MRES7100: Assignment 1A Semester 2 Assessment

Scoring

This assignment has a total of 25 marks and is worth 25% of the final grade.
There are 4 exercises, each divided into subsections.

To receive full marks:

• Each answer must include a brief explanation.

• Answers without explanations will not receive full marks.

• Keep answers concise and clear.

• For all calculations, show equations and each step, with correct SI units.

• If a question is unclear, contact the course coordinator.

Plagiarism

• Write answers in your own words.

• Do not copy text from course materials or the web.

• If external sources are used, rephrase clearly and provide the reference.

• You must solve questions independently.

• Do not collaborate with other students.

• Do not use ChatGPT or any AI tools.

• All suspiciously similar or AI-generated content will be investigated for academic misconduct.

Illustrations

• Do not copy and paste diagrams from books or online sources.

• Create freehand drawings and insert a photograph or scan of the sketch.

Submission Instructions

• Use the assessment coversheet provided on Blackboard.

• Place your answers in the spaces provided beneath each question.

• Increase answer space as needed.

• Save your work as a PDF and check formatting before uploading to Turnitin.

• Keep a backup copy of your submission.

Filename Format

Use “Print to PDF” in Word if required.

Submission Deadline

Submit through Turnitin before the due date.
You may overwrite submissions until the deadline. Only the final uploaded version is marked.

Late Submission Penalty

• Unapproved late submissions: –3 marks per day, up to 7 days.

• After 7 days: mark = 0.

Exercise 1

A T2-weighted turbo spin echo sequence for liver imaging uses the following sequence parameters:

• TR = 2 s

• TE = 20 ms

• Turbo factor = 8

• RF pulse: 3 ms Sinc

• FOV: 30 × 20 cm

• Slice thickness: 2 mm

• In-plane resolution: 0.5 × 0.5 mm

• Spectral bandwidth: 80 kHz

• Matrix size: 256 × 192

• Number of excitations (NEX): 2

Calculate the following:

(a) What are the minimum dwell time and the acquisition time per echo?

(b) What is the required readout gradient amplitude?

(c) Using a slice-selection gradient of 5 mT/m, calculate:

• The bandwidth for the slice-selective RF excitation

• The number of cycles required for the Sinc pulse

(d) What is the resolution of the image?

(e) What are the effective echo time and the length of the image acquisition time?

Notes:

• For TSE, Effective TE ≈ time at centre of k-space (echo no. ETL/2).

• Echo spacing (ESP) ≈ 3.2 ms (readout) + 1 ms rephasing delay each side.

• Approximate ESP ≈ 5 ms.

(f) How many phase rewind gradients are absolutely required, and why?

Exercise 2

Consider the image contrasts from the following brain MR images:

• TI = 165 ms

• TI = 600 ms

Both images used the same sequence type:

• TE = 10 ms

• TR = 10 s

(a) What is the type of sequence used to acquire these images?

Given explanation:
This is an Inversion Recovery (IR) sequence.
The use of TI indicates a 180° inversion pulse. Long TR (10 s) and short TE (10 ms) mean contrast is strongly T1-weighted and governed by inversion recovery behaviour.

(b) Using the sequence parameters, calculate the T1 of CSF.

(c) Draw a z-magnetisation vs TI curve.

(d) Use your diagram from (c) to describe the reversal of image contrast caused by changing TI.

Exercise 3 

An inversion recovery spin-echo echo planar imaging (EPI) sequence is used for brain imaging at 3 T.

Sequence parameters:

• TI = 600 ms

• TR = 10 s

• TE = 50 ms

• 8 phase-encoding lines

Draw a schematic diagram of the sequence showing:

• RF pulses

• Read (frequency-encode), phase, and slice gradient components

• Preparative gradients

• Gradients used to shift the echo to the edge of k-space

(b) Explain briefly, using dot points and a simple diagram, how k-space is traversed in this sequence and the consequences for data handling and reconstruction.

(c) What is the predominant image weighting? Briefly justify.

