Towards a quantitative theory of epidermal calcium profile formation in unwounded skin

We propose and mathematically examine a theory of calcium profile formation in unwounded mammalian epidermis based on: changes in keratinocyte proliferation, fluid and calcium exchange with the extracellular fluid during these cells' passage through the epidermal sublayers, and the barrier functions of both the stratum corneum and tight junctions localised in the stratum granulosum. Using this theory, we develop a mathematical model that predicts epidermal sublayer transit times, partitioning of the epidermal calcium gradient between intracellular and extracellular domains, and the permeability of the tight junction barrier to calcium ions. Comparison of our model's predictions of epidermal transit times with experimental data indicates that keratinocytes lose at least 87% of their volume during their disintegration to become corneocytes. Intracellular calcium is suggested as the main contributor to the epidermal calcium gradient, with its distribution actively regulated by a phenotypic switch in calcium exchange between keratinocytes and extracellular fluid present at the boundary between the stratum spinosum and the stratum granulosum. Formation of the extracellular calcium distribution, which rises in concentration through the stratum granulosum towards the skin surface, is attributed to a tight junction barrier in this sublayer possessing permeability to calcium ions that is less than 15 nm/s in human epidermis and less than 37 nm/s in murine epidermis. Future experimental work may refine the presented theory and reduce the mathematical uncertainty present in the model predictions.

Experimental study of Australian sugarcane bagasse pulp permeability

In this experimental study the permeability of Australian bagasse chemical pulps obtained from different bagasse fractions were measured in a simple permeability cell and the results compared to one another as well as to eucalypt, Argentinean bagasse and pine pulps. The pulps were characterised in terms of the permeability parameters, the specific surface area, Sv, and the swelling factor, α. It was found that the bagasse fraction used affects these parameters. Fractionation of whole bagasse prior to pulping produced pulps that have permeability properties that compare favourably with eucalypt pulp. The values of Sv and α for bagasse pulp also depend on whether a constant or a variable Kozeny factor is used.

Expression of Potato virus Y cytoplasmic inclusion protein in tobacco results in disorganization of parenchyma cells, distortion of epidermal cells, and induces mitochondrial and chloroplast abnormalities, formation of membrane whorls and atypical lipid accumulation

Infection of plant cells by potyviruses induces the formation of cytoplasmic inclusions ranging in size from 200 to 1000 nm. To determine if the ability to form these ordered, insoluble structures is intrinsic to the potyviral cytoplasmic inclusion protein, we have expressed the cytoplasmic inclusion protein from Potato virus Y in tobacco under the control of the chrysanthemum ribulose-1,5-bisphosphate carboxylase small subunit promoter, a highly active, green tissue promoter. No cytoplasmic inclusions were observed in the leaves of transgenic tobacco using transmission electron microscopy, despite being able to clearly visualize these inclusions in Potato virus Y infected tobacco leaves under the same conditions. However, we did observe a wide range of tissue and sub-cellular abnormalities associated with the expression of the Potato virus Y cytoplasmic inclusion protein. These changes included the disruption of normal cell morphology and organization in leaves, mitochondrial and chloroplast internal reorganization, and the formation of atypical lipid accumulations. Despite these significant structural changes, however, transgenic tobacco plants were viable and the results are discussed in the context of potyviral cytoplasmic inclusion protein function.

