3. Biomedical engineers are developing a new fertility drug. Absorption Elimination For it to be effective,...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
3. Biomedical engineers are developing a new fertility drug. Absorption Elimination For it to be effective, enough drug must be present Pharmacokinetics in the blood for a sufficient period of time. The blood concentration of the drug (ug/ml) over time (h) determines the patient's overall drug exposure, which is the critical pharmacokinetic measure to determine dosing amounts. The critical overall exposure level for the new drug was determined to be 135 µg-h/ml. Researchers gave the drug to an animal at time t=0, and monitored the drug blood concentration at regular intervals. The data are presented below: Blood Concentration of Drug (µg/ml) Time Since Drug Delivery (h) 4 4 7 11 Amount of drug in blond Drig is taken 7 18 Cas Highest cancum of vid AUC (Area Under the Curve) D Time 3 2 25 32 39 a) Te 46 Cmini I drig b a. (4pts) Model the data as a 3rd degree polynomial and solve for the coefficients using the normal equations. b. (4pts) Using your model from (a), interpolate to find the expected blood concentration at 30 hours after taking the drug, and at 0 hours. In three sentences or less, are your results reasonable? c. (6pts) Use calculus to determine the time at which your model from part (a) predicts the animal will experience the maximum concentration of drug, Cmax, in its blood. What is the predicted value of Cmax? Give your answer in a complete sentence. d. (12pts) Use Lagrange Polynomials to construct a piecewise 3rd degree polynomial to model the data. Hint: Your polynomial will have two pieces. e. (6pts) Plot the data (as individual points), your interpolating polynomial from (a) as a smooth curve, your piecewise interpolating polynomial from (c) as a smooth curve, and the values of the interpolation found in part (b) as individual points, all on the same graph. Label your axes, and provide a legend. f. (8pts) Using the available data (not your models), estimate approximately how many hours after taking the drug you should wait before reaching the critical overall drug exposure level. Justify your answer in two sentences or less. 3. Biomedical engineers are developing a new fertility drug. Absorption Elimination For it to be effective, enough drug must be present Pharmacokinetics in the blood for a sufficient period of time. The blood concentration of the drug (ug/ml) over time (h) determines the patient's overall drug exposure, which is the critical pharmacokinetic measure to determine dosing amounts. The critical overall exposure level for the new drug was determined to be 135 µg-h/ml. Researchers gave the drug to an animal at time t=0, and monitored the drug blood concentration at regular intervals. The data are presented below: Blood Concentration of Drug (µg/ml) Time Since Drug Delivery (h) 4 4 7 11 Amount of drug in blond Drig is taken 7 18 Cas Highest cancum of vid AUC (Area Under the Curve) D Time 3 2 25 32 39 a) Te 46 Cmini I drig b a. (4pts) Model the data as a 3rd degree polynomial and solve for the coefficients using the normal equations. b. (4pts) Using your model from (a), interpolate to find the expected blood concentration at 30 hours after taking the drug, and at 0 hours. In three sentences or less, are your results reasonable? c. (6pts) Use calculus to determine the time at which your model from part (a) predicts the animal will experience the maximum concentration of drug, Cmax, in its blood. What is the predicted value of Cmax? Give your answer in a complete sentence. d. (12pts) Use Lagrange Polynomials to construct a piecewise 3rd degree polynomial to model the data. Hint: Your polynomial will have two pieces. e. (6pts) Plot the data (as individual points), your interpolating polynomial from (a) as a smooth curve, your piecewise interpolating polynomial from (c) as a smooth curve, and the values of the interpolation found in part (b) as individual points, all on the same graph. Label your axes, and provide a legend. f. (8pts) Using the available data (not your models), estimate approximately how many hours after taking the drug you should wait before reaching the critical overall drug exposure level. Justify your answer in two sentences or less.
