving indications on patient eligibility to endovascular repair. The purpose of this work is therefore to develop a new numerical methodology to predict stent-graft final deployed shapes after surgery. The simulation process was applied on three clinical cases, using preoperative scans to generate patient-specific vessel models. The marketed devices deployed during the surgery, consisting of a main body and one or more iliac limbs or extensions, were modeled and their deployment inside the corresponding patient aneurysm was simulated. The numerical results were compared to the actual deployed geometry of the stent-grafts after surgery that was extracted from postoperative scans. We observed relevant matching between simulated and actual deployed stent-graft geometries, especially for proximal and distal stents outside the aneurysm sac which are particularly important for practitioners. Stent locations along the vessel centerlines in the three simulations were always within a few millimeters to actual stents locations. This good agreement between numerical results and clinical cases makes finite element simulation very promising for preoperative planning of endovascular repair.

Deployment of stent grafts in curved aneurysmal arteries: toward a predictive numerical tool.

The mechanical behavior of aortic stent grafts plays an important role in the success of endovascular surgery for aneurysms. In this study, finite element analysis was carried out to simulate the expansion of five marketed stent graft iliac limbs and to evaluate quantitatively their mechanical performances. The deployment was modeled in a simplified manner according to the following steps: (i) stent graft crimping and insertion in the delivery sheath, (ii) removal of the sheath and stent graft deployment in the aneurysm, and (iii) application of arterial pressure. In the most curved aneurysm and for some devices, a decrease of stent graft cross-sectional area up to 57% was found at the location of some kinks. Apposition defects onto the arterial wall were also clearly evidenced and quantified. Aneurysm inner curve presented significantly more apposition defects than outer curve. The feasibility of finite element analysis to simulate deployment of marketed stent grafts in curved aneurysm models was demonstrated. The study of the influence of aneurysm tortuosity on stent graft mechanical behavior shows that increasing vessel curvature leads to stent graft kinks and inadequate apposition against the arterial wall. Such simulation approach opens a very promising way toward surgical planning tools able to predict intra and/or post-operative short-term stent graft complications.

CCM proteins control endothelial ß1 integrin dependent response to shear stress.

Hemodynamic shear stress from blood flow on the endothelium critically regulates vascular function in many physiological and pathological situations. Endothelial cells adapt to shear stress by remodeling their cytoskeletal components and subsequently by changing their shape and orientation. We demonstrate that ß1 integrin activation is critically controlled during the mechanoresponse of endothelial cells to shear stress. Indeed, we show that overexpression of the CCM complex, an inhibitor of ß1 integrin activation, blocks endothelial actin rearrangement and cell reorientation in response to shear stress similarly to ß1 integrin silencing. Conversely, depletion of CCM2 protein leads to an elongated "shear-stress-like" phenotype even in the absence of flow. Taken together, our findings reveal the existence of a balance between positive extracellular and negative intracellular signals, i.e. shear stress and CCM complex, for the control of ß1 integrin activation and subsequent adaptation of vascular endothelial cells to mechanostimulation by fluid shear stress.

Mechanical behaviour of a fibrous scaffold for ligament tissue engineering: finite elements analysis vs. X-ray tomography imaging.

The use of biodegradable scaffolds seeded with cells in order to regenerate functional tissue-engineered substitutes offers interesting alternative to common medical approaches for ligament repair. Particularly, finite element (FE) method enables the ability to predict and optimise both the macroscopic behaviour of these scaffolds and the local mechanic signals that control the cell activity. In this study, we investigate the ability of a dedicated FE code to predict the geometrical evolution of a new braided and biodegradable polymer scaffold for ligament tissue engineering by comparing scaffold geometries issued from FE simulations and from X-ray tomographic imaging during a tensile test. Moreover, we compare two types of FE simulations the initial geometries of which are issued either from X-ray imaging or from a computed idealised configuration. We report that the dedicated FE simulations from an idealised reference configuration can be reasonably used in the future to predict the global and local mechanical behaviour of the braided scaffold. A valuable and original dialog between the fields of experimental and numerical characterisation of such fibrous media is thus achieved. In the future, this approach should enable to improve accurate characterisation of local and global behaviour of tissue-engineering scaffolds.

Macroscopic modeling for heat and water vapor transfer in dry snow by homogenization.

Dry snow metamorphism, involved in several topics related to cryospheric sciences, is mainly linked to heat and water vapor transfers through snow including sublimation and deposition at the ice-pore interface. In this paper, the macroscopic equivalent modeling of heat and water vapor transfers through a snow layer was derived from the physics at the pore scale using the homogenization of multiple scale expansions. The microscopic phenomena under consideration are heat conduction, vapor diffusion, sublimation, and deposition. The obtained macroscopic equivalent model is described by two coupled transient diffusion equations including a source term arising from phase change at the pore scale. By dimensional analysis, it was shown that the influence of such source terms on the overall transfers can generally not be neglected, except typically under small temperature gradients. The precision and the robustness of the proposed macroscopic modeling were illustrated through 2D numerical simulations. Finally, the effective vapor diffusion tensor arising in the macroscopic modeling was computed on 3D images of snow. The self-consistent formula offers a good estimate of the effective diffusion coefficient with respect to the snow density, within an average relative error of 10%. Our results confirm recent work that the effective vapor diffusion is not enhanced in snow.

