You are working as an Engineering Technician at GEMR, which specializes in designing and developingmedical equipment such as Magnetic Resonance Imaging (MRI) systems, X-ray systems, and RadioFrequency (RF) antennas coils. You will be working with the MRI and RF coils team to design a threeantenna RF coil, as shown in Figure 1(b), to be used in conjunction with an MR machine. The RF coil willbe placed on the patient head during the MR scan, see Figure 1(a). The RF coil will be exposed to an RFpulse that is in conjunction with the magnetic field of the MR scanner, Figure 1(a), receives signals fromthe brain as current flowing in the antennas. These currents are then converted into an image of thebrain as seen in Figure 1(c). Your responsibility is to carry out mathematical analysis of the RF coil topredict the performance of the antennas before they can be tested on human beings.RF PuleAntenna Aetenna 2 Aatensa 3(a)Figare 1: (a) MR machine, (b) throe loop antenmax, and (0) brain MR image Analysis 3: Based on the design of the antennas, the Standard Absorption Rate (SAR) of RF power by thepatient tissue is expected to be as follows:SAR(t) = v2t + e01t+2 where, t is time in seconds.1. Formulate a mathematical model for the dosage of exposure, D(t). Hint: the dosage is the areaunder the SAR curve.2. Plot the dosage function for the first 80 seconds.3. Manually estimate the total dosage from 40 to 60 seconds using the Mid-ordinate Rule,Trapezoidal Rule, and Simpson's Rule using 5 intervals, and again using 10 intervals. Show detailsof your steps.

Note: According to the bartleby we have to answer only first question please upload the question…

Analysis 3: Based on the design of the antennas, the Standard Absorption Rate (SAR) of RF power by the patient tissue is expected to be as follows: SAR(t) = V2t + e0.It+Z where, t is time in seconds. 1. Formulate a mathematical model for the dosage of exposure, D(t). Hint: the dosage is the area under the SAR curve.

Analysis 3: Based on the design of the antennas, the Standard Absorption Rate (SAR) of RF power by the patient tissue is expected to be as follows: SAR(t) = V2t + e0.It+Z where, t is time in seconds. 1. Formulate a mathematical model for the dosage of exposure, D(t). Hint: the dosage is the area under the SAR curve.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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You are working as an Engineering Technician at GEMR, which specializes in designing and developing
medical equipment such as Magnetic Resonance Imaging (MRI) systems, X-ray systems, and Radio
Frequency (RF) antennas coils. You will be working with the MRI and RF coils team to design a three
antenna RF coil, as shown in Figure 1(b), to be used in conjunction with an MR machine. The RF coil will
be placed on the patient head during the MR scan, see Figure 1(a). The RF coil will be exposed to an RF
pulse that is in conjunction with the magnetic field of the MR scanner, Figure 1(a), receives signals from
the brain as current flowing in the antennas. These currents are then converted into an image of the
brain as seen in Figure 1(c). Your responsibility is to carry out mathematical analysis of the RF coil to
predict the performance of the antennas before they can be tested on human beings.
RF Pule
Antenna Aetenna 2 Aatensa 3
(a)
Figare 1: (a) MR machine, (b) throe loop antenmax, and (0) brain MR image

Analysis 3: Based on the design of the antennas, the Standard Absorption Rate (SAR) of RF power by the
patient tissue is expected to be as follows:
SAR(t) = v2t + e01t+2 where, t is time in seconds.
1. Formulate a mathematical model for the dosage of exposure, D(t). Hint: the dosage is the area
under the SAR curve.
2. Plot the dosage function for the first 80 seconds.
3. Manually estimate the total dosage from 40 to 60 seconds using the Mid-ordinate Rule,
Trapezoidal Rule, and Simpson's Rule using 5 intervals, and again using 10 intervals. Show details
of your steps.

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