Bruce S. Gardiner

Intrarenal oxygenation: unique challenges and the biophysical basis of homeostasis

The kidney is faced with unique challenges for oxygen regulation, both because its function requires that perfusion greatly exceeds that required to meet metabolic demand and because vascular control in the kidney is dominated by mechanisms that regulate glomerular filtration and tubular reabsorption. Because tubular sodium reabsorption accounts for most oxygen consumption (Vo2) in the kidney, renal Vo2 varies with glomerular filtration rate. This provides an intrinsic mechanism to match changes in oxygen delivery due to changes in renal blood flow (RBF) with changes in oxygen demand. Renal Vo2 is low relative to supply of oxygen, but diffusional arterial-to-venous (AV) oxygen shunting provides a mechanism by which oxygen superfluous to metabolic demand can bypass the renal microcirculation. This mechanism prevents development of tissue hyperoxia and subsequent tissue oxidation that would otherwise result from the mismatch between renal Vo2 and RBF. Recent evidence suggests that RBF-dependent changes in AV oxygen shunting may also help maintain stable tissue oxygen tension when RBF changes within the physiological range. However, AV oxygen shunting also renders the kidney susceptible to hypoxia. Given that tissue hypoxia is a hallmark of both acute renal injury and chronic renal disease, understanding the causes of tissue hypoxia is of great clinical importance. The simplistic paradigm of oxygenation depending only on the balance between local perfusion and Vo2 is inadequate to achieve this goal. To fully understand the control of renal oxygenation, we must consider a triad of factors that regulate intrarenal oxygenation: local perfusion, local Vo2, and AV oxygen shunting.

Bubble growth and rise in soft sediments

The mechanics of uncemented soft sediments during bubble growth are not widely understood and no rheological model has found wide acceptance. We offer definitive evidence on the mode of bubble formation in the form of X-ray computed tomographic images and comparison with theory. Natural and injected bubbles in muddy cohesive sediments are shown to be highly eccentric oblate spheroids (disks) that grow either by fracturing the sediment or by reopening preexisting fractures. In contrast, bubbles in soft sandy sediment tend to be spherical, suggesting that sand acts fluidly or plastically in response to growth stresses. We also present bubble-rise results from gelatin, a mechanically similar but transparent medium, that suggest that initial rise is also accomplished by fracture. Given that muddy sediments are elastic and yield by fracture, it becomes much easier to explain physically related phenomena such as seafloor pockmark formation, animal burrowing, and gas buildup during methane hydrate melting.

Haemodynamic influences on kidney oxygenation: clinical implications of integrative physiology

Renal blood flow, local tissue perfusion and blood oxygen content are the major determinants of oxygen delivery to kidney tissue. Arterial pressure and segmental vascular resistance influence kidney oxygen consumption through effects on glomerular filtration rate and sodium reabsorption. Diffusive shunting of oxygen from arteries to veins in the cortex and from descending to ascending vasa recta in the medulla limits oxygen delivery to renal tissue. Oxygen shunting depends on the vascular network, renal haemodynamics and kidney oxygen consumption. Consequently, the impact of changes in renal haemodynamics on tissue oxygenation cannot necessarily be predicted intuitively and, instead, requires the integrative approach offered by computational modelling and multiple measuring modalities. Tissue hypoxia is a hallmark of acute kidney injury (AKI) arising from multiple initiating insults, including ischaemia–reperfusion injury, radiocontrast administration, cardiopulmonary bypass surgery, shock and sepsis. Its pathophysiology is defined by inflammation and/or ischaemia resulting in alterations in renal tissue oxygenation, nitric oxide bioavailability and oxygen radical homeostasis. This sequence of events appears to cause renal microcirculatory dysfunction, which may then be exacerbated by the inappropriate use of therapies common in peri‐operative medicine, such as fluid resuscitation. The development of new ways to prevent and treat AKI requires an integrative approach that considers not just the molecular mechanisms underlying failure of filtration and tissue damage, but also the contribution of haemodynamic factors that determine kidney oxygenation. The development of bedside monitors allowing continuous surveillance of renal haemodynamics, oxygenation and function should facilitate better prevention, detection and treatment of AKI.

