Ludovica Bernardini BLK B
How Calculus applies to the Medical world
Applications of Calculus in real life
Introduction
Since the amount of departments of medicine where Calculus is required, the focus of this presentation will be incentrated on the use of Calculus made in the surgical field.
Introduction
More specifically:
- Measuring cardiac output and blood flow ;
- Algorithms and statistical models for patient-specific surgery planning, making each procedure as effective and safe as possible;
Measuring Cardiac output and blood flow
In order to obtain a successful and precise measuring of cardiac output and blood flow, scientists needed to find a formula that could be suitable for all the characteristics blood has. The perfect formula was found to be Navier Stokes's equation.
Measuring Cardiac output and blood flow
The Navier-Stokes equation is crucial in various scientific and engineering fields, notably in biomedical engineering. It is expressed as:
- ρ is the fluid density,
- v is the fluid velocity field,
- p is the pressure,
- T is the stress tensor,
- f represents body forces.
Measuring Cardiac output and blood flow
This equation is fundamental in describing how fluids such as blood and air move and interact with their environments, making it indispensable during surgery, as constant control of heart activity is more than essential in order to continue perfoming the procedure safely.
Algorithms and statistical models for patient-specific surgery planning
Often times, surgeons need to create specific and personalised surgery plans based on their patients' needs. This is a very hard part of their job, therefore researchers and technologists have found a way to make this easier and better.
Algorithms and statistical models for patient-specific surgery planning
The best way to create and statistical models for this purpose is to use the Risch algorithm. It is named after the American mathematician Robert Henry Risch, a specialist in computer algebra who developed it in 1968.
Algorithms and statistical models for patient-specific surgery planning
The algorithm transforms the problem of integration into a problem in algebra. It is based on the form of the function being integrated and on methods for integrating rational functions, radicals, logarithms, and exponential functions. It is a method for deciding whether a function has an elementary function as an indefinite integral, and if it does, for determining that indefinite integral.
Algorithms and statistical models for patient-specific surgery planning
How a well known research carried out by the University of Waterloo, using this algorithm to plan surgeries to benefit the patients has already saved many lives, including little kids with particularly rare diseases.
Measuring tumor growth before surgery
When it comes to oncologic surgery, it is imperative to have a constant monitoring of cancer size. Before the advent of technology, this was impossible to do before surgery, but now it is more than a standard procedure.
Measuring tumor growth before surgery
Calculus has been used in cancer treatment and has helped health care providers locate the affected cells. There are different calculus applications used by physicians in cancer treatment and monitoring and their effectiveness.
Measuring tumor growth before surgery
1. Chemotherapy treatment It involves using drugs to treat the disease, and calculus is applied to monitor cancer cells, it works by destroying the affected cells and limiting their spread. The mathematical concept of calculus is applied when doctors consider the diffusion of different drugs into the bloodstream and inside the cancer cells. Calculus predicts and monitors the impact of chemotherapy on cancer tumors by using the Fractional Diffusion Equation:
Measuring tumor growth
2. The surface model This is another technique that uses calculus to show that only cells located at the surface of the tumor divide while those inside the tumor do not split. To calculate the growth, related rates with differentiation of surface area are used.
Measuring tumor growth
3. Bertalanffy’s model The approach assumes that growth will only occur proportionally with the surface area. Later, there is a decrease of tumor in its volumes due to the occurring cell death. This model concentrates on explaining the mortality curve of the human. This method has been found to provide the best explanation for lung and breast cancer growth.
Bibliography
Navier stroke equation for cardiac output and blood flow https://wjarr.com/sites/default/files/WJARR-2024-0120.pdf https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6158206/ Algorithms and statistical models for patient-specific surgery planning https://uwaterloo.ca/math-alumni-newsletter/winter-2020/feature/mathematicians-help-build-better-surgical-plans http://reference.wolfram.com/mathematica/ref/PolynomialQuotient.html Measuring tumor growth before surgery https://ivypanda.com/essays/different-applications-of-calculus-in-cancer-treatment-and-monitoring/#:~:text=Thus%2C%20calculus%20is%20used%20mainly,the%20tumor%20do%20not%20split.
