Constitutive model of brain tissue suitable for finite element analysis of surgical procedures.

Realistic finite element modelling and simulation of neurosurgical procedures present a formidable challenge. Appropriate, finite deformation, constitutive model of brain tissue is a prerequisite for such development. In this paper, a large deformation, linear, viscoelastic model, suitable for direct use with commercially available finite element software packages such as ABAQUS is constructed. The proposed constitutive equation is of polynomial form with time-dependent coefficients. The model requires four material constants to be identified. The material constants were evaluated based on unconfined compression experiment results. The analytical as well as numerical solutions to the unconfined compression problem are presented. The agreement between the proposed theoretical model and the experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude. The numerical solution using the finite element method matched the analytical solution very closely.     

根表面养分吸收通量和根围溶质浓度的近似解析解

该文用Nye-Tinker-Barber模型来研究植物根系表面的养分吸收通量和根围溶质浓度的近似解析解。将根围区域分为远场区域和近场区域, 在远场用相似变量, 在近场用尺度变换, 将远场解在根表面展开并与近场解进行待定函数的匹配, 从而获得对流扩散方程根表面通量和浓度的一阶近似解析解, 该解能够简化到扩散方程的解的形式。对氮、钾、硫、磷、镁、钙的养分吸收通量和氮、钾的浓度分别进行数值模拟, 比较模型的数值解、Roose的近似解析解和该文的近似解析解。结果表明: 在扩散方程中, 6种元素通量的解析解与Roose解析解相近, 但均高于数值解, 钾和磷的通量在短时间内迅速衰减; 钾和氮浓度的全局近似解析解与Roose解析解接近, 并与数值解的变化趋势一致。在对流扩散方程中, 除氮外的5种元素通量的近似解较Roose的解析解更接近于数值解, 且没有奇性。     

Approximate analytical solutions of root surface nutrient uptake flux and rhizosphere solute concentrations

该文用Nye-Tinker-Barber模型来研究植物根系表面的养分吸收通量和根围溶质浓度的近似解析解。将根围区域分为远场区域和近场区域, 在远场用相似变量, 在近场用尺度变换, 将远场解在根表面展开并与近场解进行待定函数的匹配, 从而获得对流扩散方程根表面通量和浓度的一阶近似解析解, 该解能够简化到扩散方程的解的形式。对氮、钾、硫、磷、镁、钙的养分吸收通量和氮、钾的浓度分别进行数值模拟, 比较模型的数值解、Roose的近似解析解和该文的近似解析解。结果表明: 在扩散方程中, 6种元素通量的解析解与Roose解析解相近, 但均高于数值解, 钾和磷的通量在短时间内迅速衰减; 钾和氮浓度的全局近似解析解与Roose解析解接近, 并与数值解的变化趋势一致。在对流扩散方程中, 除氮外的5种元素通量的近似解较Roose的解析解更接近于数值解, 且没有奇性。     

Force versus axial deflection of pipette-aspirated closed membranes

The axial deformation of a pipette-pressurized fluid membrane bag produces minuscule yet well-defined, reproducible forces. The stiffness of this ultrasensitive force transducer is tunable and largely independent of the constitutive membrane behavior. Based on a rigorous variational treatment, we present both numerical as well as approximate analytical solutions for the force-deflection relation of this unique biophysical force probe. Our numerical results predict a measurably nonlinear force-deflection behavior at moderate-to-large deformations, which we confirm experimentally using red blood cells. Furthermore, considering nearly spherical membrane shapes and enforcing proper boundary conditions, we derive an analytical solution valid at small deformations. In this linear regime the pressurized membrane bag behaves like a Hookean spring, with a spring constant that is significantly larger than previously published for the biomembrane force probe.     

Comparison of impact of two decontamination solutions on the viability of the cells in human amnion

Human amniotic membrane (HAM) is used as an allograft in regenerative medicine or as a source of pluripotent cells for stem cell research. Various decontamination protocols and solutions are used to sterilize HAM before its application, but little is known about the toxicity of disinfectants on HAM cells. In this study, we tested two decontamination solutions, commercial (BASE·128) and laboratory decontamination solution (LDS), with an analogous content of antimycotic/antibiotics for their cytotoxic effect on HAM epithelial (EC) and mesenchymal stromal cells (MSC). HAM was processed in a standard way, placed on nitrocellulose scaffold, and decontaminated, following three protocols: (1) 6 h, 37 °C; (2) 24 h, room temperature; (3) 24 h, 4 °C. The viability of EC was assessed via trypan blue staining. The apoptotic cells were detected using terminal deoxynucleotidyl transferase dUTP nick end labelling (TUNEL). The mean % (±SD) of dead EC (%DEC) from six fresh placentas was 12.9 ± 18.1. Decontamination increased %DEC compared to culture medium. Decontamination with BASE·128 for 6 h, 37 °C led to the highest EC viability (81.7%). Treatment with LDS at 24 h, 4 °C resulted in the lowest EC viability (55.9%) in the set. MSC were more affected by apoptosis than EC. Although the BASE·128 expresses lower toxicity compared to LDS, we present LDS as an alternative decontamination solution with a satisfactory preservation of cell viability. The basic formula of LDS will be optimised by enrichment with nutrient components, such as glucose or vitamins, to improve cell viability.     

