scholarly journals Emergence of power laws in the pharmacokinetics of paclitaxel due to competing saturable processes.

2008 ◽  
Vol 11 (3) ◽  
pp. 77 ◽  
Author(s):  
Jack A Tuszynski ◽  
Rebeccah E. Marsh ◽  
Michael B. Sawyer ◽  
Kenneth J.E. Vos
Keyword(s):  
Power Law ◽  
Fractional Power ◽  
Area Under The Curve ◽  
Power Laws ◽  
Dose Dependence ◽  
Power Exponent ◽  
Least Squares Regression ◽  
Time Data ◽  
Concentration Time ◽  
Wide Range

Purpose: This study presents the results of power law analysis applied to the pharmacokinetics of paclitaxel. Emphasis is placed on the role that the power exponent can play in the investigation and quantification of nonlinear pharmacokinetics and the elucidation of the underlying physiological processes. Methods: Forty-one sets of concentration-time data were inferred from 20 published clinical trial studies, and 8 sets of area under the curve (AUC) and maximum concentration (Cmax) values as a function of dose were collected. Both types of data were tested for a power law relationship using least squares regression analysis. Results: Thirty-nine of the concentration-time curves were found to exhibit power law tails, and two dominant fractal exponents emerged. Short infusion times led to tails with a single power exponent of -1.57 ± 0.14, while long infusion times resulted in steeper tails characterized by roughly twice the exponent. The curves following intermediate infusion times were characterized by two consecutive power laws; an initial short slope with the larger alpha value was followed by a crossover to a long-time tail characterized by the smaller exponent. The AUC and Cmax parameters exhibited a power law dependence on the dose, with fractional power exponents that agreed with each other and with the exponent characterizing the shallow decline. Computer simulations revealed that a two- or three-compartment model with both saturable distribution and saturable elimination can produce the observed behaviour. Furthermore, there is preliminary evidence that the nonlinear dose-dependence is correlated with the power law tails. Conclusion: Assessment of data from published clinical trials suggests that power laws accurately describe the concentration-time curves and non-linear dose-dependence of paclitaxel, and the power exponents provide insight into the underlying drug mechanisms. The interplay between two saturable processes can produce a wide range of behaviour, including concentration-time curves with exponential, power law, and dual power law tails.

scholarly journals A General Fitting Function to Estimate Apparent Reaction Orders of Kinetic Profiles

2019 ◽  
Author(s):  
Robert Pollice
Keyword(s):  
Chemical Reactions ◽  
Catalyst Deactivation ◽  
Rapid Development ◽  
Product Inhibition ◽  
Time Profile ◽  
Time Data ◽  
Concentration Time ◽  
Wide Range ◽  
Reaction Orders

The rapid development of analytical methods in recent decades has resulted in a wide range of readily available and accurate reaction-monitoring techniques, which allow for easy determination of high-quality concentration-time data of chemical reactions. However, while the acquisition of kinetic data has become routine in the development of new chemical reactions and the study of their mechanisms, not all the information contained therein is utilized because of a lack of suitable analysis tools which unnecessarily complicates mechanistic studies. Herein, we report on a general method to analyze a single concentration-time profile of chemical reactions and extract information regarding the reaction order with respect to substrates, the presence of multiple kinetic regimes, and the presence of kinetic complexities, such as catalyst deactivation, product inhibition, and substrate decomposition.<br>

scholarly journals RESTRICTIONS ON THE HYPOTHETICAL LONG RANGE INTERACTIONS FROM THE CASIMIR-TYPE NULL EXPERIMENT WITH THREE TEST BODIES

1994 ◽  
Vol 09 (29) ◽  
pp. 2671-2680 ◽  
Author(s):  
M. BORDAG ◽  
V. M. MOSTEPANENKO ◽  
I. YU. SOKOLOV
Keyword(s):  
Long Range ◽  
Power Law ◽  
Casimir Force ◽  
Power Laws ◽  
Gravitational Attraction ◽  
Spherical Lens ◽  
Plane Plate ◽  
Wide Range ◽  
Long Range Interactions

A realistic null experiment is suggested in which the Casimir force between a plane plate and a spherical lens is compensated by the force of gravitational attraction. This configuration is shown to be very sensitive to the existence of additional hypothetical forces of Yukawa-type or power laws. From the suggested null experiment the restrictions on the Yukawa constant α can be strengthened by a factor up to 1000 in a wide range 10−8 m < λ < 10−4 m and by a factor of 10 for λ from several centimeters to several meters. For power law interactions the strengthening of restrictions by a factor of 20 is possible for the force decreasing as r−5.