Thank you!
Thank you!
Applications of Calculus to real life - Bernardini Ludovica
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Transcript
Ludovica Bernardini BLK B
How Calculus applies to the Medical world
Applications of Calculus in real life
Introduction
Since the amount of departments of medicine where Calculus is required, the focus of this presentation will be incentrated on the use of Calculus made in the surgical field.
Introduction
More specifically:
Measuring Cardiac output and blood flow
In order to obtain a successful and precise measuring of cardiac output and blood flow, scientists needed to find a formula that could be suitable for all the characteristics blood has. The perfect formula was found to be Navier Stokes's equation.
Measuring Cardiac output and blood flow
The Navier-Stokes equation is crucial in various scientific and engineering fields, notably in biomedical engineering. It is expressed as:
Measuring Cardiac output and blood flow
This equation is fundamental in describing how fluids such as blood and air move and interact with their environments, making it indispensable during surgery, as constant control of heart activity is more than essential in order to continue perfoming the procedure safely.
Algorithms and statistical models for patient-specific surgery planning
Often times, surgeons need to create specific and personalised surgery plans based on their patients' needs. This is a very hard part of their job, therefore researchers and technologists have found a way to make this easier and better.
Algorithms and statistical models for patient-specific surgery planning
The best way to create and statistical models for this purpose is to use the Risch algorithm. It is named after the American mathematician Robert Henry Risch, a specialist in computer algebra who developed it in 1968.
Algorithms and statistical models for patient-specific surgery planning
The algorithm transforms the problem of integration into a problem in algebra. It is based on the form of the function being integrated and on methods for integrating rational functions, radicals, logarithms, and exponential functions. It is a method for deciding whether a function has an elementary function as an indefinite integral, and if it does, for determining that indefinite integral.
Algorithms and statistical models for patient-specific surgery planning
How a well known research carried out by the University of Waterloo, using this algorithm to plan surgeries to benefit the patients has already saved many lives, including little kids with particularly rare diseases.
Measuring tumor growth before surgery
When it comes to oncologic surgery, it is imperative to have a constant monitoring of cancer size. Before the advent of technology, this was impossible to do before surgery, but now it is more than a standard procedure.
Measuring tumor growth before surgery
Calculus has been used in cancer treatment and has helped health care providers locate the affected cells. There are different calculus applications used by physicians in cancer treatment and monitoring and their effectiveness.
Measuring tumor growth before surgery
1. Chemotherapy treatment It involves using drugs to treat the disease, and calculus is applied to monitor cancer cells, it works by destroying the affected cells and limiting their spread. The mathematical concept of calculus is applied when doctors consider the diffusion of different drugs into the bloodstream and inside the cancer cells. Calculus predicts and monitors the impact of chemotherapy on cancer tumors by using the Fractional Diffusion Equation:
Measuring tumor growth
2. The surface model This is another technique that uses calculus to show that only cells located at the surface of the tumor divide while those inside the tumor do not split. To calculate the growth, related rates with differentiation of surface area are used.
Measuring tumor growth
3. Bertalanffy’s model The approach assumes that growth will only occur proportionally with the surface area. Later, there is a decrease of tumor in its volumes due to the occurring cell death. This model concentrates on explaining the mortality curve of the human. This method has been found to provide the best explanation for lung and breast cancer growth.
Bibliography
Navier stroke equation for cardiac output and blood flow https://wjarr.com/sites/default/files/WJARR-2024-0120.pdf https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6158206/ Algorithms and statistical models for patient-specific surgery planning https://uwaterloo.ca/math-alumni-newsletter/winter-2020/feature/mathematicians-help-build-better-surgical-plans http://reference.wolfram.com/mathematica/ref/PolynomialQuotient.html Measuring tumor growth before surgery https://ivypanda.com/essays/different-applications-of-calculus-in-cancer-treatment-and-monitoring/#:~:text=Thus%2C%20calculus%20is%20used%20mainly,the%20tumor%20do%20not%20split.
Thank you!
Thank you!