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers''-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers''-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.     

Periodic solutions: a robust numerical method for an S-I-R model of epidemics

 We describe and analyze a numerical method for an S-I-R type epidemic model. We prove that it is unconditionally convergent and that solutions it produces share many qualitative and quantitative properties of the solution of the differential problem being approximated. Finally, we establish explicit sufficient conditions for the unique endemic steady state of the system to be unstable and we use our numerical algorithm to approximate the solution in such cases and discover that it can be periodic, just as suggested by the instability of the endemic steady state. Received: 1 September 1995 / Revised version: 30 April 1997     

Suppression of α‐Amylase inactivation in the presence of ethanol: Application of a two‐step model

A number of years ago we reported a two‐step inactivation mechanism for α‐amylase (enzyme) on the basis of theoretical and experimental studies in aqueous solutions. In the first step the metal (Ca²⁺) ion dissociates reversibly from the enzyme followed by an irreversible thermal inactivation of the apoenzyme. In this study we report inactivation of the enzyme in the presence of ethanol–water solutions. We noticed that as the concentration of ethanol in the aqueous solution is increased, the thermal inactivation of the enzyme is suppressed with almost no inactivation (in 1 h, 30°C) when 50% alcohol is present in the solution. These results are explained by the two‐step inactivation model. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:1271–1275, 2016     

Identifying All Moiety Conservation Laws in Genome-Scale Metabolic Networks

The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell''s metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.     

Accounting for thermodynamic non-ideality in the Guinier region of small-angle scattering data of proteins

Hydrodynamic studies of the solution properties of proteins and other biological macromolecules are often hard to interpret when the sample is present at a reasonably concentrated solution. The reason for this is that solutions exhibit deviations from ideal behaviour which is manifested as thermodynamic non-ideality. The range of concentrations at which this behaviour typically is exhibited is as low as 1–2 mg/ml, well within the range of concentrations used for their analysis by techniques such as small-angle scattering. Here we discuss thermodynamic non-ideality used previously used in the context of light scattering and sedimentation equilibrium analytical ultracentrifugation and apply it to the Guinier region of small-angle scattering data. The results show that there is a complementarity between the radially averaged structure factor derived from small-angle X-ray scattering/small-angle neutron scattering studies and the second virial coefficient derived from sedimentation equilibrium analytical ultracentrifugation experiments.     

Some combined effects of hypertonic solutions and changes in temperature on posthypertonic hemolysis of human red blood cells

The combined effects of hypertonic solutions and temperature changes on the posthypertonic hemolysis of human red blood cells have been investigated. Cells were exposed to hypertonic solutions of sodium chloride and also to hypertonic solutions of the extracellular cryoprotective additive sucrose, such as would occur during the freezing of cells in an isotonic salt solution to which 15% $\text{w}\text{v}$ sucrose had been added. In both cases the extent of posthypertonic hemolysis was increased by temperature reduction per se when the osmolality of the extracellular solution exceeded about 1400 mOsm/kg water. The posthypertonic hemolysis of cells exposed to a hypertonic solution at 0 °C was reduced with the temperature of the resuspension solution up to 35 °C.     

Characterization of highly concentrated antibody solution - A toolbox for the description of protein long-term solution stability

High protein titers are gaining importance in biopharmaceutical industry. A major challenge in the development of highly concentrated mAb solutions is their long-term stability and often incalculable viscosity. The complexity of the molecule itself, as well as the various molecular interactions, make it difficult to describe their solution behavior. To study the formulation stability, long- and short-range interactions and the formation of complex network structures have to be taken into account. For a better understanding of highly concentrated solutions, we combined established and novel analytical tools to characterize the effect of solution properties on the stability of highly concentrated mAb formulations. In this study, monoclonal antibody solutions in a concentration range of 50–200 mg/ml at pH 5–9 with and without glycine, PEG4000, and Na₂SO₄ were analyzed. To determine the monomer content, analytical size-exclusion chromatography runs were performed. ζ-potential measurements were conducted to analyze the electrophoretic properties in different solutions. The melting and aggregation temperatures were determined with the help of fluorescence and static light scattering measurements. Additionally, rheological measurements were conducted to study the solution viscosity and viscoelastic behavior of the mAb solutions. The so-determined analytical parameters were scored and merged in an analytical toolbox. The resulting scoring was then successfully correlated with long-term storage (40 d of incubation) experiments. Our results indicate that the sensitivity of complex rheological measurements, in combination with the applied techniques, allows reliable statements to be made with respect to the effect of solution properties, such as protein concentration, ionic strength, and pH shift, on the strength of protein-protein interaction and solution colloidal stability.     

