Flattened 1D fragments of fullerene C60 that exhibit robustness toward multi-electron reduction.

Fullerenes are compelling molecular materials owing to their exceptional robustness toward multi-electron reduction. Although scientists have attempted to address this feature by synthesizing various fragment molecules, the origin of this electron affinity remains unclear. Several structural factors have been suggested, including high symmetry, pyramidalized carbon atoms, and five-membered ring substructures. To elucidate the role of the five-membered ring substructures without the influence of high symmetry and pyramidalized carbon atoms, we herein report the synthesis and electron-accepting properties of oligo(biindenylidene)s, a flattened one-dimensional fragment of fullerene C60. Electrochemical studies corroborated that oligo(biindenylidene)s can accept electrons up to equal to the number of five-membered rings in their main chains. Moreover, ultraviolet/visible/near-infrared absorption spectroscopy revealed that oligo(biindenylidene)s exhibit enhanced absorption covering the entire visible region relative to C60. These results highlight the significance of the pentagonal substructure for attaining stability toward multi-electron reduction and provide a strategy for the molecular design of electron-accepting π-conjugated hydrocarbons even without electron-withdrawing groups.

Stereoselective Synthesis and Characterization of Indenone Azine-Based Electron-Accepting π-Conjugated Systems.

Invited for the cover of this issue is the group of Aiko Fukazawa at Kyoto University. The image depicts a N-N component replacing the one originally located between the exocyclic C=C bond of a cross-conjugated dibenzofulvalene. Read the full text of the article at 10.1002/chem.202300181.

Stereoselective Synthesis and Characterization of Indenone Azine-Based Electron-Accepting π-Conjugated Systems.

Indenone azines, in which the exocyclic C=C bond in dibenzopentafulvalene is replaced by an azine moiety (C=N-N=C), have been synthesized as novel electron-accepting π-conjugated scaffolds. Structural modulation at the 7,7'-positions of indenone azines enabled stereoselective syntheses of diastereomers in which the configurations of the two C=N bonds are E,E or Z,Z. X-ray crystallographic analyses revealed that all the indenone azines exhibit high coplanarity in contrast to the twisted frameworks of dibenzopentafulvalene derivatives, resulting in the formation of densely π-stacked structures. Electrochemical measurements and quantum chemical calculations revealed the electron-accepting character of indenone azines comparable to isoindigo dyes. In particular, the intramolecular hydrogen bonds of 7,7'-dihydroxy-substituted derivatives impart enhanced electron-accepting character and significantly red-shifted photoabsorption. This study demonstrates that indenone azines represent a promising candidate as electron-accepting building blocks for optoelectronic materials.

Deep learning for hetero-homo conversion in channel-domain for phase aberration correction in ultrasound imaging.

Echo imaging in ultrasound computed tomography (USCT) using the synthetic aperture technique is performed with the assumption that the speed of sound is constant in the system. However, tissue heterogeneity causes a mismatch between the predicted arrival time and the actual arrival time of the echo signal, which will result in phase aberration, leading to the quality degradation of the reconstructed B-mode image. The conventional correction methods that use the correlation of each different channel require the presence of strong point scatterers and involve the problem of local solutions due to excessive correction. In this study, we propose a novel approach to correcting the signal distortion due to sound speed heterogeneity using a deep neural network (DNN). The DNN was trained to convert the distorted radio frequency (RF) inputs for the heterogeneous medium to the distortion-free RF outputs for the homogeneous medium. The network with U-net architecture using ResNet-34 as a backbone was trained using the hetero-homo corresponding channel-domain RF data generated via numerical simulations. The trained network performed phase aberration correction in the channel-domain RF, with the B-mode images reconstructed with the corrected RF demonstrating a higher contrast and an improved resolution compared with uncorrected cases. It was also demonstrated that the DNN model is robust to both varied reflection intensities and varied sound speed heterogeneities. The successful results demonstrated that the proposed DNN-based method is effective for phase aberration correction in US imaging.

Numerical Study on a Focus-Control Method Using Breast Model With Intentionally Assigned High-Absorbing Layer Near Skin for High-Intensity Focused Ultrasound Treatment.