Mechanical response of sediments to bubble growth

Modeling the process of bubble growth in sediments requires an understanding of the physics that controls bubble shape and the interaction of the growing bubble with the sediment. To acquire this understanding we have conducted experiments in which we have injected gas through a fine capillary into natural and surrogate sediment samples and have monitored pressure during bubble growth to provide information about stress and strain. In gas injection studies with natural sediment samples, we have observed two modes of bubble growth behavior. One of these modes, characterized by a saw-tooth record of pressure as the bubble grows, is consistent with fracture of the medium. Observations indicate that bubble growth by fracture should correspond to bubbles that are coin- or disk-shaped. This shape is confirmed in observations of bubbles in natural sediments and in our studies of bubble injection into gelatin, a surrogate sediment material. Interpretation of the stress–strain results for bubble growth also required that we measure Young’s modulus, E. The measurements show E to be near 0.14 MN m2, which differs by more than 4 orders of magnitude from values that have been reported in the literature. Our measurements of E give substantially better estimates of bubble shape than are predicted using the literature values. Our data are interpreted with linear elastic fracture mechanics (LEFM) which predicts that the critical pressure for bubble growth will depend on the bubble volume, V raised to the −1/5 power. While evidence of substantial heterogeneity in sediment properties is apparent in our results, this V−1/5 dependence is confirmed. Through application of LEFM theory, we have determined the critical stress intensity factor, K1c, a material property and the principal determinant of bubble shape and growth by fracture. Our values of K1c range from ∼2.8×10−4 MN m−3/2 to ∼4.9×10−4 MN m−3/2 for our natural sediment samples from Cole Harbor, Nova Scotia. We have also estimated the critical stress intensity factor for Eckernforde Bay samples by analyzing published images of natural bubbles. The K1c obtained in this way is similar to our Cole Harbor results and is ∼5.5×10−4 MN m−3/2.

Wnt Signalling Pathway Parameters for Mammalian Cells

Wnt/β-catenin signalling regulates cell fate, survival, proliferation and differentiation at many stages of mammalian development and pathology. Mutations of two key proteins in the pathway, APC and β-catenin, have been implicated in a range of cancers, including colorectal cancer. Activation of Wnt signalling has been associated with the stabilization and nuclear accumulation of β-catenin and consequential up-regulation of β-catenin/TCF gene transcription. In 2003, Lee et al. constructed a computational model of Wnt signalling supported by experimental data from analysis of time-dependent concentration of Wnt signalling proteins in Xenopus egg extracts. Subsequent studies have used the Xenopus quantitative data to infer Wnt pathway dynamics in other systems. As a basis for understanding Wnt signalling in mammalian cells, a confocal live cell imaging measurement technique is developed to measure the cell and nuclear volumes of MDCK, HEK293T cells and 3 human colorectal cancer cell lines and the concentrations of Wnt signalling proteins β-catenin, Axin, APC, GSK3β and E-cadherin. These parameters provide the basis for formulating Wnt signalling models for kidney/intestinal epithelial mammalian cells. There are significant differences in concentrations of key proteins between Xenopus extracts and mammalian whole cell lysates. Higher concentrations of Axin and lower concentrations of APC are present in mammalian cells. Axin concentrations are greater than APC in kidney epithelial cells, whereas in intestinal epithelial cells the APC concentration is higher than Axin. Computational simulations based on Lees model, with this new data, suggest a need for a recalibration of the model. A quantitative understanding of Wnt signalling in mammalian cells, in particular human colorectal cancers requires a detailed understanding of the concentrations of key protein complexes over time. Simulations of Wnt signalling in mammalian cells can be initiated with the parameters measured in this report.

Rheology of fire-fighting foams

This paper examines the rheological properties of compressed-air foams and contains velocity profiles of foams flowing through straight horizontal tubes. It is shown that a master equation can be derived from the experimental data to account for a range of expansion ratios and pressures normally encountered during pumping of polyhedral-in-structure fire-fighting foams. The experimental data come from a Poiseuille-flow rheometer consisting of three stainless steel tubes 6.95, 9.9, 15.8 mm in diameter, with foam generated by mixing a pressurised solution of Class A foam with compressed air. Results are corrected for wall slip following the method of Oldroyd-Jastrzebski, which implies the dependence of slip coefficients on the curvature of the tube wall. The experimental results demonstrate the applicability of the volume equalisation method to the more expanded, polyhedral (e>5) and transition, bubbly-to-polyhedral (5⩾e⩾4) foams. (The method of volume equalisation was introduced by Valko and Economides to correlate the viscosity of low expansion foams (e<4), characterised by spherical bubbles.) The present results indicate that all data points align themselves along two master curves, depending on whether the foam consists of bubbles or polyhedral cells.

