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At least 1,009 records · Page 56Linked to original sources
PubMed2003

A mathematical process model for cadmium precipitation by sulfate-reducing bacterial biofilms.

Sulfate-reducing bacterial (SRB) biofilms were grown in a flowcell in which the biofilm was grown on a fixed area of support which was supplied with recirculating medium of defined composition, volume and circulation rate. Utilization rates for substrates, production rates for products and material mass-balances for substrates and Cd were determined and a mathematical model constructed based on theoretical considerations and experimental data. The rate of sulfate reduction was zero-order with respect to sulfate concentration and unaffected by the presence of 250 microM Cd. However, Cd reacted with the sulfide produced by the SRB to produce solid CdS, removing sulfide from solution. A significant fraction of colloidal CdS was formed which flocculated relatively slowly, limiting the overall rate of Cd bioprecipitation. Experiments using chemically-synthesised colloidal CdS indicated that the biofilm did not influence colloidal Cd flocculation but stimulated sedimentation of the CdS precipitate once flocculated. A mathematical model of bioprecipitation was developed in which the CdS formation rate was determined by two steps: sulfide production by the biofilm and colloidal CdS flocculation. This model accurately predicted the behaviour of further experimental runs which indicated the adequacy of the overall process description. The model also indicated that the rate of sulfate reduction and the rate of flocculation were the key variables in optimising the biofilm system for metal removal.

Bacteria↗
PubMedDate not supplied

Studies of mitochondrial respiration in muscle cells in situ: use and misuse of experimental evidence in mathematical modelling.

Applications of permeabilized cell and skinned fiber techniques in combination with methods of mathematical modelling for studies of mitochondrial function in the cell are critically evaluated. Mathematical models may be useful tools for explaining biological phenomena, but only if they are selected by fitting the computing results with real experimental data. Confocal microscopy has been used in experiments with permeabilized cardiomyocytes and myocardial fibers to determine the maximal diffusion distance from medium to the core of cells, which is shown not to exceed 8-10 microm. This is a principal index for correctly explaining high apparent Km for exogenous ADP (200-300 microM) in regulation of mitochondrial respiration in oxidative muscle cells in situ. The best fitting of the results of in silico studies may be achieved by using of the compartmentalized energy transfer model. From these results, it may be concluded that in cardiac muscle cells the mitochondria and ATPases are organized into intracellular energetic units (ICEUs) separated from the bulk phase of cytoplasm by some barriers which limit the diffusion of adenine nucleotides. In contrast, alternative models based on the concept of the cell as homogenous system do not explain the observed experimental phenomena and have led to misleading conclusions. The various sources of experimental and conceptual errors are analyzed.

Animals↗
PubMed2003

New mathematical model for the correct prediction of the exchangeable blood volume during acute normovolemic hemodilution.

BACKGROUND: The blood volume that has to be exchanged for crystalloids and/or colloids during acute normovolemic hemodilution (ANH) in order to reach a preset target hemoglobin concentration (hb) is usually predicted by the Bourke and Smith formula developed in 1974. This formula systematically overestimates the 'true' exchangeable blood volume (EBV), a fact that may potentially endanger patients because the target hb will be missed and the normovolemic anemia might turn out to be more severe than a priori intended. Our objective was to develop a more accurate mathematical model of hemodilution kinetics and to validate this new model in animals and in patients undergoing ANH. METHODS: Twenty-two anesthetized beagle dogs and 18 patients under balanced anesthesia underwent isovolemic hemodilution with hydroxyethyl starch (HAES 6%, 200 000) to a target hb of 7 g dl-1 or 9 g dl-1, respectively. Exchangeable blood volume predicted by use of the different mathematical models was compared with the blood volume actually exchanged to meet the preset target hb. RESULTS: Calculation of EBV by the Bourke and Smith formula (EBVB + S) systematically overestimated the volume actually exchanged (overestimation: dogs 15%, patients 20%), whereas our new iterative model predicted EBV (EBViterative) more reliably (overestimation: dogs 1%, patients 8%). In both cases EBVB + S differed significantly from the EBViterative. CONCLUSION: Exchangeable blood volume is predicted more accurately by the new iterative model than by the Bourke and Smith formula. The iterative model leads to an improvement in patient safety and provides a physiologically adequate basis for future studies investigating the efficacy of ANH in reducing allogenic blood transfusions.

Algorithms↗
PubMed2001

Mathematical analysis of projection errors in "paralleling technique" with respect to implant geometry.