A study into the permeability and compressibility of Australian bagasse pulp

This is an experimental study into the permeability and compressibility properties of bagasse pulp pads. Three experimental rigs were custom-built for this project. The experimental work is complemented by modelling work. Both the steady-state and dynamic behaviour of pulp pads are evaluated in the experimental and modelling components of this project. Bagasse, the fibrous residue that remains after sugar is extracted from sugarcane, is normally burnt in Australia to generate steam and electricity for the sugar factory. A study into bagasse pulp was motivated by the possibility of making highly value-added pulp products from bagasse for the financial benefit of sugarcane millers and growers. The bagasse pulp and paper industry is a multibillion dollar industry (1). Bagasse pulp could replace eucalypt pulp which is more widely used in the local production of paper products. An opportunity exists for replacing the large quantity of mainly generic paper products imported to Australia. This includes 949,000 tonnes of generic photocopier papers (2). The use of bagasse pulp for paper manufacture is the main application area of interest for this study. Bagasse contains a large quantity of short parenchyma cells called ‘pith’. Around 30% of the shortest fibres are removed from bagasse prior to pulping. Despite the ‘depithing’ operations in conventional bagasse pulp mills, a large amount of pith remains in the pulp. Amongst Australian paper producers there is a perception that the high quantity of short fibres in bagasse pulp leads to poor filtration behaviour at the wet-end of a paper machine. Bagasse pulp’s poor filtration behaviour reduces paper production rates and consequently revenue when compared to paper production using locally made eucalypt pulp. Pulp filtration can be characterised by two interacting factors; permeability and compressibility. Surprisingly, there has previously been very little rigorous investigation into neither bagasse pulp permeability nor compressibility. Only freeness testing of bagasse pulp has been published in the open literature. As a result, this study has focussed on a detailed investigation of the filtration properties of bagasse pulp pads. As part of this investigation, this study investigated three options for improving the permeability and compressibility properties of Australian bagasse pulp pads. Two options for further pre-treating depithed bagasse prior to pulping were considered. Firstly, bagasse was fractionated based on size. Two bagasse fractions were produced, ‘coarse’ and ‘medium’ bagasse fractions. Secondly, bagasse was collected after being processed on two types of juice extraction technology, i.e. from a sugar mill and from a sugar diffuser. Finally one method of post-treating the bagasse pulp was investigated. The effects of chemical additives, which are known to improve freeness, were also assessed for their effect on pulp pad permeability and compressibility. Pre-treated Australian bagasse pulp samples were compared with several benchmark pulp samples. A sample of commonly used kraft Eucalyptus globulus pulp was obtained. A sample of depithed Argentinean bagasse, which is used for commercial paper production, was also obtained. A sample of Australian bagasse which was depithed as per typical factory operations was also produced for benchmarking purposes. The steady-state pulp pad permeability and compressibility parameters were determined experimentally using two purpose-built experimental rigs. In reality, steady-state conditions do not exist on a paper machine. The permeability changes as the sheet compresses over time. Hence, a dynamic model was developed which uses the experimentally determined steady-state permeability and compressibility parameters as inputs. The filtration model was developed with a view to designing pulp processing equipment that is suitable specifically for bagasse pulp. The predicted results of the dynamic model were compared to experimental data. The effectiveness of a polymeric and microparticle chemical additives for improving the retention of short fibres and increasing the drainage rate of a bagasse pulp slurry was determined in a third purpose-built rig; a modified Dynamic Drainage Jar (DDJ). These chemical additives were then used in the making of a pulp pad, and their effect on the steady-state and dynamic permeability and compressibility of bagasse pulp pads was determined. The most important finding from this investigation was that Australian bagasse pulp was produced with higher permeability than eucalypt pulp, despite a higher overall content of short fibres. It is thought this research outcome could enable Australian paper producers to switch from eucalypt pulp to bagasse pulp without sacrificing paper machine productivity. It is thought that two factors contributed to the high permeability of the bagasse pulp pad. Firstly, thicker cell walls of the bagasse pulp fibres resulted in high fibre stiffness. Secondly, the bagasse pulp had a large proportion of fibres longer than 1.3 mm. These attributes helped to reinforce the pulp pad matrix. The steady-state permeability and compressibility parameters for the eucalypt pulp were consistent with those found by previous workers. It was also found that Australian pulp derived from the ‘coarse’ bagasse fraction had higher steady-state permeability than the ‘medium’ fraction. However, there was no difference between bagasse pulp originating from a diffuser or a mill. The bagasse pre-treatment options investigated in this study were not found to affect the steady-state compressibility parameters of a pulp pad. The dynamic filtration model was found to give predictions that were in good agreement with experimental data for pads made from samples of pretreated bagasse pulp, provided at least some pith was removed prior to pulping. Applying vacuum to a pulp slurry in the modified DDJ dramatically reduced the drainage time. At any level of vacuum, bagasse pulp benefitted from chemical additives as quantified by reduced drainage time and increased retention of short fibres. Using the modified DDJ, it was observed that under specific conditions, a benchmark depithed bagasse pulp drained more rapidly than the ‘coarse’ bagasse pulp. In steady-state permeability and compressibility experiments, the addition of chemical additives improved the pad permeability and compressibility of a benchmark bagasse pulp with a high quantity of short fibres. Importantly, this effect was not observed for the ‘coarse’ bagasse pulp. However, dynamic filtration experiments showed that there was also a small observable improvement in filtration for the ‘medium’ bagasse pulp. The mechanism of bagasse pulp pad consolidation appears to be by fibre realignment. Chemical additives assist to lubricate the consolidation process. This study was complemented by pulp physical and chemical property testing and a microscopy study. In addition to its high pulp pad permeability, ‘coarse’ bagasse pulp often (but not always) had superior physical properties than a benchmark depithed bagasse pulp.