DYNAMICAL EXPLANATION FOR THE EMERGENCE OF POWER LAW IN A STOCK MARKET MODEL

1996 ◽  
Vol 07 (01) ◽  
pp. 65-72 ◽  
Author(s):  
MOSHE LEVY ◽  
SORIN SOLOMON ◽  
GIVAT RAM
Keyword(s):  
Stock Market ◽  
Power Law ◽  
Wealth Distribution ◽  
Power Laws ◽  
Stationary Regime ◽  
Market Model ◽  
Self Organized ◽  
Wide Range ◽  
Self Organized Criticality ◽  
Sand Piles

Power laws are found in a wide range of different systems: From sand piles to word occurrence frequencies and to the size distribution of cities. The natural emergence of these power laws in so many different systems, which has been called self-organized criticality, seems rather mysterious and awaits a rigorous explanation. In this letter we study the stationary regime of a previously introduced dynamical microscopic model of the stock market. We find that the wealth distribution among investors spontaneously converges to a power law. We are able to explain this phenomenon by simple general considerations. We suggest that similar considerations may explain self-organized criticality in many other systems. They also explain the Levy distribution.

scholarly journals Power Law Duality in Classical and Quantum Mechanics

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 409
Author(s):  
Akira Inomata ◽  
Georg Junker
Keyword(s):  
Quantum Mechanics ◽  
Green Function ◽  
Power Law ◽  
Ad Hoc ◽  
Fractional Power ◽  
Power Laws ◽  
Energy Coupling ◽  
Arbitrary Power ◽  
Dual Symmetry ◽  
The Green Function

The Newton–Hooke duality and its generalization to arbitrary power laws in classical, semiclassical and quantum mechanics are discussed. We pursue a view that the power-law duality is a symmetry of the action under a set of duality operations. The power dual symmetry is defined by invariance and reciprocity of the action in the form of Hamilton’s characteristic function. We find that the power-law duality is basically a classical notion and breaks down at the level of angular quantization. We propose an ad hoc procedure to preserve the dual symmetry in quantum mechanics. The energy-coupling exchange maps required as part of the duality operations that take one system to another lead to an energy formula that relates the new energy to the old energy. The transformation property of the Green function satisfying the radial Schrödinger equation yields a formula that relates the new Green function to the old one. The energy spectrum of the linear motion in a fractional power potential is semiclassically evaluated. We find a way to show the Coulomb–Hooke duality in the supersymmetric semiclassical action. We also study the confinement potential problem with the help of the dual structure of a two-term power potential.

scholarly journals The Influence of the Different Disposition Characteristics of Snake Toxins on the Pharmacokinetics of Snake Venom

Toxins ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 188 ◽  
Author(s):  
Suchaya Sanhajariya ◽  
Geoffrey K. Isbister ◽  
Stephen B. Duffull
Keyword(s):  
Molecular Weight ◽  
Snake Venom ◽  
Time Course ◽  
Total Concentration ◽  
Weight Fraction ◽  
Pharmacokinetic Parameters ◽  
Time Data ◽  
Molecular Weights ◽  
Concentration Time ◽  
Wide Range

