Back Extrapolation Method Research Articles

Errors of the backextrapolation method in determination of the blood volume

Backextrapolation is an empirical method to calculate the central volume of distribution (for example the blood volume). It is based on the compartment model, which says that after an injection the substance is distributed instantaneously in the central volume with no time delay. The occurrence of recirculation is not taken into account. The change of concentration with time of indocyanine green (ICG) was observed in an in vitro model, in which the volume was recirculating in 60 s and the clearance of the ICG could be varied. It was found that the higher the elimination of ICG, the higher was the error of the backextrapolation method. The theoretical consideration of Schröder et al ( Biomed. Tech. 42 (1997) 7-11) was proved. If the injected substance is eliminated somewhere in the body (i.e. not by radioactive decay), the backextrapolation method produces large errors.

Estudio de la interacción precipitación-recristalización de un acero microaleado al vanadio con 0,35 % C

A method is described which allows to study the interaction recrystallization-induced precipitation by the deformation of vanadium microalloyed steel and 0.35 % C. By means of torsion tests and applying the Back Extrapolation method, the recristallized fraction at different temperatures has been determined. When the precipitation begins, the recristallized fraction does not follow the Avrami's equation. This allows to know the instant when precipitation starts (Ps) and the instant when precipitation finishes (Pf). Therefore, Recrystallization-Precipitation-Time-Temperature (RPTT) diagrams can be obtained, which graphically show the interaction Recrystallization-Precipitation and simultaneously allows the determination of the static recrystallization critical temperature (SRCT). This temperature represents the limit between the two phases, before and after precipitation.

Diagrama de Recristalización-Precipitación-Tiempo-Temperatura (RPTT) de un acero microaleado al vanadio

A method developed in the CENIM is described which allows to study the interaction recrystallization-induced precipitation by the deformation of vanadium microalloyed steel. By means of torsion test and applying the back extrapolation method, has been determined the recristallized fraction to diferent temperatures. When the precipitation begins, the recristallized fraction is separated of the Avrami's equation and this allows to know the instant the precipitation begins (Ps) and the instant the precipitation finishes (Pf). Thereby can be traced the Recrystallization- Precipitation-Time-Temperature (PTT) diagrams, which graphically show the interaction Recrystallization-Precipitation and simultaneously allows the determination of the static recrystallization critical temperature (SCRT). The mentioned temperature represents the limit between the two phases, before and after of the precipitation.

Influence of microalloy type and content on induced precipitation kinetics in microalloyed steels

Using torsion tests, and applying the back extrapolation method, the statically recrystallized fraction has been determined for low carbon microalloyed steels with different V, Nb and Ti contents, at different temperatures and an equivalent strain of 0.20%. At temperatures below the static recrystallization critical temperature (SRCT), or the temperature at which strain induced precipitation commences, recrystallized fraction against time curves show a plateau caused by precipitations. The formation of the plateau makes it possible to evaluate precipitation-time-temperature (PTT) diagrams, and thus to know the precipitation kinetics. The PTT diagrams show that an increase in the microalloy content raises SRCT and reduces incubation time. For similar Nb, V and Ti contents, Nb is the element which raises SRCT the most. Der statische Rekristallisierungsanteil mikrolegierter Stähle mit verschiedenen Gehalten an Vanadium, Niob und Titan wurde durch Torsionsversuche bei unterschiedlichen Temperaturen ermittelt. Hieraus lassen sich Rekristallisierungsanteil-Zeit-Kurven erstellen, die bei Temperaturen unterhalb der kritischen Rekristallisierungtemperatur (SRCT) ein Plateau zeigen. Das Auftreten dieser Zone mit konstantem Rekristallisierungsanteil ermöglicht es, Auscheidung-Zeit-Temperatur-(PTT)-Diagramme aufzustellen und die Auscheidungskinetik kennenzulernen. Die PTT-Diagramme zeigen, daß die SRCT mit steigendem Gehalt an Mikrolegierungselementen ansteigt und die Inkubationszeit abnimmt. Auf jeden Fall bewirkt Niob einen stärkeren Anstieg der SRCT als Vanadium oder Titan

Static Recrystallization Modelling of Hot Deformed Microalloyed Steels at Temperatures below the Critical Temperature.

Using torsion tests and applying the back extrapolation method a model has been constructed to predict the recrystallized fraction of deformed austenite in Nb, V and Ti microalloyed steels at temperatures below the temperature at which the inhibition of recrystallization commences due to induced precipitation, This temperature, named static recrystallization critical temperature, is modelled as a function of grain size, strain and the solubility temperature. A discussion is made of the importance of being able to predict SRCT in order to effectively apply the model of static recrystallization at temperatures both above and below it. It is demonstrated that Niobium precipitates delay the recrystallization most.