The expression of ADAM-9 and -10 in prostate cancer and their regulation by dihydrotestosterone, insulin-like growth Factor-1 and epidermal growth factor

Prostrate Cancer(PCa)is the most common cause of cancer death amongst Western males. PCa occurs in two distinct stages. In its early stage, growth and development is dependent primarily on male sex hormones (androgens) such as testosterone, although other growth factors have roles maintaining PCa cell survival in this stage. In the later stage of PCa development, growth and.maintenance is independent of androgen stimulation and growth factors including Insulin-like Growth Factor -1 (IGf.:·l) and Epidermal Growth Factor (EGF) are thought to have more crucial roles in cell survival and PCa progression. PCa, in its late stages, is highly aggressive and metastatic, that is, tumorigenic cells migrate from the primary site of the body (prostate) and travel via the systemic and lymphatic circulation, residing and colonising in the bone, lymph node, lung, and in more rare cases, the brain. Metastasis involves both cell migration and tissue degradation activities. The degradation of the extracellular matrix (ECM), the tissue surrounding the organ, is mediated in part by members of a family of 26 proteins called the Matrix Metalloproteases (MMPs), whilst ceil adhesion molecules, of which proteins known as Integrins are included, mediate ce11 migration. A family of proteins known as the ADAMs (A Disintegrin . And Metalloprotease domain) were a recently characterised family at the commencement of this study and now comprise 34 members. Because of their dual nature, possessing an active metaiioprotease domain, homologous to that of the MMPs, and an integrin-binding domain capable of regulating cell-cell and cell-ECM contacts, it was thought likely that members of the ADAMs family may have implications for the progression of aggressive cancers such as those ofthe prostate. This study focussed on two particular ADAMs -9 and -10. ADAM-9 has an active metalloprotease domain, which has been shown to degrade constituents of the ECM, including fibronectin, in vitro. It also has an integrin-binding capacity through association with key integrins involved in PCa progression, such as a6~1. ADAM-10 has no such integrin binding activities, but its bovine orthologue, MADM, is able to degrade coHagen type IV, a major component of basement membranes. It is likely human ADAM-10 has the same activity. It is also known to cleave Ll -a protein involved in cell anchorage activities - and collagen type XVII - which is a principal component of the hemidesmosomes of cellular tight junctions. The cleavage of these proteins enables the cell to be released from the surrounding environment and commence migratory activities, as required in metastasis. Previous studies in this laboratory showed the mRNA expression of the five ADAMs -9,- 10, -11, -15 and -17 in PCa cell lines, characteristic of androgen-dependent and androgen independent disease. These studies were furthered by the characterisation of AD AM-9, -10 and -17 mRNA regulation by Dihydrotestosterone (DHT) in the androgen-responsive cell line (LNCaP). ADAM-9 and -10 mRNA levels were elevated in response to DHT stimulation. Further to these observations, the expression of ADAM-9 and -10 was shown in primary prostate biopsies from patients with PCa. ADAM-1 0 was expressed in the cytoplasm and on the ceH membrane in epithelial and basal cells ofbenign prostate glands, but in high-grade PCa glands, ADAM-I 0 expression was localised to the nucleus and its expression levels appeared to be elevated when compared to low-grade PCa glands. These studies provided a strong background for the hypothesis that ADAM-9 and -10 have key roles in the development ofPCa and provided a basis for further studies.The aims of this study were to: 1) characterise the expression, localisation and levels, of ADAM-9 and -10 mRNA and protein in cell models representing characteristics of normal through androgen-dependent to androgen-independent PCa, as well as to expand the primary PCa biopsy data for ADAM-9 and ADAM-10 to encompass PCa bone metastases 2) establish an in vitro cell system, which could express elevated levels of ADAM-1 0 so that functional cell-based assays such as cell migration, invasion and attachment could be carried out, and 3) to extend the previous hormonal regulation data, to fully characterise the response of ADAM-9 and -10 mRNA and protein levels to DHT, IGF-1, DHT plus IGF-1 and EGF in the hormonal/growth factor responsive cell line LNCaP. For aim 1 (expression of ADAM-9 and -10 mRNA and protein), ADAM-9 and -10 mRNA were characterised by R T -PCR, while their protein products were analysed by Western blot. Both ADAM-9 and -10 mRNA and protein were expressed at readily detectable levels across progressively metastatic PCa cell lines model that represent characteristics of low-grade,. androgen-dependent (LNCaP and C4) to high-grade, androgen-independent (C4-2 and C4-2B) PCa. When the non-tumorigenic prostate cell line RWPE-1 was compared with the metastatic PCa cell line PC-3, differential expression patterns were seen by Western blot analysis. For ADAM-9, the active form was expressed at higher levels in RWPE-1, whilst subcellular fractionation showed that the active form of ADAM-9 was predominantly located in the cell nucleus. For ADAM-I 0, in both of the cell Jines, a nuclear specific isoform of the mature, catalytically active ADAM-I 0 was found. This isoforrn differed by -2 kDa in Mr (smaller) than the cytoplasmic specific isoform. Unprocessed ADAM-I 0 was readily detected in R WPE-1 cell lines but only occasionally detected in PC-3 cell lines. Immunocytochemistry using ADAM-9 and -10 