BIOMENG 321 : Continuum Modelling in Bioengineering

Engineering

2025 Semester One (1253) (15 POINTS)

Course Prescription

An introduction to continuum modelling approaches to bioengineering problems across a range of spatial scales. Topics include: tensor analysis, molecular and cellular mechanics of striated muscle; finite deformation elasticity and constitutive relations for soft biological materials; conservation equations for momentum, mass and heat transfer in fluids; viscous flow; boundary layers; pure conduction and diffusion; advective transport of mass and heat.

Course Overview

Soft tissues and fluids such as muscles, internal organs, blood and lymph comprise a large proportion of our bodies. Their behaviour is characterised by large deformations (e.g. contractions of the heart), flow and transport of chemical substances (e.g. oxygen) and heat (e.g. sweating). This course will build upon the continuum modelling concepts introduced in BIOMENG 221 to develop a rigourous mathematical framework for analysing stresses and strains in such biological media.  

The course is divided into 2 modules, each of 6 weeks duration. The first module will cover tensor analysis and biological soft tissue mechanics. The second module will cover biofluid mechanics and heat/mass transfer. 

Course Requirements

Prerequisite: BIOMENG 221, ENGSCI 211 Restriction: ENGSCI 343

Capabilities Developed in this Course

Capability 3: Knowledge and Practice
Capability 4: Critical Thinking
Capability 5: Solution Seeking

Learning Outcomes

By the end of this course, students will be able to:
  1. Use and apply index notation to express and operate on vectors and tensors and prove tensor identities. (Capability 3.1)
  2. Compare and contrast spatial and material coordinate systems. (Capability 4.1)
  3. Analyse large deformation kinematics with respect to material coordinates. (Capability 3.1)
  4. Define stress tensors with respect to spatial and material coordinates. (Capability 4.2)
  5. Derive and analyse constitutive equations for isotropic and anisotropic tissues. (Capability 4.1 and 5.1)
  6. Understand and analyse mathematical models of muscle contraction. (Capability 4.2 and 5.1)
  7. Derive, analyse and solve the laws of mass and momentum conservation for a fluid with appropriate simplifications. (Capability 4.1, 4.2 and 5.1)
  8. Derive, explain and apply mathematical expressions for the rotation, deformation and material derivative of a fluid element. (Capability 3.2 and 4.2)
  9. Select and apply appropriate constitutive models to analyse the flow of blood in large and small vessels. (Capability 3.2 and 4.2)
  10. Derive, analyse and solve the equations of heat and mass transfer in a flowing medium. (Capability 3.1 and 4.2)

Assessments

Assessment Type Percentage Classification
Assignments 12% Individual Coursework
Laboratories 20% Individual Coursework
Quizzes 8% Individual Coursework
Tests 20% Individual Test
Final Exam 40% Individual Examination
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6 7 8 9 10
Assignments
Laboratories
Quizzes
Tests
Final Exam

Assignments and lab reports are penalised at 4% of the total mark for each hour. No late submissions are permitted for quizzes. 

The final exam will be in-person, invigilated (Mode C). Students must sit the exam to pass the course. Otherwise, a DNS (did not sit) result will be returned.

A passing mark is 50% or higher, according to University policy.

Workload Expectations

This course is a standard 15 point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.

For this course, you can expect an average weekly workload comprising 4 hours of pre-recorded lectures, reading and thinking about the content, 2 hours of in-class problem solving and discussion, and 4 hours of work on assignments, quizzes, laboratories and/or test preparation.

Delivery Mode

Campus Experience

Attendance is expected at scheduled activities including problem-solving sessions, quizzes and labs to complete components of the course.

Lectures will be available as recordings. 

The course will not include live online events.

The activities for the course are scheduled as a standard weekly timetable.

Learning Resources

Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).

Please remember that the recording of any class on a personal device requires the permission of the instructor.

A full reading list is provided on Canvas/Talis.

Health & Safety

Students must ensure they are familiar with their Health and Safety responsibilities, as described in the university's Health and Safety policy.

Student Feedback

At the end of every semester students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback and respond with summaries and actions.

Your feedback helps teachers to improve the course and its delivery for future students.

Class Representatives in each class can take feedback to the department and faculty staff-student consultative committees.

In 2024, 100% of respondents to the Summative Evaluation Tool (SET) survey were satisfied with the quality of the course and found that regular attendance at the problem-solving sessions and lecture quizzes were helpful for learning. No changes to the course content or delivery are planned.

Academic Integrity

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework, tests and examinations as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. A student's assessed work may be reviewed against electronic source material using computerised detection mechanisms. Upon reasonable request, students may be required to provide an electronic version of their work for computerised review.

Class Representatives

Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.

Inclusive Learning

All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.

Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website http://disability.auckland.ac.nz

Special Circumstances

If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.

If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.

This should be done as soon as possible and no later than seven days after the affected test or exam date.

Learning Continuity

In the event of an unexpected disruption we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and your assessment is fair, and not compromised. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator, and if disruption occurs you should refer to the University Website for information about how to proceed.

Student Charter and Responsibilities

The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html.

Disclaimer

Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.

In this course you may be asked to submit your coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.