"Standardized" radiographs acquired in paralleling technique serve for monitoring of marginal bone levels around endosseous implants. Under clinical conditions, parallel adjustment of the film to the implant is beset with great difficulties. A mathematical model matching clinical conditions was developed to evaluate projection geometry within an interval of clinically relevant angulations (+/- 10 degrees from parallel position). Radiographs of two implants (Frialit 2, Friadent AG, Mannheim, Germany; Implant No. 1: 3.8 mm, length 10 mm; Implant No. 2: 6.5 mm, length 13 mm) were separately produced per angulation (2 degrees increments) at one focus-object distance (FO=322.9 mm). Implant images were repeatedly measured along their midline/vertical edge, local magnification (MF) was calculated and the values were compared to the computed ones. Projected dimensions of the implants were calculated for a second distance (232.3 mm). The experimentally acquired data were in agreement with the mathematical calculation. MF calculated for assessment along the vertical edge varied less (+/-1.94% from mean value) than along the midline (+/-2.74%), with a range of 1.037-1.068 (FO=322.9 mm) and 1.061-1.099 (FO=232.3 mm) for implant No.1, and 1.060-1.101 (FO=232.3 mm) and 1.037-1.069 (FO=322.9 mm) for Implant No. 2. Magnification revealed a mean variation of 4%. Radiographic evaluation of periimplant bone level should not exceed a precision of 0.5 mm, when parallelism between film and implant is not guaranteed and FO is less than 380 mm.

Alveolar Bone Loss↗
PubMed2006

Mechanistic mathematical modelling of mercaptopurine effects on cell cycle of human acute lymphoblastic leukaemia cells.

The antimetabolite mercaptopurine (MP) is widely used to treat childhood acute lymphoblastic leukaemia (ALL). To study the dynamics of MP on the cell cycle, we incubated human T-cell leukaemia cell lines (Molt-4 sensitive and resistant subline and P12 resistant) with 10 microM MP and measured total cell count, cell cycle distribution, percent viable, percent apoptotic, and percent dead cells serially over 72 h. We developed a mathematical model of the cell cycle dynamics after treatment with MP and used it to show that the Molt-4 sensitive controls had a significantly higher rate of cells entering apoptosis (2.7-fold, P<0.00001) relative to the resistant cell lines. Additionally, when treated with MP, the sensitive cell line showed a significant increase in the rate at which cells enter apoptosis compared to its controls (2.4-fold, P<0.00001). Of note, the resistant cell lines had a higher rate of antimetabolite incorporation into the DNA of viable cells (>1.4-fold, P<0.01). Lastly, in contrast to the other cell lines, the Molt-4 resistant subline continued to cycle, though at a rate slower relative to its control, rather than proceed to apoptosis. This led to a larger S-phase block in the Molt-4 resistant cell line, but not a higher rate of cell death. Gene expression of apoptosis, cell cycle, and repair genes were consistent with mechanistic dynamics described by the model. In summary, the mathematical model provides a quantitative assessment to compare the cell cycle effects of MP in cells with varying degrees of MP resistance.

Antimetabolites, Antineoplastic↗
PubMed1975

Hepatic albumin and urea synthesis: The mathematical modelling of the dynamics of [14C]carbonate-derived guanidine-labelled arginine in the isolated perfused rat liver.

A mathematical model was constructed to define the dynamics of incorporation of radioactivity into urea carbon and the guanidine carbon of arginine in plasma albumin after the rapid intraportal-venous administration of Na214CO3 in the isolated perfused rat liver. 2. The model was formulated in terms of compartmental analysis and additional experiments were designed to provide further information on subsystem dynamics and to discriminate between alternative model structures. 3. Evidence for the rapid-time-constant of labelling of intracellular arginine was provided by precursor-product analysis of precursor [14C]carboante and product [14C]urea in the perfusate. 4. Compartmental analysis of the dynamics of newly synthesized urea was based on the fate of exogenous [13C]urea, endogenous [14C]urea and the accumulation of [12C]urea in perfusate water, confirming the early completion of urea carbon labelling, the absence of continuing synthesis of labelled urea, and the presence of a small intrahepatic urea-delay pool. 5. Analysis of the perfusate dynamics of endogenously synthesized and exogenously administered [6-14C]arginine indicated that although the capacity for extrahepatic formation of [14C]-urea exists, little or no arginine formed within the intrahepatic urea cycle was transported out of the liver. However, the presence of a rapidly turning-over intrahepatic arginine pool was confirmed. 6. On the basis of these subsystem analyses it was possible to offer feasible estimations for the parameters of the mathematical model. However, it was not possible to stimulate the form and magnitude of the dynamics of newly synthesized labelled urea and albumin which were simultaneously observed after administration of [14C]carbonate on the basis of a preliminary model which postulated that both products were derived from a single hepatic pool of [16-14C]arginine. On the other hand these observed dynamics could be satisfied to a two-compartment arginine model, which also provided an explanation for discrepancies observed between albumin synthesis measured radioisotopically and immunologically. This was based on a relative overestimation of [14C]urea specific radioactivity resulting from the rapid dynamics of [14C]carbonate and the [14C]urea subsystem relative to the labelled albumin subsystem. The effects of arginine compartmentalization could be minimized in the model by minor slowing of the rate of [14C]carbonate turnover or by constant infusion of [14C]carbonate, both of which permitted valid determination of albumin-synthesis rates.