Growth of disk-shaped bubbles in sediments

Disc-shaped methane bubbles, often observed in marine sediments, result from growth in a medium that elastically resists expansion of the bubbles and yields by fracture. We have modeled this process to obtain estimates of growth times by using a reaction-diffusion model coupled to a linear elastic fracture mechanics (LEFM). For comparison, we also modeled the growth of a constant eccentricity bubble in a nonresistant medium. Discoidal bubbles that grow in sediments that obey LEFM grow much faster than spherical bubbles (two- to fourfold faster for the times and conditions tested here) and become more eccentric with time (aspect ratios falling from 0.3 to 0.03 ove r8do fgrowth). In addition, their growth is not continuous but punctuated by fracture events. Furthermore, under some conditions, LEFM predicts that bubble growth can become arrested, which is not possible for a bubble in a nonresistant medium, even for nonspherical bubbles. Cessation of growth occurs when the dissolved gas concentration gradient near the bubble surface disappears as a result of the increase in bubble gas pressure needed to overcome sediment elasticity. Copyright

METHODS FOR STUDYING THE PHYSIOLOGY OF KIDNEY OXYGENATION

1 An improved understanding of the regulation of kidney oxygenation has the potential to advance preventative, diagnostic and therapeutic strategies for kidney disease. Here, we review the strengths and limitations of available and emerging methods for studying kidney oxygen status. 2 To fully characterize kidney oxygen handling, we must quantify multiple parameters, including renal oxygen delivery (DO2) and consumption (VO2), as well as oxygen tension (Po2). Ideally, these parameters should be quantified both at the whole‐organ level and within specific vascular, tubular and interstitial compartments. 3 Much of our current knowledge of kidney oxygen physiology comes from established techniques that allow measurement of global kidney DO2 and VO2, or local tissue Po2. When used in tandem, these techniques can help us understand oxygen mass balance in the kidney. Po2 can be resolved to specific tissue compartments in the superficial cortex, but not deep below the kidney surface. We have limited ability to measure local kidney tissue DO2 and VO2. 4 Mathematical modelling has the potential to provide new insights into the physiology of kidney oxygenation, but is limited by the quality of the information such models are based on. 5 Various imaging techniques and other emerging technologies have the potential to allow Po2 mapping throughout the kidney and/or spatial resolution of Po2 in specific renal tissues, even in humans. All currently available methods have serious limitations, but with further refinement should provide a pathway through which data obtained from experimental animal models can be related to humans in the clinical setting.

Yield stress measurements of aqueous foams in the dry limit

This paper reports measurements of yield stress of aqueous foams approaching the dry foam limit using a pendulum device. Traditionally, the vane rheometer has been used to measure the yield stress in liquids that exhibit wall slip. However, using the simple and inexpensive pendulum technique, shear rates many orders of magnitudes lower can be achieved. The pendulum was used to observe the change in yield stress for the foam as the gas fraction and bubble size increased. The local gas fraction in the foam was found by measuring the sonic velocity, and the bubble size was determined photographically. Strong support is found for the existence of a true yield stress in aqueous foams at the dry foam limit. Yield stress results, once scaled by σ/〈R〉, agree well with data from previous studies.

A mathematical model of diffusional shunting of oxygen from arteries to veins in the kidney

To understand how arterial-to-venous (AV) oxygen shunting influences kidney oxygenation, a mathematical model of oxygen transport in the renal cortex was created. The model consists of a multiscale hierarchy of 11 countercurrent systems representing the various branch levels of the cortical vasculature. At each level, equations describing the reactive-advection-diffusion of oxygen are solved. Factors critical in renal oxygen transport incorporated into the model include the parallel geometry of arteries and veins and their respective sizes, variation in blood velocity in each vessel, oxygen transport (along the vessels, between the vessels and between vessel and parenchyma), nonlinear binding of oxygen to hemoglobin, and the consumption of oxygen by renal tissue. The model is calibrated using published measurements of cortical vascular geometry and microvascular Po(2). The model predicts that AV oxygen shunting is quantitatively significant and estimates how much kidney Vo(2) must change, in the face of altered renal blood flow, to maintain cortical tissue Po(2) at a stable level. It is demonstrated that oxygen shunting increases as renal Vo(2) or arterial Po(2) increases. Oxygen shunting also increases as renal blood flow is reduced within the physiological range or during mild hemodilution. In severe ischemia or anemia, or when kidney Vo(2) increases, AV oxygen shunting in proximal vascular elements may reduce the oxygen content of blood destined for the medullary circulation, thereby exacerbating the development of tissue hypoxia. That is, cortical ischemia could cause medullary hypoxia even when medullary perfusion is maintained. Cortical AV oxygen shunting limits the change in oxygen delivery to cortical tissue and stabilizes tissue Po(2) when arterial Po(2) changes, but renders the cortex and perhaps also the medulla susceptible to hypoxia when oxygen delivery falls or consumption increases.