specific antibodies confirmed nuclear, cytoplasmic and membrane expression of both ADAMs in these two cell lines. To examine the possibility of ADAM-9 and -10 being shed into the extracellular environment, membrane vesicles that are constitutively shed from the cell surface and contain membrane-associated proteins were collected from the media of the prostate cell lines RWPE-1, LNCaP and PC-3. ADAM-9 was readily detectable in RWPE- 1 and LNCaP cell membrane vesicles by Western blot analysis, but not in PC-3 cells, whilst the expression of ADAM-I 0 was detected in shed vesicles from each of these prostate cell lines. By Laser Capture Microdissection (LCM), secretory epithelial cells of primary prostate gland biopsies were isolated from benign and malignant glands. These secretory cells, by Western blot analysis, expressed similar Mr bands for ADAM-9 and -10 that were found in PCa cell lines in vitro, indicating that the nuclear specific isoforrn of ADAM-I 0 was present in PCa primary tumours and may represent the predominantly nuclear form of ADAM-I 0 expression, previously shown in high-grade PCa by immunohistochemistry (IHC). ADAM-9 and -10 were also examined by IHC in bone metastases taken from PCa patients at biopsy. Both ADAMs could be detected at levels similar to those shown for Prostate Specific Antigen (PSA) in these biopsies. Furthermore, both ADAM-9 and -10 were predominantly membrane- bound with occasional nuclear expression. For aim 2, to establish a cell system that over-expressed levels of ADAM-10, two fulllength ADAM-I 0 mammalian expression vectors were constructed; ADAM-I 0 was cloned into pcDNA3.1, which contains a CMV promoter, and into pMEP4, containing an inducible metallothionine promoter, whose activity is stimulated by the addition of CdC}z. The efficiency of these two constructs was tested by way of transient transfection in the PCa cell line PC-3, whilst the pcDNA3.1 construct was also tested in the RWPE-1 prostate cell line. Resultant Western blot analysis for all transient transfection assays showed that levels of ADAM-I 0 were not significantly elevated in any case, when compared to levels of the housekeeping gene ~-Tubulin, despite testing various levels of vector DNA, and, for pMEP4, the induction of the transfected cell system with different degrees of stimulation with CdCh to activate the metallothionine promoter post-transfection. Another study in this laboratory found similar results when the same full length ADAM-10 sequence was cloned into a Green Fluorescent Protein (GFP) expressing vector, as no fluorescence was observed by means of transient tran sfection in the same, and other, PCa cell lines. It was hypothesised that the Kozak sequence included in the full-length construct (human ADAMI 0 naturally occurring sequence) is not strong enough to initiate translation in an artificial system, in cells, which, as described in Aim 1, are already expressing readily detectable levels of endogenous ADAM-10. As a result, time constraints prevented any further progress with Aim 2 and functional studies including cell attachment, invasion and migration were unable to be explored. For Aim 3, to characterise the response of ADAM-9 and -10 mRNA and protein levels to DHT, IGF-1, DHT plus IGF-1 and EGF in LNCaP cells, the levels of ADAM-9 and -10 mRNA were not stimulated by DHT or IGF-I alone, despite our previous observations that initially characterised ADAM-9 and -10 mRNA as being responsive to DHT. However, IGF-1 in synergy with DHT did significantly elevate mRNA levels ofboth ADAMs. In the case of ADAM-9 and -10 protein, the same trends of stimulation as found at the rnRNA level were shown by Western blot analysis when ADAM-9 and -10 signal intensity was normalised with the housekeeping protein ~-Tubulin. For EGF treatment, both ADAM-9 and -10 mRNA and protein levels were significantly elevated, and further investigation vm found this to be the case for each of these ADAMs proteins in the nuclear fractions of LNCaP cells. These studies are the first to describe extensively, the expression and hormonal/growth factor regulation of two members of the ADAMs family ( -9 and -1 0) in PCa. These observations imply that the expression of ADAM-9 and -10 have varied roles in PCa whilst it develops from androgen-sensitive (early stage disease), through to an androgeninsensitive (late-stage), metastatic disease. Further studies are now required to investigate the several key areas of focus that this research has revealed, including: • Investigation of the cellular mechanisms that are involved in actively transporting the ADAMs to the cell's nuclear compartment and the ADAMs functional roles in the cell nucleus. • The construction of a full-length human ADAM-10 mammalian expression construct with the introduction of a new Kozak sequence, that elevates ADAM-I 0 expression in an in vitro cell system are required, so that functional assays such as cell invasion, migration and attachment may be carried out to fmd the functional consequences of ADAM expression on cellular behaviour. • The regulation studies also need to be extended by confirming the preliminary observations that the nuclear levels of ADAMs may also be elevated by hormones and growth factors such as DHT, IGF-1 and EGF, as well as the regulation of levels of plasma membrany vesicle associated ADAM expression. Given the data presented in this study, it is likely the ADAMs have differential roles throughout the development of PCa due to their differential cellular localisation and synergistic growth-factor regulation. These observations, along with those further studies outlined above, are necessary in identifying these specific components ofPCa metastasis to which the ADAMs may contribute.