Animals↗
PubMed2003

Mathematical modelling and simulation for planning critical care capacity.

Using average number of patients expected in a year, average length of stay and a target occupancy level to calculate the number of critical care beds needed is mathematically incorrect because of nonlinearity and variability in the factors that control length of stay. For a target occupancy in excess of 80%, this simple calculation will typically underestimate the number of beds required. More seriously, it provides no quantitative guidance information about other aspects of critical care demand such as the numbers of emergency patients transferred, deferral rates for elective patients and overall utilisation. The combination of appropriately analysing raw data and detailed mathematical modelling provides a much better method for estimating numbers of beds required. We describe this modelling approach together with evidence of its performance.

Bed Occupancy↗
PubMed2002

A mathematical model of the impact of infused targeted cytotoxic agents on brain tumours: implications for detection, design and delivery.

Motivated by the recent development of highly specific agents for brain tumours, we develop a mathematical model of the spatio-temporal dynamics of a brain tumour that receives an infusion of a highly specific cytotoxic agent (e.g. IL-4-PE, a cytotoxin comprised of IL-4 and a mutated form of Pseudomonas exotoxin). We derive an approximate but accurate mathematical formula for the tumour cure probability in terms of the tumour characteristics (size at time of detection, proliferation rate, diffusion coefficient), drug design (killing rate, loss rate and convection constants for tumour and tissue), and drug delivery (infusion rate, infusion duration). Our results suggest that high specificity is necessary but not sufficient to cure malignant gliomas; a nondispersed spatial profile of pretreatment tumour cells and/or good drug penetration are also required. The most important levers to improve tumour cure appear to be earlier detection, higher infusion rate, lower drug clearance rate and better convection into tumour, but not tissue. In contrast, the tumour cure probability is less sensitive to a longer infusion duration and enhancements in drug potency and drug specificity.

Antineoplastic Agents↗
PubMed2001

Study and application of a mathematical model for the provisional assessment of areas and nasal resistance, obtained using acoustic rhinometry and active anterior rhinomanometry.

Nasal resistance (NR) depends on the geometrical features and tortuosity of the nasal airway and on the air flow. Knowing the longitudinal distribution of cross-sectional areas (CSAs) in the nasal cavity (which can be obtained using acoustic rhinometry) and the laminar nasal resistance (obtainable by processing the rhinomanometric results), it is possible to calculate, utilizing a mathematical model elaborated on the basis of fluid dynamics, the differential nasal resistance (NRdiff) and the cumulative nasal resistance (NRcum), thus localizing the position at which the highest resistance is concentrated and the related longitudinal distribution. Using a mathematical model, we integrated the sigmoid curves DeltaP/Q of rhinomanometry with the cross-sectional areas obtained using acoustic rhinometry, thus obtaining the normal distribution of differential and cumulative nasal resistances. Afterwards, we empirically reduced the cross-sectional areas corresponding to the head, body, tail and the whole inferior turbinate, recalculating the differential and cumulative nasal resistance distribution curves. The results show that reduction of up to 50% of cross-sectional areas does not substantially affect the resistivity role of the nasal valve, while greater reductions move the highest resistivity point to an area at the junction of the body and the head of the inferior turbinate. The study of the differential nasal resistance trend curves as a function of the reduction of cross-sectional areas shows that the resistance variation of the body and the whole inferior turbinate prevail with reductions of up to 40%, while the variation of cross-sectional areas of the body bordering the inferior turbinate head is predominant with higher reductions. The cross-sectional areas of the nasal airway cavity with highest resistivity are mainly located in an anterior position, where the differential nasal resistances are higher, but there are substantial variations produced by reducing the cross-sectional area of the posterior nasal airway. A similar model can produce provisional values for the results obtainable with functional nasal surgery.

Acoustics↗
PubMed2002

Mathematical modelling of antifungal action.