Snake venom is comprised of a combination of different proteins and peptides with a wide range of molecular weights and different disposition processes inherent to each compound. This causes venom to have a complex exposure profile. Our study investigates 1) how each molecular weight fraction (toxin) of venom contributes to the overall time course of the snake venom, and 2) the ability to determine toxin profiles based on the profile of the overall venom only. We undertook an in silico simulation and modelling study. Sixteen variations of venom, comprising of two to nine toxins with different molecular weights were investigated. The pharmacokinetic parameters (i.e., clearance,  C L , and volume of distribution,  V ) of each toxin were generated based on a log-linear relationship with molecular weight. The concentration–time data of each toxin were simulated for 100 virtual patients using MATLAB and the total concentration–time data of each toxin were modelled using NONMEM. We found that the data of sixteen mixtures were best described by either two- or three-compartment models, despite the venom being made up of more than three different toxins. This suggests that it is generally not possible to determine individual toxin profiles based on measurements of total venom concentrations only.

scholarly journals Pharmacokinetics of oral fluconazole when used for prophylaxis in bone marrow transplant recipients.

1997 ◽  
Vol 41 (5) ◽  
pp. 914-917 ◽  
Author(s):  
A El-Yazigi ◽  
M Ellis ◽  
P Ernst ◽  
D Spence ◽  
R Hussain ◽  
...  
Keyword(s):  
Bone Marrow ◽  
Bone Marrow Transplant ◽  
High Performance ◽  
Hemorrhagic Cystitis ◽  
Area Under The Curve ◽  
Compartment Model ◽  
Marrow Transplant ◽  
Distribution Area ◽  
Time Data ◽  
Concentration Time

The pharmacokinetics of fluconazole was investigated in 20 bone marrow transplant patients following oral administration of 200 mg of this drug. Blood samples were collected from each patient at different time intervals within 48 h after the first dose, and fluconazole was measured in plasma by high-performance liquid chromatography with UV detection. Urine was collected from 14 of these patients and analyzed similarly. The plasma concentration-time data exhibited the characteristics of the one-compartment model with first-order absorption quite well. The means +/- standard deviations of half-lives for absorption and elimination, peak concentration, time to peak, mean residence time, apparent volumes of distribution, area under the curve, and apparent oral clearance observed in these patients were 2.84 +/- 1.34 h, 19.94 +/- 18.7 h, 4.45 +/- 1.86 microg/ml, 8.34 +/- 5.97 h, 39.57 +/- 20.5 h, 0.874 +/- 0.48 liter/kg, 156.0 +/- 60.6 microg x h/ml, and 0.0256 +/- 0.0138 liter/h x kg, respectively. The amount of fluconazole excreted in urine in 24 h was 67.1 +/- 83 mg, which represents 33.55% +/- 41.6% of the dose administered. Patients who developed hemorrhagic cystitis excreted significantly (P < or = 0.0094) more fluconazole in 24 h than did those who did not.

scholarly journals The shape of dendritic tips

2020 ◽  
Vol 378 (2171) ◽  
pp. 20190243 ◽  
Author(s):  
Dmitri V. Alexandrov ◽  
Peter K. Galenko
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Dendritic Growth ◽  
Binary Systems ◽  
Fractional Power ◽  
Power Laws ◽  
Theme Issue ◽  
Special Case ◽  
Dendritic Shape ◽  
Good Agreement

The present article is focused on the shapes of dendritic tips occurring in undercooled binary systems in the absence of convection. A circular/globular shape appears in limiting cases of small and large Péclet numbers. A parabolic/paraboloidal shape describes the tip regions of dendrites whereas a fractional power law defines a shape behind their tips in the case of low/moderate Péclet number. The parabolic/paraboloidal and fractional power law shapes are sewed together in the present work to describe the dendritic shape in a broader region adjacent to the dendritic tip. Such a generalized law is in good agreement with the parabolic/paraboloidal and fractional power laws of dendritic shapes. A special case of the angled dendrite is considered and analysed in addition. The obtained results are compared with previous experimental data and the results of numerical simulations on dendritic growth. This article is part of the theme issue ‘Patterns in soft and biological matters’.

scholarly journals POWER-LAW DISTRIBUTIONS BASED ON EXPONENTIAL DISTRIBUTIONS: LATENT SCALING, SPURIOUS ZIPF'S LAW, AND FRACTAL RABBITS

