Numerical simulation of convective and diffusive transport effects on a high-pressure-induced inactivation process

High-pressure-induced conversions, such as the inactivation of enzymes or of microorganisms, are dependent on the applied pressure and the temperature of the process. The former can be considered to be a spatially homogeneous quantity, while the latter, being a transport quantity, varies over space and time. Here we question whether the uniformity of a high-pressure conversion can be disturbed by convective and conductive heat and mass transport conditions. Enzyme inactivation is taken as a model process for a high-pressure conversion. To cover a broad range of parameters and to consider scale-up effects, the investigation is based on mathematical modeling and numerical simulation for different sizes of the pressure chamber and different solvent viscosities. Apart from viscosity, the physical properties of the enzyme solutions are assumed to be identical in all cases. Therefore, matrix effects other than that of viscosity are excluded. Moreover, the authors postulate that viscosity solely acts on the continuum mechanical scale of momentum exchange but not on the molecular scale on the inactivation kinetics. It has been found that nonuniform thermal conditions can strongly influence the result of a high-pressure process. A variation of the activity retention between 28% and 48% can be observed after 20 minutes for a 0.8-L high-pressure chamber and a matrix fluid with a viscosity comparable to that of edible oils. The same process carried out in a 6.3-L device leads to an activity retention that varies between 16% and 40%. From the analysis of the time scales for the inactivation and for hydrodynamic and thermal compensation, it can be deduced that a nonuniform activity retention has to be expected if the inactivation time scale is larger than the hydrodynamic time scale and smaller than the thermal compensation time scale.     

Simultaneous multiple toe transfers in hand reconstruction

Our experience with simultaneous transfer of two or more toe units to the same hand where multiple digits were missing is presented. Forty-six toes from 38 feet were transferred to reconstruct 19 hands in 19 patients. The transfers consisted of 7 combined second and third toe units and 32 single toes. Three patients had a primary and 16 patients had a secondary reconstruction. There was one complete and one partial failure. The two-point discrimination ranged from 6 mm to protective sensation. Total active movement averaged 57 degrees in the thumb and 127, 93, 71, and 68 degrees, respectively, in the fingers reconstructed at middle phalanx, proximal phalanx, metacarpophalangeal joint, and metacarpal head. Pulp-to-pulp pinch averaged 2.4 kg in patients who had thumbs reconstructed and averaged 3.0 kg in patients who had normal thumbs. There was no cold intolerance, and no significantly disabled foot occurred except one with scissoring deformity. Simultaneous multiple toe transfer in hand reconstruction is feasible without increased complications both in primary and secondary wound conditions. It is time-effective and cost-effective.     

Numerical modelling of conductive and convective heat transfers in retinal laser applications

The control of the temperature increase is an important issue in retinal laser treatments. Within the fundus of the eye heat, generated by absorption of light, is transmitted by diffusion in the retinal pigment epithelium and in the choroid and lost by convection due to the choroidal blood flow. The temperature can be spatially and temporally determined by solving the heat equation. In a former analytical model this was achieved by assuming uniform convection for the whole fundus of the eye. A numerical method avoiding this unrealistic assumption by considering convective heat transfer only in the choroid is used here to solve the heat equation. Numerical results are compared with experimental results obtained by using a novel method of noninvasive optoacoustic retinal temperature measurements in rabbits. Assuming global convection the perfusion coefficient was evaluated to 0.07 s^?1, whereas a value of 0.32 s^?1 – much closer to values found in the literature (between 0.28 and 0.30 s^?1) – was obtained when choroidal convection was assumed, showing the advantage of the numerical method. The modelling of retinal laser treatment is thus improved and could be considered in the future to optimize treatments by calculating retinal temperature increases under various tissues and laser properties. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison of convective and diffusive absorption of nutrients by growing roots

With the roots assumed growing at an exponential rate the effects of the diffusive and convective components of flux and nutrient uptake are examined in a non-dimensional setting. Two cases considered are root-root on no root-root competition. Several examples are presented to illustrate the general effects of interroot competition.Contribution from the Purdue Agric. Exp. Stn., West Lafayette, IN, 47907. Journal Paper Number7656.     