Finite element analysis of the mechanical performances of 8 marketed aortic stent-grafts.

PURPOSE: To assess numerically the flexibility and mechanical stresses undergone by stents and fabric of currently manufactured stent-grafts. METHODS: Eight marketed stent-graft limbs (Aorfix, Anaconda, Endurant, Excluder, Talent, Zenith Flex, Zenith LP, and Zenith Spiral-Z) were modeled using finite element analysis. A numerical benchmark combining bending up to 180° and pressurization at 150 mmHg of the stent-grafts was performed. Stent-graft flexibility, assessed by the calculation of the luminal reduction rate, maximal stresses in stents, and maximal strains in fabric were assessed. RESULTS: The luminal reduction rate at 90° was <20% except for the Talent stent-graft. The rate at 180° was higher for Z-stented models (Talent, Endurant, Zenith, and Zenith LP; range 39%-78%) than spiral (Aorfix, Excluder, and Zenith Spiral-Z) or circular-stented (Anaconda) devices (range 14%-26%). At 180°, maximal stress was higher for Z-stented stent-grafts (range 370-622 MPa) than spiral or circular-stented endografts (range 177-368 MPa). At 90° and 180°, strains in fabric were low and did not differ significantly among the polyester stent-grafts (range 0.5%-7%), while the expanded polytetrafluoroethylene fabric of the Excluder stent-graft underwent higher strains (range 11%-18%). CONCLUSION: Stent design strongly influences mechanical performances of aortic stent-grafts. Spiral and circular stents provide greater flexibility, as well as lower stress values than Z-stents, and thus better durability.

Severe bending of two aortic stent-grafts: an experimental and numerical mechanical analysis.

Stent-grafts (SGs) are commonly used for treating abdominal aortic aneurysms (AAAs) and numerical models tend to be developed for predicting the biomechanical behavior of these devices. However, due to the complexity of SGs, it is important to validate the models. In this work, a validation of the numerical model developed in Demanget et al. (J. Mech. Behav. Biomed. Mater. 5:272-282, 2012) is presented. Two commercially available SGs were subjected to severe bending tests and their 3D geometries in undeformed and bent configurations were imaged from X-ray microtomography. Dedicated image processing subroutines were used in order to extract the stent centerlines from the 3D images. These skeletons in the undeformed configurations were used to set up SG numerical models that are subjected to the boundary conditions measured experimentally. Skeletons of imaged and deformed stents were then quantitatively compared to the numerical simulations. A good agreement is found between experiments and simulations. This validation offers promising perspectives to implementing the numerical models in a computer-aided tool and simulating the endovascular treatments.

Computational comparison of the bending behavior of aortic stent-grafts.

Secondary interventions after endovascular repair of abdominal aortic aneurysms are frequent because stent-graft (SG) related complications may occur (mainly endoleak and SG thrombosis). Complications have been related to insufficient SG flexibility, especially when devices are deployed in tortuous arteries. Little is known on the relationship between SG design and flexibility. Therefore, the aim of this study was to simulate numerically the bending of two manufactured SGs (Aorfix--Lombard Medical (A) and Zenith--Cook Medical Europe (Z)) using finite element analysis (FEA). Global SG behavior was studied by assessing stent spacing variation and cross-section deformation. Four criteria were defined to compare flexibility of SGs: maximal luminal reduction rate, torque required for bending, maximal membrane strains in graft and maximal Von Mises stress in stents. For angulation greater than 60°, values of these four criteria were lower with A-SG, compared to Z-SG. In conclusion, A-SG was more flexible than Z-SG according to FEA. A-SG may decrease the incidence of complications in the setting of tortuous aorto-iliac aneurysms. Our numerical model could be used to assess flexibility of further manufactured as well as newly designed SGs.

Periodic homogenization and consistent estimates of transport parameters through sphere and polyhedron packings in the whole porosity range.

This paper presents a study of transport parameters (diffusion, dynamic permeability, thermal permeability, trapping constant) of porous media by combining the homogenization of periodic media (HPM) and the self-consistent scheme (SCM) based on a bicomposite spherical pattern. The link between the HPM and SCM approaches is first established by using a systematic argument independent of the problem under consideration. It is shown that the periodicity condition can be replaced by zero flux and energy through the whole surface of the representative elementary volume. Consequently the SCM solution can be considered as a geometrical approximation of the local problem derived through HPM for materials such that the morphology of the period is "close" to the SCM pattern. These results are then applied to derive the estimates of the effective diffusion, the dynamic permeability, the thermal permeability and the trapping constant of porous media. These SCM estimates are compared with numerical HPM results obtained on periodic arrays of spheres and polyhedrons. It is shown that SCM estimates provide good analytical approximations of the effective parameters for periodic packings of spheres at porosities larger than 0.6, while the agreement is excellent for periodic packings of polyhedrons in the whole range of porosity.