To prevent undesirable skin burns that occur in high-intensity focused ultrasound (HIFU) treatment, we numerically study focus-control methods, such as phase compensation (PC) and amplitude adaptation (AA). We intentionally assign a high-absorbing layer (HAL) near the part of the skin, where heat generation and tissue ablation are observed, because of high energy loss in the interface between water and breast skin. Results show that PC improves the effectiveness of focusing by enhancing the focal peak and reducing the focal deviation; however, PC does not suppress skin burn. AA and PC eliminate skin burns only if appropriate amplitude weights are applied. A preliminary discussion on three algorithms for obtaining amplitude weights is conducted as follows; First, we switched off transducer channels using distance-to-HAL. This algorithm eliminates skin burns while causing other undesirable burns by preserving 100% input energy. Second, we use cross-correlated amplitude weights. It eliminates skin burn after properly limiting large-amplitude weights while producing focal necrosis in a smaller and slower manner. Third, we introduced root-mean-square (rms) level of back-propagated wave (BPW) into cross-correlated amplitude weights. This new algorithm produces focal ablation in 20 s without causing any skin burn. Although longer irradiation time brings back skin burn, the result is satisfying since short irradiation time is needed in HIFU treatment to avoid exceeding the physical endurance of human patients. Moreover, this work indicates that focus-control associated with an acoustic peak is insufficient. The effects of the high attenuation area are significant and should be captured.

Gas Adsorption and Diffusion Behaviors in Interfacial Systems Composed of a Polymer of Intrinsic Microporosity and Amorphous Silica: A Molecular Simulation Study.

We investigate the adsorption and diffusion behaviors of CO2, CH4, and N2 in interfacial systems composed of a polymer of intrinsic microporosity (PIM-1) and amorphous silica using grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations. We build model systems of mixed matrix membranes (MMMs) with PIM-1 chains sandwiched between silica surfaces. Gas adsorption analysis using GCMC simulations shows that gas molecules are preferentially adsorbed in microcavities distributed near silica surfaces, resulting in an increase in the solubility coefficients of CO2, CH4, and N2 compared to bulk PIM-1. In contrast, diffusion coefficients obtained from MD simulations and then calibrated using the dual-mode sorption model show different tendencies depending on gas species: CO2 diffusivity decreases in MMMs compared to PIM-1, whereas CH4 and N2 diffusivities increase. These differences are attributed to competing effects of silica surfaces: the emergence of larger pores as a result of chain packing disruption, which enhances gas diffusion, and a quadrupole-dipole interaction between gas molecules and silica surface hydroxyl groups, which retards gas diffusion. The former has a greater impact on CH4 and N2 diffusivities, whereas the latter has a greater impact on CO2 diffusivity due to the strong quadrupole-dipole interaction between CO2 and surface hydroxyls. These findings add to our understanding of gas adsorption and diffusion behaviors in the vicinity of PIM-1/silica interfaces, which are unobtainable in experimental studies.

Automatic Aortic Valve Cusps Segmentation from CT Images Based on the Cascading Multiple Deep Neural Networks.

Accurate morphological information on aortic valve cusps is critical in treatment planning. Image segmentation is necessary to acquire this information, but manual segmentation is tedious and time consuming. In this paper, we propose a fully automatic aortic valve cusps segmentation method from CT images by combining two deep neural networks, spatial configuration-Net for detecting anatomical landmarks and U-Net for segmentation of aortic valve components. A total of 258 CT volumes of end systolic and end diastolic phases, which include cases with and without severe calcifications, were collected and manually annotated for each aortic valve component. The collected CT volumes were split 6:2:2 for the training, validation and test steps, and our method was evaluated by five-fold cross validation. The segmentation was successful for all CT volumes with 69.26 s as mean processing time. For the segmentation results of the aortic root, the right-coronary cusp, the left-coronary cusp and the non-coronary cusp, mean Dice Coefficient were 0.95, 0.70, 0.69, and 0.67, respectively. There were strong correlations between measurement values automatically calculated based on the annotations and those based on the segmentation results. The results suggest that our method can be used to automatically obtain measurement values for aortic valve morphology.

Important Regulatory Roles of Erythrocytes in Platelet Adhesion to the von Willebrand Factor on the Wall under Blood Flow Conditions.