Boundary element method analysis for the bioheat transfer equation.

In this paper, the boundary element method (BEM) approach is applied to solve the Pennes (1948) bioheat equation. The objective is to develop the BEM formulation and demonstrate its feasibility. The basic BEM formulations for the transient and steady-state cases are first presented. To demonstrate the usefulness of the BEM approach, numerical solutions for 2-D steady-state problems are obtained and compared to analytical solutions. Further, the BEM formulation is applied to model a conjugate problem for an artery imbedded in a perfused heated tissue. Analytical solution is possible when the conduction in the x-direction is negligible. The BEM and analytical results have very good agreement.     

Solution properties of Cu(II)-sarcosinehydroxamic acid

Species distribution and relevant stability constants of species present in aqueous solutions of Cu(II) with bidentate sarcosinehydroxamic acid (CH₃NHCH₂CONHOHHl) have been obtained by analytical potentiometry at 25 °C and I = 0.1 M (NaClO₄). Together with ESR of frozen solutions measurements, these results show the existence of four different complex copper(II) species, one of which as a dimeric one. The solution electronic spectra are also reported. The structure of the complexes are discussed and conclusions are drawn based on absorption and ESR spectra.     

Aggregation of biopharmaceuticals in human plasma and human serum

Analytical methods based on light microscopy, 90° light-scattering and surface plasmon resonance (SPR) allowed the characterization of aggregation that can occur when antibodies are mixed with human plasma. Light microscopy showed that aggregates formed when human plasma was mixed with 5% dextrose solutions of Herceptin^® (trastuzumab) or Avastin^® (bevacizumab) but not Remicade^® (infliximab). The aggregates in the plasma-Herceptin^®-5% dextrose solution were globular, size range 0.5–9 μm, with a mean diameter of 4 μm. The aggregates in the plasma-Avastin^®-5% dextrose samples had a mean size of 2 μm. No aggregation was observed when 0.9% NaCl solutions of Herceptin^®, Avastin^® and Remicade^® were mixed with human plasma. 90° light-scattering measurements showed that aggregates were still present 2.5 h after mixing Herceptin^® or Avastin^® with 5% dextrose-plasma solution. A SPR method was utilized to qualitatively describe the extent of interactions of surface-bound antibodies with undiluted human serum. Increased binding was observed in the case of Erbitux^® (cetuximab), whereas no binding was measured for Humira^® (adalimumab). The binding of sera components to 13 monoclonal antibodies was measured and correlated with known serum binding properties of the antibodies. The data presented in this paper provide analytical methods to study the intrinsic and buffer-dependent aggregation tendencies of therapeutic proteins when mixed with human plasma and serum.     

The laboratory germination of crisp lettuce seeds under moisture stress

Seeds of the crisp lettuce cultivar Pennlake were germinated using all combinations of six ‘initial’ solutions of polyethylene glycol 6000 (PEG) with osmotic potentials ranging from 0 to -8 bars and seven ‘secondary’ solutions of PEG with osmotic potentials ranging from 0 to -10 bars, to which seeds were moved after 24 or 48 h in the ‘initial’ solution. The number of seeds germinating decreased at more negative osmotic potentials of both ‘initial’ and ‘secondary’ solutions but there was an interaction between germination temperature and the osmotic potential of the ‘initial’ solution. At an ‘initial’ solution osmotic potential of 0 bars germination at 20°C exceeded that at 10°C. As the osmotic potential of the ‘initial’ solution decreased germination at 20°C decreased more than at 10°C so that at the more negative osmotic potentials germination at 10°C exceeded that at 20°C. However seeds ungerminated after 14 days germinated normally when transferred back to water, so that the average final germination was 99.5%. The results suggest that major fluctuations in soil water potential in a seedbed are unlikely to influence seed germination per se provided that a period of 24 to 48 h at 0 bars tension is available at some time. The timing of such a period relative to sowing will have a considerable effect on the time of germination and hence the time of emergence. It is concluded that factors other than the direct effect of soil moisture content on germination are involved in reducing seedling emergence under fluctuating soil moisture conditions in the field.     