Expert Answer:
Answer rating: 100% (QA)
a To model the data as a 3rd degree polynomial we can use the normal equations Lets denote the blood concentration of the drug as C and the time since ... View the full answer
Related Book For
Auditing and Assurance Services A Systematic Approach
ISBN: 978-1259162343
9th edition
Authors: William Messier, Steven Glover, Douglas Prawitt
Posted Date:
Students also viewed these finance questions
-
Engineers are developing a new design of a jet engine for an unmanned aerial vehicle (i.e., a drone). During testing, to simulate flight, air is supplied to the jet engine through an attached round...
-
Your engineers are developing a new product to launch next year that will require both software and hardware innovations. The software team requests a budget of $5 million and forecasts an 80% chance...
-
Assume that you are developing a new system for a local real estate agency. The agency wants to keep a database of its own property listings and also wants to have access to the citywide multiple...
-
Explain the benefits of graphs over tables in presenting data.
-
What is a compensating control?
-
A confidentiality agreement sets the expectations of each employee and sets job performance standards. A. True B. False
-
Why do we need different levels of testing? Cant we just test the finished software?
-
Below is a list of activities for Purple Cow Incorporated. Required: For each activity, indicate the impact on the accounting equation. After doing so for all transactions, ensure that the accounting...
-
Protax is a professional tax preparation software for tax accountants. The cost of the software is $7000 per year using "pay as you go" pricing, so on top of the yearly subscription charge, protax...
-
Newlyweds Jamie Lee and Ross have had several milestones in the past year. They are newly married, recently purchased their first home, and now have twins on the way! Jamie Lee and Ross have to...
-
1) Describe how you will advertise or raise customer awareness for your business, and your budget 2) Describe how customers will gain access to your produce or service. what channels of sale you will...
-
You are creating payments for vendors. You have $100,000 in your bank account. The total amount of vendor invoices is $150,000. Which two actions should you perform? Each correct answer presents part...
-
Why is Income a useful variable to look at when forecasting Sales? describe reason.
-
Nominal GDP Real GDP 2000 9817 9817 2001 10128 9890 2002 10470 10049 2003 10971 10321 2004 11734 10756 Nominal and Real GDP values are in billions of dollars a) Year 2000 is the based year. Find the...
-
Which letter would be used to define a 1-Regulator? and which letter would be used to define a 2-Risk Management and Compliance? Map the following terms to their location in the three lines of...
-
Maria was the sole proprietor of an unincorporated business for many years. In September of 2023, she decided to dissolve her business and retire. She sold a small office building she had used...
-
Corpus delicti may be proved by a combination of direct and circumstantial evidence or by either alone. When an attempt is made to prove corpus delicti by circumstantial evidence, the general rule is...
-
Create a data model for one of the processes in the end-of-chapter Exercises for Chapter 4. Explain how you would balance the data model and process model.
-
Multiple Choice 1. The tick mark most likely indicates that the amount was traced to the a. December cash disbursements journal. b. Outstanding check list of the applicable bank reconciliation. c....
-
Preview Company, a diversified manufacturer, has five divisions that operate throughout the United States and Mexico. Preview has historically allowed its divisions to operate autonomously. Corporate...
-
Multiple Choice 1. An auditors primary consideration regarding an entitys internal controls is whether they a. Prevent management override. b. Relate to the control environment. c. Reflect...
-
A gene is a segment of DNA that contains the information to produce a functional product. The functional product of most genes is a. DNA. b. mRNA. c. a polypeptide. d. none of the above.
-
Which of the following is not a constituent of a cells proteome? a. An enzyme b. A cytoskeletal protein c. A transport protein in the plasma membrane d. An mRNA
-
The function of the genetic code is to a. promote transcription. b. specify the amino acids within a polypeptide. c. alter the sequence of DNA. d. do none of the above.
Statistical Mechanics Theory And Molecular Simulation 2nd Edition - ISBN: 978-0198825562 - Free Book
Study smarter with the SolutionInn App