Influence of Alloying Elements in Solution on Static Recrystallization Kinetics of Hot Deformed Steels.

Using torsion tests and applying the back extrapolation method, a study has been made of the influence on static recrystallization kinetics of the most common elements (C, Si, Mn, Mo) in low alloy steels and the most common elements (Ti, V, Nb) in microalloyed steels. In the latter case, this influence is studied only at the temperatures at which these elements are in solution, except for Titanium which was partially precipitated in the form of nitrides. Activation energy is the parameter most sensitive to variations in the chemical composition and an expression has been determined to predict its value as a function of the content of each alloying element. Of the different non precipitate-forming alloys sillicon is shown to be the element which most delays recrystallization. Carbon and vanadium in solution have no influence on recrystallization kinetics. It is demonstrated that Nb is the microalloying element which most delays recrystallization.

Influence of Strain on Induced Precipitation Kinetics in Microalloyed Steels.

Using torsion tests and applying the back extrapolation method, the statically recrystallized fraction of low carbon microalloyed steels containing vanadium, niobium and titanium, respectively, has been determined for different temperatures and strains. From the recrystallized fraction against time curves it is possible to draw precipitation-time-temperature (PTT) diagrams. These diagrams show that the strain does not affect precipitation kinetics in an independent manner, but that this influence is related with the microalloy content. The greater the strain applied, the shorter the incubation time of induced precipitation, but this influence diminishes as the microalloy content increases. It is also demonstrated that the incubation time is practically independent of the nature of the metal microalloy (V, Ti, Nb). In this sense, new expressions are proposed to relate the incubation and precipitation end times with the strain and the microalloy content. A model is also established for precipitation kinetics at the curve nose temperature.

Static recrystallization of austenite and strain induced precipitation kinetics in titanium microalloyed steels

Using torsion tests and applying the back extrapolation method the recrystallized fraction of austenite was measured at two strains (0.20 and 0.35) and several temperature makes it possible steels. Graphical representation of the activation energy vs the inverse of the temperature makes it possible to determine the static recrystallization critical temperature (SRCT) of each steel as a function of the strain. With the results obtained, a model was constructed for the recrystallized fraction both at temperatures above and below the SRCT, and this, together with other equations already published, permits calculation of the residual strain and austenite grain size which the steel is expected to have at the end of rolling and before the γ → α transformation. Graphs of the recrystallized fraction vs time show the kinetics of strain induced precipitation and PTT diagrams (precipitation-time-temperature) were constructed for the three steels. It is noted that the degree to which the strain affects the precipitation kinetics decreases as the titanium content of the steel is increased.

Static Recrystallization of Hot Deformed Austenite and Induced Precipitation Kinetics in Vanadium Microalloyed Steels.

Using torsional tests and applying the back extrapolation method the kinetics of the static recrystallization of hot deformed austenite has been studied in three microalloyed steels with different vanadium contents and this has been modelled at temperatures above and below the static recrystallization critical temperature (SRCT). The SRCT has been found to be a function of the strain, the austenite grain size and naturally the microalloy contents, in this case N and V. A study has also been made of the kinetics of the precipitation induced by the strain and the precipitation-time-temperature (PTT) diagrams have been determined for the three steels. The no-recrystallization temperature (Tnr) has also been determined and the conclusion was reached that the difference between the Tnr and SRCT is mainly due to the austenite grain size, which is smaller in the determination of the Tnr due to the successive recrystallizations which occur before precipitation takes place.

An experimental study on subsequent yield surface after finite shear prestraining

An equimodulus surface is introduced and the subsequent yield surface after large finite shear prestraining is experimentally investogated. Fully annealed, thin-walled copper tubular specimens were subjected to large torsional loading and partial unloading; strain gages were carefully mounted on the specimen after the application of pure shear loading. Specimens were then subjected to various combined tension-torsion loadings. Influences of he von Mises and Tresca equivalent offset strains on the subsequent yield surfaces are studied. On examining the experimental results reported in this article, it was found that the smaller the offset strains, the more distorted are the subsequent yield surfaces. At the torsional preloading point, a rounded corner was developed, whereas in the region opposite to the preloading point, the subsequent yield surface was flattened. When large von Mises offset strains were used, the corresponding subsequent yield surfaces passed through the von Mises loading surface. But this was not the case when Tresca offset strains were used. The subsequent yield surface determined by the back extrapolation method was almost completely outside the von Mises loading surface. On the other hand, the subsequent yield surface determined by the back extrapolation method was close to the Tresca loading surface. It is also found that the equimodulus surface is distorted and cannot simply be described by the combined kinematic and isotropic hardening rule.