Simultaneous identification of duplications and lateral gene transfers

The incongruency between a gene tree and a corresponding species tree can be attributed to evolutionary events such as gene duplication and gene loss. This paper describes a combinatorial model where so-called DTL-scenarios are used to explain the differences between a gene tree and a corresponding species tree taking into account gene duplications, gene losses, and lateral gene transfers (also known as horizontal gene transfers). The reasonable biological constraint that a lateral gene transfer may only occur between contemporary species leads to the notion of acyclic DTL-scenarios. Parsimony methods are introduced by defining appropriate optimization problems. We show that finding most parsimonious acyclic DTL-scenarios is NP-hard. However, by dropping the condition of acyclicity, the problem becomes tractable, and we provide a dynamic programming algorithm as well as a fixed-parameter tractable algorithm for finding most parsimonious DTL-scenarios.     

Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study

A two-dimensional model for quantitative evaluation of the effect of convective and diffusive substrate transport on biofilm heterogeneity was developed. The model includes flow computation around the irregular biofilm surface, substrate mass transfer by convection and diffusion, biomass growth, and biomass spreading. It was found that in the absence of detachment, biofilm heterogeneity is mainly determined by internal mass transfer rate of substrates and by the initial percentage of carrier-surface colonization. Model predictions show that biofilm structures with highly irregular surface develop in the mass transfer-limited regime. As the nutrient availability increases, there is a gradual shift toward compact and smooth biofilms. A smaller fraction of colonized carrier surface leads to a patchy biofilm. Biofilm surface irregularity and deep vertical channels are, in this case, caused by the inability of the colonies to spread over the whole substratum surface. The maximum substrate flux to the biofilm was greatly influenced by both internal and external mass transfer rates, but not affected by the inoculation density. In general, results of the present model were similar to those obtained by a simple diffusion-reaction-growth model.     

Convective gas transport in the pulmonary acinus: Comparing roles of convective and diffusive lengths

To investigate the relative importance of convection and diffusion in the transport of oxygen in the pulmonary acinus, it is often useful to locate the transition from convection-dominated to diffusion-dominated transport. Traditionally, this is done by estimating the values of a Peclet number. This dimensionless number compares the bulk ductal flow velocity at an acinar generation with a diffusion velocity over a characteristic length scale. Here, we revisit the convection–diffusion transition by comparing the relative importance of convective and diffusive lengths. We introduce the ratio of such lengths (L_conv/L_diff) to quantify the extent of convective transport in the acinus over an inhalation phase. We distinguish between convection along the acinar airways and within alveoli, respectively. Results for L_conv/L_diff suggest that convection in acinar ducts may play a potential role in more peripheral airways compared with values obtained for a Peclet number. Within alveoli, however, independent of acinar depth, oxygen transport is governed by diffusion as soon as molecules enter within alveolar cavities.     

Evaluation of a closed system,diffusive and humidity-induced convective throughflow ventilation on the growth and physiology of cauliflower in vitro

The effects of ethylene inhibitors (silver nitrate – AgNO₃ and silver thiosulphate – Ag₂S₂O₃ as inhibitors of ethylene activity, cobalt chloride – CoCl₂ as inhibitor of ethylene biosynthesis) and ethylene stimulator (aminocyclopropane-1-carboxylic acid – ACC) were studied on the growth of cauliflower (Brassica oleracea L.) seedlings cultured in closed vessels (60 cm³). The addition of ethylene inhibitors have significant stimulatory effects on the growth and development of seedlings and the effects were greatest with 10 μM AgNO₃, the fresh weight of leaves was 2.6×, and the leaf area 2.8× those of the control (no additives). The effects of various methods of ventilation (humidity-induced convective through-flow ventilation, diffusive ventilation and sealed condition) on the growth and physiology of in vitrocauliflower seedlings were also investigated. The seedlings were cultured either in the presence or absence of AgNO₃ (inhibitors of ethylene activity) and ACC (a precursor). Ethylene and CO₂ levels in the head-space of the culture vessels were monitored. The humidity-induced through-flow ventilation system has shown to be effective for improving growth, leaf chlorophyll content and the rate of net photosynthesis and preventing symptoms of hyperhydricity, such as leaf epinasty, and franginess, reduction of leaf area etc. In contrast, the results also indicated that the sealing of culture vessels could have serious inhibitory effects on growth and development, induce hyperhydricity and reduce leaf chlorophyll content. In the light period, CO₂ depletion occurred in the head-space of the sealed vessels (ca. 40 μl l^-1), the CO₂ concentration increased with increasing efficiency of the ventilation. No ethylene accumulation was noticed in the head-space of the culture vessels when humidity-induced throughflow ventilation was applied; however, high ethylene accumulation occurred in sealed vessels. This revised version was published online in June 2006 with corrections to the Cover Date.     