The role of erythrocytes in platelet adhesion to von Willebrand factor (VWF) on the vessel wall through their membrane glycoprotein (GP)Ibα under blood flow conditions has not yet been elucidated. Blood specimens containing fluorescent-labeled platelets and native, biochemically fixed, or artificial erythrocytes at various hematocrits were perfused on the surface of VWF immobilized on the wall at a shear rate of 1,500 s-1. The rates of platelet adhesion were measured under each condition. The computer simulation of platelet adhesion to the VWF on the wall at the same shear rate was conducted by solving the governing equations with a finite-difference method on a K computer. The rates of platelet adhesion were calculated at various hematocrit conditions in the computational domain of 100 µm (x-axis) × 400 µm (y-axis) × 100 µm (z-axis). Biological experiments demonstrated a positive correlation between the rates of platelet adhesion and hematocrit values in native, fixed, and artificial erythrocytes. (r = 0.992, 0.934, and 0.825 respectively, p < 0.05 for all). The computer simulation results supported the hematocrit-dependent increase in platelet adhesion rates on VWF (94.3/second at 10%, 185.2/second at 20%, and 327.9/second at 30%). These results suggest that erythrocytes play an important role in platelet adhesion to VWF. The augmented z-axis fluctuation of flowing platelets caused by the physical presence of erythrocytes is speculated to be the cause of the hematocrit-dependent increase in platelet adhesion.

Localized motion imaging for monitoring HIFU therapy: Comparison of modulating frequencies and utilization of square modulating wave.

High-intensity focused ultrasound (HIFU) has been successfully used as a minimally invasive cancer therapy method. For monitoring the therapy, the amplitude-modulated (AM) localized motion imaging (LMI) method had been proposed. This paper compares the performance of AM-LMI while using different sine modulating wave frequencies and proposes the utilization of square modulating waves to gain the advantages of both high and low modulating frequencies. A single element therapy transducer with a 2 MHz central frequency was driven by sine modulating waves with different frequencies (approximate 34, 67, 102, 168, and 201 Hz) and by square modulating waves with two frequencies (34 and 67 Hz). An imaging probe with a 5 MHz central frequency and a 20 MHz sampling frequency was mounted in the center hole of the therapy transducer to acquire pulse-echo data, which were used to estimate the tissue oscillation amplitude induced by the acoustic radiation force of the HIFU beam. The decrease ratio of the oscillation amount was then utilized to estimate the coagulated lesion length during the therapy. The comparison of modulating frequencies demonstrated that a higher frequency could bring higher sensitivity to small lesions, while a lower frequency not only gives greater noise robustness but also promotes the ability to estimate lengths of larger lesions. The utilization of a square modulating wave demonstrated its utility to produce tissue oscillation with multiple frequencies and gain the advantages of both high and low modulating frequencies.

Biomechanical Gain in Joint Excursion from the Curvature of the Achilles Tendon: Role of the Geometrical Arrangement of Inflection Point, Center of Rotation, and Calcaneus.

The dorsal movement of the Achilles tendon during ankle rotation is restricted by anatomical obstructions. Previously, we demonstrated that the anatomical obstruction provides a gain (gainAT) in the proximal displacement of the calcaneus compared to the change in the Achilles tendon length. Here, we empirically validate and extend our previous modeling study by investigating the effects of a broad range of obstruction locations on gainAT. The largest gainAT could be achieved when the obstruction was located on the most ventral and distal sides within the physiological range of the Achilles tendon, irrespective of the ankle position.

Numerical study on sector-vortex phased irradiation method using annular array transducer in High-Intensity Focused Ultrasound treatment.

Sector-vortex phased irradiation from annular array transducer was numerically studied with breast model constructed from MRI data of real patient. Phase compensation (PC) based on time reversal pre-computation was applied in order to handle phase delay caused by heterogeneity of breast tissues, and results showed great effectiveness on single-focus case, insignificant effectiveness on multi-focus cases with 4 and 8 phase-sectors, but ineffectiveness on multi-focus case with 12 phase-sectors, where enormous undesired outer ablation occurred. For single-focus case, phase compensation not only produced real focus very close to targeted site (0.1 mm deviation), but also decreased thermal peak ratio (outer/focal) largely by 30%. However, phase compensation did not increase total ablated size. For multi-focus cases with 4 and 8 phase-sectors, deformed focal shapes by tissue heterogeneity were restored by phase compensation, but the 4-phase-sector case had higher thermal peak ratio and smaller ablation than 8-phase-sector case for strong cancelling effect between phase-sector borders. Ineffectiveness of phase compensation on multi-focus case with 12 phase-sectors had three considerable reasons. 1st, inequality of piezo-element number between sectors; 2nd, heterogeneous attenuation of breast model; 3rd, insufficient number of piezo-elements per sector; where the 2nd reason originated from breast model, and other two reasons were related to array transducer. This research gave several preliminary indications. 1st, ineffectiveness of phase compensation occurs on case with large phase-sector number when using annular array transducer; 2nd, with same input energy and same irradiation time, sector-vortex phased irradiation creates smaller focal ablation, but withstands longer than single-focus irradiation free of outer ablation; 3rd, phase-difference π between neighboring phase-sectors is disadvantageous because of energy loss; 4th, phase compensation is effective on single-focus for improving pinpoint ablation but not for increasing total ablated size.