In this paper a simplified modelling approach indicated that yeast growth was inhibited by an antifungal drug according to an exponential function. In addition, the corresponding inhibition rate followed a hyperbolic function the parameters of which permit us to determine the percentage of maximum inhibition and the minimum inhibitory concentration for 80%. From the equation of a hyperbola it was also possible to calculate an affinity constant Kaff corresponding to the inverse of the concentration of antifungal drugs giving half the maximal inhibition. The affinity constant was demonstrated to be characteristic of the yeast strain and of the antifungal drug employed. Simulation of the mathematical modelling enabled determination of a theoretical inhibition level corresponding to strong concentrations of antifungal drugs which cannot be carried out for technical reasons (precipitates, opacity etc.). The interest of this mathematical modelling of growth and inhibition to predict the doses of antifungals which can act synergistically is discussed.

Amphotericin B↗
PubMed2003

Seeking mathematical strategies in sperm function analysis: between scylla and charybdis?

During the last decades, essential progresses in reproductive biotechnology were achieved, implying development of special spermatological techniques. The major problem was to set up simple, rapid, precise and adequate evaluation methods. The key aspect to be considered in all assays of sperm fertilizing function is capacitation. As not all spermatozoa respond to fertilizing conditions in a similar manner, it seems to be logical to assess samples via their response to these specific conditions. For the spermatological practice, the sensitivity of methodology for assessment and analysis of data with respect to differences in individual response, in heterogeneity of the population, and proper temporal characterization of the response is crucial for the improvement of evaluation procedures. Currently, most used statistical analytical tools in spermatology do not always fulfil these essential sensitivity requirements. We structured our paper concerning different fields of mathematical science (distribution analysis, fractal geometry, functional approximation and differentiation) related to the modern insights in sperm function analysis. The spectrum of methods we are going to review in this paper is restricted to basic ideas to illustrate how the accuracy and sensitivity of sperm evaluation assays may be improved by applying adequate elementary tools of the mathematical analysis.

Animals↗
PubMed1999

Mathematical modelling of morphogenesis in fungi: a key role for curvature compensation ('autotropism') in the local curvature distribution model.

The assumption that the mushroom stem has the ability to undergo autonomic straightening enables a mathematical model to be written that accurately mimics the gravitropic reaction of the stems of Coprinus cinereus. The straightening mechanism is called curvature compensation here, but is equivalent to the 'autotropism' that often accompanies the gravitropic reactions of axial organs in plants. In the consequently revised local curvature distribution model, local bending rate is determined by the difference between the 'bending signal' (generated by gravitropic signal perception systems) and the 'straightening signal' (proportional to the local curvature at the given point). The model describes gravitropic stem bending in the standard assay with great accuracy but has the virtue of operating well outside the experimental data set used in its derivation. It is shown, for example, that the mathematical model can be fitted to the gravitropic reactions of stems treated with metabolic inhibitors by a change of parameters that parallel the independently derived physiological interpretation of inhibitor action. The revised local curvature distribution model promises to be a predictive tool in the further analysis of gravitropism in mushrooms.

Calcimycin↗
PubMed2002

Effect of rotary blood pump failure on left ventricular energetics assessed by mathematical modeling.

In this study, we used a mathematical model to study the influence of backflow through a failing rotary blood pump. We performed simulations based on animal experiments that were published earlier by Nishida et al., who used the Medos Microdiagonal pump to assess the acute effect of sudden pump failure. The mathematical model consists of validated cardiac and arterial modules and a pump module. We could evaluate the influence of pump failure with mechanoenergetic parameters and wall stress obtained from model output. Simulations were performed at baseline and after 15 min of backflow in a control group and a heart failure group. Simulation results agreed well with the experiment. Stroke volume, aortic flow, and stress time integral increased significantly because of pump failure. However, total systemic flow and arterial pressure were not altered by backflow, and a life-threatening situation did not appear.

Animals↗
PubMed2002

Mathematic modeling of the risk of HBV, HCV, and HIV transmission by window-phase donations not detected by NAT.

