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SI Units: 2019 Redefinition01:13

SI Units: 2019 Redefinition

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Measurement is an indispensable part of analytical chemistry. The result of measurement helps quantify a substance's physical property and compare it with the physical property of another substance. Each measurement comprises two components - a number indicating the magnitude and a unit of measurement as a standard for comparison. Further, the same quantity can be measured using different units of measurement, which leads to differences in magnitude.
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Fundamental Mathematical Principles in Pharmacokinetics: Mathematical Expressions and Units01:19

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Mathematical principles play a crucial role in pharmacokinetics, providing a framework for understanding and quantifying drug distribution and elimination dynamics in the body. By utilizing mathematical expressions and units, pharmacologists can accurately characterize the behavior of drugs, optimize dosing regimens, and predict therapeutic outcomes.
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The fundamental mathematical principles, such as calculus and graphs, play crucial roles in analyzing drug movement and determining pharmacokinetic parameters. Differential calculus examines rates of change and helps to determine the dissolution rate of drugs in biofluids, as well as how drug concentrations change over time. For instance, it can help calculate the rate of elimination of a drug from the body based on its concentration-time profile.
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In a spring-mass-damper system, the second-order differential equation describes the dynamic behavior of the system. When transformed into the Laplace domain under zero initial conditions, this equation can be effectively analyzed and manipulated. The transformation into the Laplace domain converts differential equations into algebraic equations, simplifying the process of isolating the output.
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Fundamental Mathematical Principles in Pharmacokinetics: Rate and Order of Reaction01:15

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In pharmacokinetics, the rates and order of reactions play a crucial role in understanding how the body processes drugs and help us comprehend drug absorption, distribution, metabolism, and elimination. A critical concept in pharmacokinetics is the rate constant, which quantifies the speed of a reaction. It provides valuable information about the kinetics of drug elimination. The rate constant allows us to determine the rate at which drugs are eliminated from the body.
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Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
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Generation of Comprehensive Thoracic Oncology Database - Tool for Translational Research
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The 2019 mathematical oncology roadmap.

Russell C Rockne1, Andrea Hawkins-Daarud, Kristin R Swanson

  • 1Department of Computational and Quantitative Medicine, Division of Mathematical Oncology, City of Hope National Medical Center, Duarte, CA 91010, United States of America. Author to whom any correspondence should be addressed.

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Mathematical Oncology uses mathematics to personalize cancer medicine. This approach aids in early detection, predicting therapy response, and creating adaptive treatment plans for better patient outcomes.

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Area of Science:

  • Mathematical Oncology
  • Computational Biology
  • Systems Biology
  • Bioinformatics

Background:

  • Mathematics is increasingly integral to cancer research, spanning theoretical studies to clinical trials.
  • Mathematical Oncology encompasses diverse fields relying on mathematical methodologies.
  • This field ranges from basic science to applied research in cancer.

Purpose of the Study:

  • To differentiate Mathematical Oncology from related fields.
  • To highlight specific research areas within Mathematical Oncology.
  • To emphasize the role of mathematics in personalizing cancer medicine.

Main Methods:

  • Utilizing patient-specific clinical data for modeling and simulation.
  • Developing individualized screening and therapy response prediction models.
  • Designing adaptive, patient-specific treatment strategies to combat resistance.

Main Results:

  • Demonstrates the application of mathematical models in personalized cancer care.
  • Facilitates earlier cancer detection through tailored screening strategies.
  • Enables prediction of treatment efficacy and resistance, guiding adaptive therapies.

Conclusions:

  • Mathematical Oncology is key to advancing personalized medicine in cancer research.
  • Patient-specific data and mathematical modeling drive individualized cancer care.
  • Establishing standards for model sharing and reproducibility is crucial for progress.