A penalized spline fitting method to optimize geometric parameters of arterial centerlines extracted from medical images.

In order to grasp the spatial and temporal evolution of vascular geometry, three-dimensional (3D) arterial bending structure and geometrical changes of arteries and stent grafts (SG) must be quantified using geometrical parameters such as curvature and torsion along the vasculature centerlines extracted from medical images. Here, we develop a robust method for constructing smooth centerlines based on a spline fitting method (SFM) such that the optimized geometric parameters of curvature and torsion can be obtained independently of digitization noise in the images. Conventional SFM consists of the 3rd degree spline basis function and 2nd derivative penalty term. In contrast, the present SFM uses the 5th degree spline basis function and 3rd and 4th derivative penalty terms, the coefficients of which are derived by the Akaike information criterion. The results show that the developed SFM can reduce the errors of curvature and torsion compared to conventional SFM. We then apply the present SFM to the centerline of the SG in an abdominal aortic aneurysm (AAA), and those of bilateral internal carotid arteries (ICA) in 6 cases: 3 cases with aneurysms and 3 cases without any aneurysm. The SG centerlines were obtained from temporal medical images at three scan times. The strong peak of the curvature could be clearly observed in the distal area of the SG, the inversion of the torsion at 0 months in the middle area of SG disappeared over time, and the torsions around the SG bifurcation at the three time periods were inverted. The curvature-torsion graphs along the ICA centerlines superimposing five aneurysmal positions were useful for investigating the relationship between arterial bending structure and aneurysmal positions. Both ICAs had curvature peak values higher than 0.4 within the ICA syphons. The ICA torsion graphs indicated that left and right ICA tended to be a right- and left-handed helix, respectively. In the left ICA syphon, the biggest aneurysm could be observed downstream of the salient torsion inversion. All aneurysms for 3 cases were positioned at the downstream of the inverted torsion.

Characterization of Brain-Targeted Drug Delivery Enhanced by a Combination of Lipid-Based Microbubbles and Non-Focused Ultrasound.

The combination of focused ultrasound (FUS) and microbubbles, an ultrasound (US) contrast agent, has attracted much attention for its ability to open the blood brain barrier (BBB) and deliver drugs to the brain parenchyma. FUS can concentrate US energy in a restricted space, whereas non-focused US can affect a wide area of tissue. Non-focused US is also promising for drug delivery to the brain and other tissues. We have previously developed lipid-based microbubbles (LBs), and demonstrated that non-focused US and LBs have potential for drug delivery to tumor tissues. In this study, to achieve efficient and safe brain-targeted drug delivery, we evaluated the characteristics of BBB opening using non-focused US and LBs. Our results indicated that LBs could induce BBB opening with non-focused US. US frequency and intensity affected the efficiency of BBB opening and brain damage, and showed that the dose of LBs was also related to the efficiency of BBB opening. Furthermore, the combination of non-focused US and LBs could deliver macromolecules at 2000 kDa to the brain, and the induction of BBB opening was found to be reversible. These results suggest that the combination of non-focused US and LBs has potential as a brain-targeted drug delivery system.

Prediction of binding characteristics between von Willebrand factor and platelet glycoprotein Ibα with various mutations by molecular dynamic simulation.