Two strings to the systems biology bow: co-extracting the metabolome and proteome of yeast

Experimental samples are valuable and can represent a significant investment in time and resources. It is highly desirable at times to obtain as much information as possible from a single sample. This is especially relevant for systems biology approaches in which several ‘omics platforms are studied simultaneously. Unfortunately, each platform has a particular extraction methodology which increases sample number and sample volume requirements when multiple ‘omics are analyzed. We evaluated the integration of a yeast extraction method; specifically we explored whether fractions from a single metabolite extraction could be apportioned to multiple downstream ‘omics analytical platforms. In addition, we examined how variations to a chloroform/methanol yeast metabolite extraction regime influence metabolite recoveries. We show that protein suitable for proteomic analysis can be recovered from a metabolite extraction and that recovery of lipids, while reproducible, are not wholly quantitative. Higher quenching solution temperatures (?30 °C) can be used without significant leakage of intracellular metabolites when lower fermentation temperatures (20 °C) are employed. However, extended residence time in quenching solution, in combination with vigorous washing of quenched cell pellets, leads to extensive leakage of intracellular metabolites. Finally, there is minimal difference in metabolite amounts obtained when metabolite extractions are performed at 4 °C compared to extractions at ?20 °C. The evaluated extraction method delivers material suitable for metabolomic and proteomic analyses from the same sample preparation.     

Accurate modelling of unsteady flows in collapsible tubes

The context of this paper is the development of a general and efficient numerical haemodynamic tool to help clinicians and researchers in understanding of physiological flow phenomena. We propose an accurate one-dimensional Runge–Kutta discontinuous Galerkin (RK-DG) method coupled with lumped parameter models for the boundary conditions. The suggested model has already been successfully applied to haemodynamics in arteries and is now extended for the flow in collapsible tubes such as veins. The main difference with cardiovascular simulations is that the flow may become supercritical and elastic jumps may appear with the numerical consequence that scheme may not remain monotone if no limiting procedure is introduced. We show that our second-order RK-DG method equipped with an approximate Roe's Riemann solver and a slope-limiting procedure allows us to capture elastic jumps accurately. Moreover, this paper demonstrates that the complex physics associated with such flows is more accurately modelled than with traditional methods such as finite difference methods or finite volumes. We present various benchmark problems that show the flexibility and applicability of the numerical method. Our solutions are compared with analytical solutions when they are available and with solutions obtained using other numerical methods. Finally, to illustrate the clinical interest, we study the emptying process in a calf vein squeezed by contracting skeletal muscle in a normal and pathological subject. We compare our results with experimental simulations and discuss the sensitivity to parameters of our model.     

Influence of alkaline concentration on molecular association structure and viscoelastic properties of curdlan aqueous systems

Curdlan is an extracellular polysaccharide produced from soil microorganism Alcaligens faecalis var. 10C3K, and the linear structure consists of β-1,3-glycoside linkages. Curdlan is not soluble in water but it is soluble in alkaline aqueous solution, and we can obtain the gel when curdlan alkaline solution is heated above 60°C or neutralized by acids. In the present study, the gelation mechanism and dispersing structure of curdlan in the alkaline solutions are studied in terms of correlation between the molecular association structure and viscoelastic properties, using static light scattering and rheological measurements. The degree of association for the curdlan molecules in dilute solution increases with decreasing alkaline concentration. The viscoelastic properties also depend strongly on the alkaline concentration. The concentrated curdlan solution shows almost Newtonian flow at high alkaline concentrations and shows a gel-like behavior at low alkaline concentrations. It was elucidated that the molecular association in the dilute solution reflects on the viscoelastic properties of the concentrated solution and that the gelation mechanism is related to the association structure of curdlan molecules. In the case of lower NaOH concentration systems, the molecular association is likely to consist of a hydrophobic core and hydrophilic surface. The gelation mechanism above 60°C is considered to include the dissociation process of the molecular association and reformation of the network structure. © 1997 John Wiley & Sons, Inc. Biopoly 42: 479–487, 1997     

Hemolysis of human red blood cells by freezing and thawing in solutions containing sucrose: relationship with posthypertonic hemolysis and solute movements

Human red blood cells were frozen at temperatures down to ?9 °C in solutions containing sucrose, and the hemolysis on thawing was measured. This was compared with the hemolysis caused by exposing the cells to high concentrations of sucrose and then resuspending them in more dilute solutions at 4 °C. The effects of the hypertonic solutions of sucrose on potassium, sodium, and sucrose movements were also investigated. It was found that sucrose does not prevent damage to the cells by very hypertonic solutions (whether during freezing and thawing or at 4 °C) but it does reduce hemolysis of cells previously exposed to these solutions if present in the resuspension (or thawing) solution. Evidence is presented that the damaging effects of the hypertonic solutions of sucrose occurring during freezing are associated with changes in cell membrane permeability but that posthypertonic hemolysis is not primarily associated with a “loading” of the cells with extracellular solutes in the hypertonic phase. It is concluded that sucrose may reduce hemolysis of red blood cells by slow freezing and thawing by reducing colloid osmotic swelling of cells with abnormally permeable membranes.