Active regulation of the epidermal calcium profile

A distinct calcium profile is strongly implicated in regulating the multi-layered structure of the epidermis. However, the mechanisms that govern the regulation of this calcium profile are currently unclear. It clearly depends on the relatively impermeable barrier of the stratum corneum (passive regulation) but may also depend on calcium exchanges between keratinocytes and extracellular fluid (active regulation). Using a mathematical model that treats the viable sublayers of unwounded human and murine epidermis as porous media and assumes that their calcium profiles are passively regulated, we demonstrate that these profiles are also actively regulated. To obtain this result, we found that diffusion governs extracellular calcium motion in the viable epidermis and hence intracellular calcium is the main source of the epidermal calcium profile. Then, by comparison with experimental calcium profiles and combination with a hypothesised cell velocity distribution in the viable epidermis, we found that the net influx of calcium ions into keratinocytes from extracellular fluid may be constant and positive throughout the stratum basale and stratum spinosum, and that there is a net outflux of these ions in the stratum granulosum. Hence the calcium exchange between keratinocytes and extracellular fluid differs distinctly between the stratum granulosum and the underlying sublayers, and these differences actively regulate the epidermal calcium profile. Our results also indicate that plasma membrane dysfunction may be an early event during keratinocyte disintegration in the stratum granulosum.