Blood plasma catecholamine concentration of poult embryos during the transition from diffusive to convective respiration

1. Plasma catecholamines were determined in turkey embryos. 2. Decreased eggshell permeability depressed dopamine and epinephrine, but increased permeability also depressed epinephrine. 3. Norepinephrine (NE) was greatest before transition to convective respiration when hypoxia occurs. 4. NE was associated inversely with eggshell permeability. 5. Catecholamines appear to assist the embryo during hatching hypoxia.     

A multiscale theoretical model for diffusive mass transfer in cellular biological media

An integrated methodology is developed for the theoretical analysis of solute transport and reaction in cellular biological media, such as tissues, microbial flocs, and biofilms. First, the method of local spatial averaging with a weight function is used to establish the equation which describes solute conservation at the cellular biological medium scale, starting with a continuum-based formulation of solute transport at finer spatial scales. Second, an effective-medium model is developed for the self-consistent calculation of the local diffusion coefficient in the cellular biological medium, including the effects of the structural heterogeneity of the extra-cellular space and the reversible adsorption to extra-cellular polymers. The final expression for the local effective diffusion coefficient is: D(Abeta)=lambda(beta)D(Aupsilon), where D(Aupsilon) is the diffusion coefficient in water, and lambda(beta) is a function of the composition and fundamental geometric and physicochemical system properties, including the size of solute molecules, the size of extra-cellular polymer fibers, and the mass permeability of the cell membrane. Furthermore, the analysis sheds some light on the function of the extra-cellular hydrogel as a diffusive barrier to solute molecules approaching the cell membrane, and its implications on the transport of chemotherapeutic agents within a cellular biological medium. Finally, the model predicts the qualitative trend as well as the quantitative variability of a large number of published experimental data on the diffusion coefficient of oxygen in cell-entrapping gels, microbial flocs, biofilms, and mammalian tissues.     

Comparison of residual osseous mass between vascularized and nonvascularized onlay bone transfers

Composite flaps containing vascularized frontal bone were transferred on muscle pedicles in immature rabbits. Vascular continuity was maintained on one side and interrupted on the other. Bone weights at 16 weeks following transfer were compared with those of unoperated controls. The conventional bone graft demonstrated significant reduction in osseous mass. The vascularized bone maintained its mass compared with unoperated controls. Vascularized bone transfer appears to be the preferred surgical technique whenever possible.     

Ligand-receptor interaction rates in the presence of convective mass transport.

The rate of binding of a ligand to receptors on the cell surface can be diffusion limited. We analyze the kinetics of binding, diffusion-limited in a stationary liquid, in the presence of convective mass transport. We derive a formula that expresses the reaction kinetics in terms of the mass transfer coefficient. A moderately transport-limited kinetics is not readily recognizable from the shape of the binding curve and may lead to erroneous estimates of the rate coefficients. We apply our results to practically important cases: a cell suspension in a stirred volume of liquid and a confluent cell colony under a laminar stream. Using typical numbers characterizing the ligand-receptor interactions, we show that stirring and perfusion can be important factors determining the reaction rates. With the confluent colony, the early reaction kinetics requires a different treatment, and we provide it for the case of low receptor occupancy. We show that, even with a fast perfusion, a cell monolayer can transiently generate a zone of depletion of the ligand, and that would affect the early stages of the reaction. Our results are expressed in a simple analytical form and can be used for the design and interpretation of experimental data.     

Enzyme-mediated proteolysis of fibrous biopolymers: Dissolution front movement in fibrin or collagen under conditions of diffusive or convective transport