Fractals ◽  
2015 ◽  
Vol 23 (02) ◽  
pp. 1550009 ◽  
Author(s):  
YANGUANG CHEN
Keyword(s):  
Exponential Distribution ◽  
Power Law ◽  
Power Laws ◽  
Power Exponent ◽  
Power Law Distribution ◽  
Exponential Distributions ◽  
Real Power ◽  
The Real ◽  
Dimension Space ◽  
Power Law Distributions

The difference between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law distribution with the exponential distribution has been seldom researched. This paper is devoted to exploring the relationships between exponential laws and power laws from the angle of view of urban geography. Using mathematical derivation and numerical experiments, I reveal that a power-law distribution can be created through a semi-moving average process of an exponential distribution. For the distributions defined in a one-dimension space (e.g. Zipf's law), the power exponent is 1; while for those defined in a two-dimension space (e.g. Clark's law), the power exponent is 2. The findings of this study are as follows. First, the exponential distributions suggest a hidden scaling, but the scaling exponents suggest a Euclidean dimension. Second, special power-law distributions can be derived from exponential distributions, but they differ from the typical power-law distributions. Third, it is the real power-law distributions that can be related with fractal dimension. This study discloses an inherent link between simplicity and complexity. In practice, maybe the result presented in this paper can be employed to distinguish the real power laws from spurious power laws (e.g. the fake Zipf distribution).

scholarly journals Power Laws Derived from a Bayesian Decision-Making Model in Non-Stationary Environments

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 718
Author(s):  
Shuji Shinohara ◽  
Nobuhito Manome ◽  
Yoshihiro Nakajima ◽  
Yukio Pegio Gunji ◽  
Toru Moriyama ◽  
...  
Keyword(s):  
Decision Making ◽  
Power Law ◽  
Power Laws ◽  
Step Length ◽  
Bayesian Decision ◽  
Power Law Distribution ◽  
Confidence Levels ◽  
Self Confidence ◽  
Lack Of Information ◽  
Wide Range

The frequency of occurrence of step length in the migratory behaviour of various organisms, including humans, is characterized by the power law distribution. This pattern of behaviour is known as the Lévy walk, and the reason for this phenomenon has been investigated extensively. Especially in humans, one possibility might be that this pattern reflects the change in self-confidence in one’s chosen behaviour. We used simulations to demonstrate that active assumptions cause changes in the confidence level in one’s choice under a situation of lack of information. More specifically, we presented an algorithm that introduced the effects of learning and forgetting into Bayesian inference, and simulated an imitation game in which two decision-making agents incorporating the algorithm estimated each other’s internal models. For forgetting without learning, each agents’ confidence levels in their own estimation remained low owing to a lack of information about the counterpart, and the agents changed their hypotheses about the opponent frequently, and the frequency distribution of the duration of the hypotheses followed an exponential distribution for a wide range of forgetting rates. Conversely, when learning was introduced, high confidence levels occasionally occurred even at high forgetting rates, and exponential distributions universally turned into power law distribution.

scholarly journals A General Fitting Function to Estimate Apparent Reaction Orders of Kinetic Profiles

2019 ◽  
Author(s):  
Robert Pollice
Keyword(s):  
Chemical Reactions ◽  
Catalyst Deactivation ◽  
Rapid Development ◽  
Product Inhibition ◽  
Time Profile ◽  
Time Data ◽  
Concentration Time ◽  
Wide Range ◽  
Reaction Orders

The rapid development of analytical methods in recent decades has resulted in a wide range of readily available and accurate reaction-monitoring techniques, which allow for easy determination of high-quality concentration-time data of chemical reactions. However, while the acquisition of kinetic data has become routine in the development of new chemical reactions and the study of their mechanisms, not all the information contained therein is utilized because of a lack of suitable analysis tools which unnecessarily complicates mechanistic studies. Herein, we report on a general method to analyze a single concentration-time profile of chemical reactions and extract information regarding the reaction order with respect to substrates, the presence of multiple kinetic regimes, and the presence of kinetic complexities, such as catalyst deactivation, product inhibition, and substrate decomposition.<br>

Sign in / Sign up

Export Citation Format

Share Document