BACKGROUND: Blood transfusion centers around the world have introduced minipool NAT to reduce the risk of HBV, HCV, and HIV transmission by blood donations drawn in the infectious window phase. What would be the reduction in the residual risk when minipool NAT would be replaced by single-donation NAT? STUDY DESIGN AND METHODS: A mathematic model was developed to estimate the probability of virus transmission by blood transfusion when NAT screening methods are used for virologic safety testing. The major assumptions used are threefold: 1) The viral nucleic acid concentrations in the early window phase of infection double in 2.8 (HBV), 0.74 (HCV), and 0.90 (HIV) days. 2) The detectability of low copy numbers of viral DNA or RNA by the screening assay can be described with a probit model. 3) The probability of infection depends linearly on the logarithm of the administered dose, with 50-percent infectivity rates at 10 (HBV and HCV) or 1000 (HIV) viral nucleic acid copies per transfusion unit (estimates based on NAT studies with samples of known infectivity in chimpanzees). RESULTS: A reasonably simple equation was obtained that allows studying the effect of the sensitivity of the NAT assay and of the pool size used for screening on the residual risk of transfusion-transmitted infection. The computations are illustrated by using observed sensitivity estimates of various NAT methods. By using epidemiologic data among European donors over 1997 as baseline, the calculations predict that the incidence of virus transmission per 10-million RBC transfusions reduces with the following numbers when lowering the test pool size from 96 to 1 (single-donation testing): HBV from 11 to 13 to 3.3 to 5.1, HCV from 1.7 to 2.0 to 0.5 to 0.8, and HIV from 0.47 to 0.62 to 0.010 to 0.045 (ranges for the different NAT screening methods). CONCLUSION: A proper mathematic model for the calculation of residual infection risk by blood transfusion helps understand the impact of introducing new NAT methods for blood safety testing.

Blood Donors↗
PubMed2003

Mathematical theory of molecular motors and a new approach for uncovering motor mechanism.

Molecular motors operate in an environment dominated by thermal fluctuations. A molecular motor may produce an active force at the reaction site to directly move the motor forward. Alternatively a molecular motor may generate a unidirectional motion by rectifying thermal fluctuations. In this case, the chemical reaction establishes free energy barriers to block the backward fluctuations. The effect of the chemical reaction on the motor motion can be represented by the motor potential profile (rectifying barrier andor active driving force). Different motor mechanisms are characterised by different motor potential profiles. The mathematical theory and properties of molecular motors are discussed and a mathematical framework is developed for extracting the motor potential profile from measured time series of motor position. As an example, we discuss the binding zipper model for the F(1) ATPase, which was motivated mainly by the fact that the motor potential profile of the F(1) ATPase is nearly a constant slope.

Journal Article↗
PubMed2004

Reduction of mathematical models of signal transduction networks: simulation-based approach applied to EGF receptor signalling.

Biological systems and, in particular, cellular signal transduction pathways are characterised by their high complexity. Mathematical models describing these processes might be of great help to gain qualitative and, most importantly, quantitative knowledge about such complex systems. However, a detailed mathematical description of these systems leads to nearly unmanageably large models, especially when combining models of different signalling pathways to study cross-talk phenomena. Therefore, simplification of models becomes very important. Different methods are available for model reduction of biological models. Importantly, most of the common model reduction methods cannot be applied to cellular signal transduction pathways. Using as an example the epidermal growth factor (EGF) signalling pathway, we discuss how quantitative methods like system analysis and simulation studies can help to suitably reduce models and additionally give new insights into the signal transmission and processing of the cell.

Algorithms↗
PubMed2002

The ICP-dependency of resistance to cerebrospinal fluid outflow: a new mathematical method for CSF-parameter calculation in a model with H-TX rats.

The international The simultaneous measurement of the resistance and compliance during a single investigation minimizes the patients exertion. In contrast to the classical method it is not necessary that the ICP reaches a plateau. Our mathematical method diverges with t he description of a pressure dependent slope of the function for the resistance from the static examination models. We proved our mathematical method by the use of a dynamic infusion test in 10 H-Tx rats without hydrocephalus and five hydrocephalic H-Tx rats. For that we are able to take the non linearity of the CSF resorption into consideration.

Animals↗
PubMed2000

Hepatitis C kinetics: mathematical modeling of viral response to therapy.

Mathematical models have been used to study the dynamics of HIV. Using these same principles, the dynamics of hepatitis C virus (HCV) are reviewed during interferon (IFN) therapy. After initiating IFN treatment, there is an IFN dose-dependent exponential decline in viral RNA levels within the first 48 hours. This rapid 1.0 to 2.0 log decline was best explained by an effect of IFN in inhibiting viral production with a varying degree of effectiveness. By applying mathematical principles, viral serum half-life was estimated to be 3.0 hours and viral production rat was calculated to be 1.0 x 10(12) virions per day. After this rapid first-phase decline there was a slower second phase decline in viral levels that was highly variable between subjects. This phase was dependent on the rate of elimination of HCV-infected liver cells. The rapidity of the second phase proved to be the best predictor of early viral clearance. The use of these models to understand the life cycle of viruses and their response to therapy is reviewed.

Antiviral Agents↗