Brief Summary of Assessment Requirements

Task: Complete MRES7100 Assignment 1A (25 marks; 25% of final grade). Four exercises cover MRI sequence design, timing and gradient calculations, contrast theory, k-space/EPI schematics and interpretation. Every answer must include a short explanation; calculations must show equations, steps and SI units. Hand-drawn sketches only (scan/photograph for submission). No collaboration or AI tools. Late penalties apply.

Key pointers to cover in your answers

• Exercise 1 (9 marks): compute dwell time & echo acquisition time; readout gradient amplitude; slice-select RF bandwidth and Sinc cycles (given slice gradient); confirm image resolution; compute effective TE and total acquisition length for a TSE (use turbo factor / ESP); state required phase-rewind gradients and justify why. Show formulas (bandwidth ↔ gradient × slice thickness etc.), units and neat stepwise calculations.

• Exercise 2 (7 marks): identify sequence type from TI/TR/TE; use inversion recovery theory to estimate T₁ of CSF from given TI contrast behaviour; provide a labelled z-magnetisation vs TI sketch; explain how changing TI reverses image contrast (which tissues are nulled or bright at each TI).

• Exercise 3 (9 marks): draw a clear timing diagram for an IR spin-echo EPI (RF pulses, read/phase/slice gradients, pre-phasing/rephasing and blip gradients), explain k-space traversal for EPI (ordering, echo train, readout bandwidth needs, susceptibility to distortions) and state the predominant image weighting with a brief justification.

How the Academic Mentor Guided the Student 

Below is how the mentor structured the support so the student met the brief, with what to do for each exercise.

1) Setup and interpretation of the brief

• Goal: Ensure the student understood marks breakdown, obligatory explanations, units and hand-drawing rules.

• Action: Mentor reviewed the sequence parameters and clarified definitions (dwell time, ESP, turbo factor/ETL, effective TE, spectral bandwidth, NEX, matrix/FOV relationships).

Practical parameter calculations

Step A Dwell time & acquisition time per echo

• Approach taught: derive dwell time = 1 / (readout bandwidth per pixel), where readout bandwidth per pixel = spectral bandwidth / readout matrix size (frequency-encode points). Show substitution, compute dwell time (s) and multiply by points per echo for echo acquisition time.

• Why: dwell time determines sampling interval and minimum echo acquisition window.

Step B Readout gradient amplitude

• Approach taught: use k-space relationship Δk = 1/FOV and Gread = (γ Δk) / (bandwidth per pixel) or directly from spatial frequency relation G=bandwidthγ⋅FOVG = \frac{\text{bandwidth}}{\gamma \cdot \text{FOV}}G=γ⋅FOVbandwidth. Mentor showed unit consistency (T/m).

• Why: required gradient strength sets frequency encoding scale.

Step C Slice RF bandwidth & Sinc cycles

• Approach taught: slice bandwidth (Hz) = Gslice (T/m) × γ (Hz/T) × slice thickness (m). Mentor then computed number of cycles ≈ (RF duration × RF bandwidth) to estimate Sinc cycles; explained tradeoff between pulse duration, bandwidth and slice profile.

• Why: correct slice select and minimal slice profile ripple.

Step D Image resolution

• Approach taught: resolution = FOV / matrix size for each axis (report mm). Show how in-plane resolution relates to matrix and FOV values given.

Step E Effective TE & acquisition length

• Approach taught: for TSE effective TE corresponds to echo index at k-space centre (ETL/2). Mentor demonstrated how to compute ESP (given readout + rephasing delays) and total acquisition time = ESP × number of phase-encode lines / turbo factor (accounting for NEX if needed). Also explained approximating ESP when given multiple delays.

• Why: effective TE controls contrast; acquisition length affects motion sensitivity and scan time.

Step F Phase rewind gradients

• Approach taught: identify minimum phase rewinds required to refocus transverse phase after frequency readouts (one rewind per readout train or one for each echo in some implementations). Mentor explained practical reasons (remove residual dephasing from readout, position k-space start at edge) and when extra rewinds are used if multiple RF pulses or crusher gradients are present.