INTRODUCTION: Binding of platelet glycoprotein (GP)Ibα with von-Willebrand factor (VWF) exclusively mediates the initial platelet adhesion to injured vessel wall. To understand the mechanism of biomedical functions, we calculated the dynamic fluctuating three-dimensional (3D) structures and dissociation energy for GPIbα with various single amino-acid substitution at G233, which location is known to cause significant changes in platelet adhesive characteristics. MATERIAL AND METHODS: Molecular dynamics (MD) simulation was utilized to calculate 3D structures and Potential of Mean Force (PMF) for wild-type VWF bound with wild-type, G233A (equal function), G233V (gain of function), and G233D (loss of function) GPIbα. Simulation was done on water-soluble condition with time-step of 2 × 10-15 s using NAnoscale Molecular Dynamics (NAMD) with Chemistry at HARvard Molecular Mechanics (CHARMM) force field. Initial structure for each mutant was obtained by inducing single amino-acid substitution to the stable water-soluble binding structure of wild-type. RESULTS: The most stable structures of wild-type VWF bound to GPIbα in wild-type or any mutant did not differ. However, bond dissociation energy defined as difference of PMF between most stable structure and the structure at 65 Šmass center distances in G233D was 4.32 kcal/mol (19.5%) lower than that of wild-type. Approximately, 2.07 kcal/mol energy was required to dissociate VWF from GPIbα with G233V at mass center distance from 48 to 52 Å, which may explain the apparent "gain of function" in G233V. CONCLUSION: The mechanism of substantially different biochemical characteristics of GPIbα with mutations in G233 location was predicted from physical movement of atoms constructing these proteins.

Photoinduced binding of malachite green copolymer to parallel G-quadruplex DNA.

Designing ligands that selectively target G-quadruplex DNAs has gained attention due to their possible roles in regulation of gene expression and as anti-cancer agents. In this article, we report irradiation-induced ligand binding to G-quadruplex DNAs which offers a novel approach to targeting specific G-quadruplexes. Photoinduced binding to G-quadruplex DNAs was observed for copolymers of poly(vinyl alcohol) carrying a malachite green moiety (PVAMG). This molecule has an aromatic ring with cationic charge, which after irradiation becomes a binding site for G-quadruplex DNA. PVAMGs acted as neutral polymers with no binding affinity under dark conditions. The photoinduced binding was revealed by fluorescence spectroscopy, NMR spectroscopy, UV melting curve, and DNA polymerase stop assay. PVAMGs showed preference to parallel G-quadruplex structures over mixed parallel/antiparallel structures. PVAMGs were found to be noncytotoxic under both dark and irradiated conditions up to a concentration of 20 µM.

Potential different impact of inhibition of thrombin function and thrombin generation rate for the growth of thrombi formed at site of endothelial injury under blood flow condition.

INTRODUCTION: Thrombin inhibitor and anti-Xa are now widely used in clinical practice. However, the difference between thrombin inhibitor and anti-Xa in prevention of thrombosis is still to be elucidated. MATERIALS AND METHODS: Computer simulator implementing the function of platelet, coagulation, fibrinolysis and blood flow was developed. The function of thrombin is defined as to activated platelet at the rate of 0.01 s-1 and to produce fibrin at the rate of 0.1 s-1 in control. The effect of thrombin inhibitor was settled to reduce the rate of platelet activation and fibrin generation changed from 10 to 100% as compared to the control. The local thrombin generation rate on activated platelet was settled as 1.0 s-1 as a control. The effect of anti-Xa was settled to reduce to thrombin generation rate on activated platelet from 10% to 100% as compared to the control. The sizes of thrombi formed at site of endothelial injury in the presence and absence of thrombin inhibitor and anti-Xa were compared. RESULTS AND CONCLUSIONS: The size of thrombi formed by 30-s perfusion of blood at site of endothelial injury reduced both in the presence of thrombin inhibitor and anti-Xa. There was significant positive relationship between thrombin inhibitor effect and the size of formed thrombi with R value of 0.96. (p < 0.0001) However, the sizes of thrombi were not influence by anti-Xa until it decreased 30% or less as compared to control. There was no significant relationship between anti-Xa effect and the size of formed thrombi. (R = 0.39, p = 0.09) Our results suggest the different dose-dependent effects of thrombin inhibitor and anti-Xa on thrombus formation at least in specific conditions. Computer simulation may help to predict quantitative antithrombotic effects of various antithrombotic agents.

Effects of breast structure on high-intensity focused ultrasound focal error.