The internal stress in a Ti-5 Al-2.5Sn alloy at 300 K

The internal stress σ i produced by deforming a Ti-5Al-2.5Sn alloy (0.56 at.% O eq) of 19 μm grain size at 300 K was investigated employing a number of techniques. Two sets of values for σ i were obtained: one was represented by the back-extrapolation method (type I) and the other by the conventional short relaxation time decremental unloading method (type II). The latter yielded higher values than the former and had a temperature dependence greater than that of any of the various moduli of titanium. The fact that σ i determined by the type II methods had a stronger temperature dependence than the moduli suggests that it includes a thermally activated component in addition to the athermal long-range internal stress. Support for this is provided by the observations that the temperature dependence of σ i in titanium determined by the type II methods is sensitively dependent on the interstitial content and that for considerably longer relaxation times or higher test temperatures the values for the decremental unloading method approach those for the back-extrapolation method.

Theoretical justification for the midpoint back-extrapolation method of estimating apparent volume of distribution of drugs after a short intravenous infusion

Theoretical justification for the midpoint back-extrapolation method of estimating apparent volume of distribution of drugs after a short intravenous infusion

The establishment of cloned cell lines from Yoshida sarcomas having differential sensitivities to methylene dimethane sulphonate in vivo and their cross-sensitivity to X-rays, UV and other alkylating agents

Cloned cell lines have been established from Yoshida ascites tumour lines known to be sensitive and resistant to methylene dimethanesulphonate (MDMS) in vivo. The two lines have similar population doubling times and cell cycle times, but the relative lengths of different phases of the cycle differ, the S phase in particular being considerably longer in the resistant line. Cell survival studies by agar cloning and by the back-extrapolation method have shown that the line sensitive to MDMS is cross-sensitive to HN 2 and to UV irradiation. The two cell lines show similar sensitivities to methyl methanesulponate (MMS) and X-rays.

Symposium on regulation of the cardiovascular system in health and disease: regulation of blood volume.

HomeCirculationVol. 21, No. 6SYMPOSIUM ON REGULATION OF THE CARDIOVASCULAR SYSTEM IN HEALTH AND DISEASE Free AccessResearch ArticlePDF/EPUBAboutView PDFSections ToolsAdd to favoritesDownload citationsTrack citationsPermissions ShareShare onFacebookTwitterLinked InMendeleyReddit Jump toFree AccessResearch ArticlePDF/EPUBSYMPOSIUM ON REGULATION OF THE CARDIOVASCULAR SYSTEM IN HEALTH AND DISEASE Regulation of Blood Volume LYSLE H. PETERSON and E. B. REEVE LYSLE H. PETERSONLYSLE H. PETERSON Guest EditorFrom the Department of Medicine, University of Colorado School of Medicine, Denver, Colo. Search for more papers by this author and E. B. REEVEE. B. REEVE Guest EditorFrom the Department of Medicine, University of Colorado School of Medicine, Denver, Colo. Search for more papers by this author Originally published1 Jun 1960https://doi.org/10.1161/01.CIR.21.6.1176Circulation. 1960;21:1176–1183 Previous Back to top Next FiguresReferencesRelatedDetailsCited By Polidori D and Rowley C (2014) Optimal back-extrapolation method for estimating plasma volume in humans using the indocyanine green dilution method, Theoretical Biology and Medical Modelling, 10.1186/1742-4682-11-33, 11:1, Online publication date: 1-Dec-2014. Low J, Johnston E and McBride R (1965) Blood volume adjustments in the normal obstetric patient with particular reference to the third trimester of pregnancy, American Journal of Obstetrics and Gynecology, 10.1016/0002-9378(65)90250-4, 91:3, (356-363), Online publication date: 1-Feb-1965. Henegar G (1963) The Importance of Blood Volume Determination in Surgical Patients, Surgical Clinics of North America, 10.1016/S0039-6109(16)36895-5, 43:1, (187-199), Online publication date: 1-Feb-1963. June 1, 1960Vol 21, Issue 6 Advertisement Article InformationMetrics © 1960 American Heart Association, Inc.https://doi.org/10.1161/01.CIR.21.6.1176 Originally publishedJune 1, 1960 PDF download Advertisement