A continuum model of the growth of engineered epidermal skin substitutes

We present a porous medium model of the growth and deterioration of the viable sublayers of an epidermal skin substitute. It consists of five species: cells, intracellular and extracellular calcium, tight junctions, and a hypothesised signal chemical emanating from the stratum corneum. The model is solved numerically in Matlab using a finite difference scheme. Steady state calcium distributions are predicted that agree well with the experimental data. Our model also demonstrates epidermal skin substitute deterioration if the calcium diffusion coefficient is reduced compared to reported values in the literature.

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Mass transfer properties (permeability and mass diffusivity) of four australian hardwood species

Characterization of mass transfer properties was achieved in the longitudinal, radial, and tangential directions for four Australian hardwood species: spotted gum, blackbutt, jarrah, and messmate. Measurement of mass transfer properties for these species was necessary to complement current vacuum drying modeling research. Water-vapour diffusivity was determined in steady state using a specific vapometer. Permeability was determined using a specialized device developed to measure over a wide range of permeability values. Permeability values of some species and material directions were extremely low and undetectable by the mass flow meter device. Hence, a custom system based on volume evolution was conceived to determine very low, previously unpublished, wood permeability values. Mass diffusivity and permeability were lowest for spotted gum and highest for messmate. Except for messmate in the radial direction, the four species measured were less permeable in all directions than the lowest published figures, demonstrating the high impermeability of Australian hardwoods and partly accounting for their relatively slow drying rates. Permeability, water-vapour diffusivity, and associated anisotropic ratio data obtained for messmate were extreme or did not follow typical trends and is consequently the most difficult of the four woods to dry in terms of collapse and checking degradation. © The State of Queensland, Department of Agriculture, Fisheries and Forestry, 2012.

The cell surface glycoprotein CUB domain-containing protein 1 (CDCP1) contributes to epidermal growth factor receptor-mediated cell migration

Epidermal growth factor (EGF) activation of the EGF receptor (EGFR) is an important mediator of cell migration, and aberrant signaling via this system promotes a number of malignancies including ovarian cancer. We have identified the cell surface glycoprotein CDCP1 as a key regulator of EGF/EGFR-induced cell migration. We show that signaling via EGF/EGFR induces migration of ovarian cancer Caov3 and OVCA420 cells with concomitant up-regulation of CDCP1 mRNA and protein. Consistent with a role in cell migration CDCP1 relocates from cell-cell junctions to punctate structures on filopodia after activation of EGFR. Significantly, disruption of CDCP1 either by silencing or the use of a function blocking antibody efficiently reduces EGF/EGFR-induced cell migration of Caov3 and OVCA420 cells. We also show that up-regulation of CDCP1 is inhibited by pharmacological agents blocking ERK but not Src signaling, indicating that the RAS/RAF/MEK/ERK pathway is required downstream of EGF/EGFR to induce increased expression of CDCP1. Our immunohistochemical analysis of benign, primary, and metastatic serous epithelial ovarian tumors demonstrates that CDCP1 is expressed during progression of this cancer. These data highlight a novel role for CDCP1 in EGF/EGFR-induced cell migration and indicate that targeting of CDCP1 may be a rational approach to inhibit progression of cancers driven by EGFR signaling including those resistant to anti-EGFR drugs because of activating mutations in the RAS/RAF/MEK/ERK pathway.

Permeability estimation conditioned to geophysical downhole log data in sandstones of the northern Galilee Basin, Queensland : methods and application

This study uses borehole geophysical log data of sonic velocity and electrical resistivity to estimate permeability in sandstones in the northern Galilee Basin, Queensland. The prior estimates of permeability are calculated according to the deterministic log–log linear empirical correlations between electrical resistivity and measured permeability. Both negative and positive relationships are influenced by the clay content. The prior estimates of permeability are updated in a Bayesian framework for three boreholes using both the cokriging (CK) method and a normal linear regression (NLR) approach to infer the likelihood function. The results show that the mean permeability estimated from the CK-based Bayesian method is in better agreement with the measured permeability when a fairly apparent linear relationship exists between the logarithm of permeability and sonic velocity. In contrast, the NLR-based Bayesian approach gives better estimates of permeability for boreholes where no linear relationship exists between logarithm permeability and sonic velocity.