BACKGROUND: The development of imaging technologies and breast cancer screening allowed early detection of breast cancers. High-intensity focused ultrasound (HIFU) is a non-invasive cancer treatment, but the success of HIFU ablation was depending on the system type, imaging technique, ablation protocol, and patient selection. Therefore, we aimed to determine the relationship between breast tissue structure and focal error during breast cancer HIFU treatment. METHODS: Numerical simulations of the breast cancer HIFU ablation were performed using digital breast phantoms constructed using the magnetic resonance imaging data obtained from 12 patients. RESULTS: The focal shapes were distorted despite breast tissue representing soft tissue. Focal errors are caused by the complex distribution of fibroglandular tissue, and they depend on the target position and the arrangement of the transducer. We demonstrated that the focusing ratio increases with the decrease in the local acoustic inhomogeneity, implying that it may be used as an indicator to reduce the HIFU focal error depending on the breast structure. CONCLUSIONS: The obtained results demonstrated that the focal error observed during the breast cancer HIFU treatment is highly dependent on the structure of fibroglandular tissue. The optimal arrangement of the transducer to the target can be obtained by minimizing the local acoustic inhomogeneity before the breast cancer HIFU treatment.

A Multi-modality Approach Towards Elucidation of the Mechanism for Human Achilles Tendon Bending During Passive Ankle Rotation.

The in vitro unconstrained Achilles tendon is nearly straight, while in vivo experiments reveal that the proximal region of the Achilles tendon, adjacent to Kager's fat pad, bends ventrally during plantarflexion but remains nearly straight during dorsiflexion. Tendon bending is an important factor in determining the displacement of the foot compared to the shortening of the muscle fibers. The objective of this study was to elucidate the various mechanisms that could cause tendon bending, which currently remain unknown. Examination of Thiel-embalmed cadavers, with preservation of native articular joint mobility, revealed that the Achilles tendon still bent ventrally even when its surrounding tissues, including the skin surface, Kager's fat pad, and distal portions of the soleus muscle were removed. Shear modulus and collagen fiber orientation were distributed homogeneously with respect to the longitudinal line of the tendon, minimizing their causative contributions to the bending. Given that tendon bending is not caused by either the nature of the deformations of the tissues surrounding the Achilles tendon or its physical properties, we conclude that it results from the geometric architecture of the Achilles tendon and its configuration with respect to the surrounding tissues.

Mutual influence of molecular diffusion in gas and surface phases.

We develop molecular transport simulation methods that simultaneously deal with gas- and surface-phase diffusions to determine the effect of surface diffusion on the overall diffusion coefficients. The phenomenon of surface diffusion is incorporated into the test particle method and the mean square displacement method, which are typically employed only for gas-phase transport. It is found that for a simple cylindrical pore, the diffusion coefficients in the presence of surface diffusion calculated by these two methods show good agreement. We also confirm that both methods reproduce the analytical solution. Then, the diffusion coefficients for ink-bottle-shaped pores are calculated using the developed method. Our results show that surface diffusion assists molecular transport in the gas phase. Moreover, the surface tortuosity factor, which is known to be uniquely determined by physical structure, is influenced by the presence of gas-phase diffusion. This mutual influence of gas-phase diffusion and surface diffusion indicates that their simultaneous calculation is necessary for an accurate evaluation of the diffusion coefficients.

Effect of capillary condensation on gas transport properties in porous media.

We investigate the effect of capillary condensation on gas diffusivity in porous media composed of randomly packed spheres with moderate wettability. To simulate capillary phenomena at the pore scale while retaining complex pore networks of the porous media, we employ density functional theory (DFT) for coarse-grained lattice gas models. The lattice DFT simulations reveal that capillary condensations preferentially occur at confined pores surrounded by solid walls, leading to the occlusion of narrow pores. Consequently, the characteristic lengths of the partially wet structures are larger than those of the corresponding dry structures with the same porosities. Subsequent gas diffusion simulations exploiting the mean-square displacement method indicate that while the effective diffusion coefficients significantly decrease in the presence of partially condensed liquids, they are larger than those in the dry structures with the same porosities. Moreover, we find that the ratio of the porosity to the tortuosity factor, which is a crucial parameter that determines an effective diffusion coefficient, can be reasonably related to the porosity even for the partially wet porous media.