A stochastic approach to the filling dynamics of a porous medium: full/empty pores duality symmetry and the emergence of Darcy's law

The understanding of fluid transport through porous media is a challenging problem which solution will be of benefit to the many and various applications involving porous structures such as membrane filtration for biological or industrial needs or water flow through granular media. But the more significant gain of such a physical understanding certainly regards the fundamental side where so many issues remain unanswered. The main difficulties to face on the way to the solution of that problem regard the triple complexity of porous media: the influence of the topology of the interconnected voids network, including disorder, the coupling between the matrix elasticity (compliance) and the fluid flow and last, the prominent role of the spatial correlations of the filling of the pores. All these manifestations of such an acute complexity of porous media can affect the flow dynamics. For instance, likely non-linearities expressing these complex couplings can result in instabilities, modifying drastically the fluid flow regimes. To propose new theoretical ways to tackle the complexity of porous media, we investigated a mathematical model of the (incompressible) fluid transfer through a disordered voids network based on a stochastic discrete description. Constrained by the fundamental mass conservation law, we obtain the equations ruling the porous structure filling dynamics as the continuum limit of the discrete model (effective fluid) through a mathematical procedure which is discussed, putting emphasis on the encountered technical difficulties. Two consequences of the effective continuum description are more especially presented: the emergence of the famous Darcy's law and its connection to the network topology and the prediction of a full/empty pores duality symmetry. The steady non-equilibrium pores filling state is obtained and found to follow a Fermi-Dirac type law. The analogy with the single occupation of lattice sites by fermions is highlighted together with the interpretation of duality symmetry with the corresponding hole-particle symmetry. Possible applications of our formalism to lubricating films wetting rough surfaces are discussed as well as the description of cerebrospinal fluid flow through porous elastic brain matter which plays a central role in intracranial dynamics

Etude physique de la dynamique des ventricules cérébraux : application aux hydrocéphalies

Nous avons construit un modèle physique permettant la description de la dynamique des ventricules cérébraux, ainsi que ses couplages au cerveau et aux compartiments environnants, que ceux-ci soient de nature mécanique ou par échanges de fluides. Par les lois de la thermodynamique et de la mécanique des milieux continus, nous avons mis en évidence deux instabilités de la dynamique ventriculaire qui pourraient s'avérer être les causes des hydrocéphalies. Notre approche est essentiellement de nature théorique et numérique

Phantom Study of an In-House Amplitude-Gating Respiratory Method with Silicon Photomultiplier Technology Positron Emission Tomography/Computed Tomography.

International audiencePURPOSE: The objective of this phantom study was to determine whether breathing-synchronized, silicon photomultiplier (SiPM)-based PET/CT has a suitable acquisition time for routine clinical use. METHODS: Acquisitions were performed in list mode on a 4-ring SiPM-based PET/CT system. The experimental setup consisted of an external respiratory tracking device placed on a commercial dynamic thorax phantom containing a sphere filled with [F-18]-fluorodeoxyglucose. Three-dimensional sinusoidal motion was imposed on the sphere. Data were processed using frequency binning and amplitude binning (the "DMI" and "OFFLINE" methods, respectively). PET sinograms were reconstructed with a Bayesian penalized likelihood algorithm. RESULTS: Respiratory gating from a 150-sec acquisition was successful. The DMI and OFFLINE methods gave similar activity profiles but both were slightly shifted in space; the latter profile was closest to the reference acquisition. CONCLUSION: With SiPM PET/CT systems, the amplitude-based processing of breathing-synchronized data is likely to be feasible in routine clinical practice

Arterial hypertension impact on cerebral blood flow in patients with Alzheimer’s disease

BACKGROUND: Studies show the potential deterioration of brain vascularization and probable involvement of hypertension in Alzheimer disease (AD). OBJECTIVE: The objective was to evaluate the potential impact of hypertension on cerebral vascular flows in a sample of Alzheimer's patients. METHODS: 19 patients with AD, including 10 with hypertension (aHT+) and 9 without hypertension (aHT-) were recruited. They underwent clinical evaluation and phase-contrast MRI protocol for flow assessment. Cerebral arterial flow distributions were evaluated using kurtosis and skewness indices at the intracranial and extracranial levels. RESULTS: No significant differences were found in the mean arterial flow, pulse flow and kurtosis between the levels in the AD aHT+ population. There was a significant difference in skewness between extra- and intracranial levels (p = 0.01). No significant differences were found in the mean arterial flow between the levels in the AD aHT- population. A significant difference was observed in the pulse flow (p = 0.03), kurtosis (p = 0.02) and skewness (p = 0.008) between the levels. At the extracranial level we did not find any significant differences in the mean arterial flow, pulse flow or skewness between aHT+ and aHT-. There was a significant difference in kurtosis at the extracranial level between the aHT+ and aHT- (p = 0.03). At the intracranial level, there were no significant differences in all parameters. CONCLUSION: Results showed a difference between cerebral vasculature in AD for aHT+ and aHT- groups. This is probably related to the loss of arterial compliance induced by the degradation of the vascular system.</p

Estimation of the Lateral Ventricles Volumes from a 2D Image and Its Relationship with Cerebrospinal Fluid Flow

Purpose. This work suggests a fast estimation method of the lateral ventricles volume from a 2D image and then determines if this volume is correlated with the cerebrospinal fluid flow at the aqueductal and cerebral levels in neurodegenerative diseases. Materials and Methods. FForty-five elderly patients suffering from Alzheimer’s disease (19), normal pressure hydrocephalus (13), and vascular dementia (13) were involved and underwent anatomical and phase contrast MRI scans. Lateral ventricles and stroke volumes were assessed on anatomical and phase contrast scans, respectively. A common reference plane was used to calculate the lateral ventricles’ area on 2D images. Results. The largest volumes were observed in hydrocephalus patients. The linear regression between volumes and areas was computed, and a strong positive correlation was detected (R2=0.9). A derived equation was determined to represent the volumes for any given area. On the other hand, no significant correlations were detected between ventricles and stroke volumes (R2≤0.15). Conclusion. Lateral ventricles volumes are significantly proportional to the 2D reference section area and could be used for patients’ follow-up even if 3D images are unavailable. The cerebrospinal fluid fluctuations in brain disorders may depend on many physiological parameters other than the ventricular morphology