A numerical model based on the convective-diffusive transport of reacting and adsorbing proteolytic enzymes within erodible fibrous biopolymers was used to predict lysis fronts moving across biogels such as fibrin or collagen. The fiber structure and the transport properties of solutes in fibrin (or collagen) were related to the local extent of dissolution within the dissolving structure. An accounting for solubilization of adsorbed species into solution from the eroding fiber phase provided for complete conservation of mass in reacting systems containing over 10 species. At conditions of fibrinolysis typical of clinical situations, the model accurately predicted the dynamic rate of lysis front movement for plasmin, urokinase, and tissue plasminogen activator (tPA)-mediated lysis of fibrin gels measured in vitro. However, under conditions of extremely fast fibrinolysis using high enzyme concentrations, fibrinolytic fronts moved very rapidly (>0.1 mm/mm)-faster than predicted for diffusionlimited reactions-at nearly constant velocity for over 2 h, indicating non-Fickian behavior. This was due to proteolysis-mediated retraction of dissolving fibrin fibers that resulted in fiber convection and front-sharpening within 3 mum of the reaction front, as observed by digitally enhanced microscopy. In comparing the model to fibrinolysis measurements using human lys(77)-plasmin, the average first order rate constant for non-crosslinked fibrin bond cleavage by fibrin-bound plasmin was calculated to be 5s(-1) assuming that 10 cleavages per fibrin monomer were required to solubilize each monomer. The model accurately predicted lysis front movement using pressure-driven permeation of plasmin or urokinase into fibrin as well as literature data obtained under well- mixed conditions for tPA-mediated fibrinolysis. This numerical formulation provides predictive capability for optimization of proteolytic systems which include thrombolytic therapy, wound healing, controlled drug release, and tissue engineering applications. (c) 1995 John Wiley & Sons, Inc.     

A convective mass transfer model for determining intestinal wall permeabilities: laminar flow in a circular tube

A convective mass transfer model as analyzed and developed for use in determining intestinal wall permeabilities from external perfusion experiments. Analysis of the model indicates that the ratio of the exit to inlet concentration $\text{C}{}_{\mathrm{m}}\text{C}{}_0$ is a function of only two dimensionless independent variables, the wall permeability, $\text{P}{}_{\mathrm{w}}{}^1$ and Graetz number, Gz = πDL/2Q. The Graetz number contains the independent variables of interest, length, diflusivity, and flow rate. The radius of the intestine is included implicitly in the flow rate. Since $\text{C}{}_{\mathrm{m}}\text{C}{}_0$ and Gz are the experimental quantities, and the solution to the model system contains P_ω¹ implicitly, a convenient approximate method is developed which allows a direct calculation of P_ω¹. This method is in error by 10–20% in the worst cases. The approach is illustrated by application to the determination of the wall permeabilities for two non polar compounds.     

Radially softening diffusive motions in a globular protein

Molecular dynamics simulation, quasielastic neutron scattering and analytical theory are combined to characterize diffusive motions in a hydrated protein, C-phycocyanin. The simulation-derived scattering function is in approximate agreement with experiment and is decomposed to determine the essential contributions. It is found that the geometry of the atomic motions can be modeled as diffusion in spheres with a distribution of radii. The time dependence of the dynamics follows stretched exponential behavior, reflecting a distribution of relaxation times. The average side chain and backbone dynamics are quantified and compared. The dynamical parameters are shown to present a smooth variation with distance from the core of the protein. Moving outward from the center of the protein there is a progressive increase of the mean sphere size, accompanied by a narrowing and shifting to shorter times of the relaxation time distribution. This smooth, "radially softening" dynamics may have important consequences for protein function. It also raises the possibility that the dynamical or "glass" transition with temperature observed experimentally in proteins might be depth dependent, involving, as the temperature decreases, progressive freezing out of the anharmonic dynamics with increasing distance from the center of the protein.     

Simultaneous determination of ten antiarrhythic drugs and a metabolite in human plasma by liquid chromatography--tandem mass spectrometry

A simple, accurate and selective LC-MS/MS method was developed and validated for simultaneous quantification of ten antiarrhythic drugs (diltiazem, amiodarone, mexiletine, propranolol, sotalol, verapamil, bisoprolol, metoprolol, atenolol, carvedilol) and a metabolite (norverapamil) in human plasma. Plasma samples were simply pretreated with acetonitrile for deproteinization. Chromatographic separation was performed on a Capcell C(18) column (50mmx2.0mm, 5microm) using a gradient mixture of acetonitrile and water (both containing 0.02% formic acid) as a mobile phase at flow rate of 0.3ml/min. The analytes were protonated in the positive electrospray ionization (ESI) interface and detected in multiple reaction monitoring (MRM) mode. Calibration curves were linear over wide ranges from sub- to over-therapeutic concentration in plasma for all analytes. Intra- and inter-batch precision of analysis was <12.0%, accuracy ranged from 90% to 110%, average recovery from 85.0% to 99.7%. The validated method was successfully applied to therapeutic drug monitoring (TDM) of antiarrhythic drugs in routine clinical practice.