Contrast and T₁ estimation

Sequence identification

• Approach taught: identify inversion recovery from presence of TI and long TR; explain physics: 180° inversion then recovery before readout.

T₁ of CSF

• Approach taught: show inversion recovery signal equation Mz(TI)=M0(1−2e−TI/T1)M_z(TI) = M_0(1 - 2e^{-TI/T1})Mz(TI)=M0(1−2e−TI/T1) (for full inversion) or appropriate rearrangement. Mentor walked through solving for T₁ given observed nulling TI (if TI that nulls CSF is known) or using relative contrasts to estimate T₁ numerically. Emphasised including units and assumptions.

Sketch and explanation

• Approach taught: draw z-magnetisation curve from -M₀ immediately after inversion to +M₀ asymptote, mark TI values (165 ms and 600 ms) and show their positions relative to zero crossing; explain how tissue with different T₁s (fat, GM, CSF) will appear bright/ dark at each TI.

• Why: visual explanation supports concise written justification of contrast reversal.

IR spin-echo EPI schematic and k-space handling

Timing diagram

• Approach taught: sketch time axis with 180° inversion, 90° excitation, then EPI readout block showing a long gradient-echo train (read gradient oscillating), blip (phase-encode) gradients between read lines, slice gradients and preparatory crushers. Mentor emphasised labelling rephrase and prephasing lobes and the gradient used to shift echo to k-space edge.

K-space traversal & data handling

• Approach taught: explain EPI traversal: rapid zigzag/even-odd readout lines filling many k-space lines per excitation (consecutive lines during single echo train). Dot points to include: ordering (sequential or centric variants), need for Nyquist/odd–even correction, sensitivity to off-resonance and distortion, requirement for high readout bandwidth and careful Nyquist/phase correction during reconstruction.

Predominant weighting

• Approach taught: reason that the inversion recovery element imparts T₁ (inversion) contrast because TI controls relative magnetisation at readout; note TE=50 ms in EPI introduces some T₂/T2* influence but with TR long and specific TI for IR, the dominant contrast is determined by inversion recovery. Mentor coached a concise justification: list which parameter dominates contrast and why.

5) Verification, sketches and final report assembly

• Approach taught: verify numerical results (unit checks, magnitude sanity), annotate all sketches, include short explanations for each numeric result and sketch, and compile a one-page summary of assumptions. Mentor reminded to save as PDF, use cover sheet and follow filename format.

Final Outcome

Deliverables produced

• Exercise 1: step-by-step calculations with equations, unit checks and numeric answers for dwell time, echo acquisition, readout gradient amplitude, slice RF bandwidth and Sinc cycles, resolution, effective TE and acquisition length, plus justification of required phase-rewind gradients. All quantities shown as functions/expressions where appropriate.

• Exercise 2: correct identification of IR sequence; worked method to estimate CSF T₁ (equation and rearrangement shown), hand-drawn z-magnetisation vs TI curve with TI markers and short textual explanation of contrast reversal.

• Exercise 3: clear hand-drawn timing diagram with labelled RF and gradient lobes (read, phase, slice, prephasing), concise dot-point explanation of EPI k-space traversal and reconstruction implications, and a short reasoned statement of predominant contrast weighting.

How it was achieved

• Stepwise calculations and symbolic rearrangements were used so an examiner can follow logic. Hand sketches were photographed and embedded. All answers include short explanations linking physical meaning to the numerical results. The student validated results numerically and performed sanity/unit checks under mentor guidance.

Learning Objectives Covered

• Apply MR physics principles to compute acquisition parameters (dwell time, ESP, gradient amplitudes).

• Translate sequence parameters (TR, TE, TI, ETL) into image contrast and timing outcomes.

• Use inversion recovery signal models to interpret TI-dependent contrast and estimate T₁.

• Draw and interpret pulse-sequence timing diagrams and k-space traversal for EPI.

• Explain reconstruction challenges (odd–even, distortion, bandwidth tradeoffs) in fast imaging.

• Present calculations clearly with physical justification, correct SI units and concise explanations matching assessment instructions and academic integrity requirements.

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