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Biomedical Engineering Cheatsheet

A quick reference guide for key concepts, formulas, and techniques in biomedical engineering, covering biomechanics, biomaterials, bioinstrumentation, and bioimaging.

Biomechanics

Stress and Strain

Stress (σ)

Force per unit area: σ = F/A
Where:
F = Force (N)
A = Area (m²)
Units: Pascals (Pa) or N/m²

Strain (ε)

Change in length per unit length: ε = ΔL/L₀
Where:
ΔL = Change in length (m)
L₀ = Original length (m)
Strain is dimensionless.

Young’s Modulus (E)

Measure of stiffness: E = σ/ε
Units: Pascals (Pa) or N/m²

Shear Stress (τ)

Force acting parallel to the surface per unit area: τ = F/A
Units: Pascals (Pa) or N/m²

Shear Strain (γ)

Change in angle: γ = Δx/L₀
Where:
Δx = Displacement (m)
L₀ = Original length (m)
Strain is dimensionless.

Shear Modulus (G)

Measure of resistance to shear deformation: G = τ/γ
Units: Pascals (Pa) or N/m²

Viscoelasticity

Viscoelastic materials exhibit both viscous and elastic characteristics when undergoing deformation.

Key Concepts:

  • Creep: Time-dependent deformation under constant load.
  • Stress Relaxation: Time-dependent decrease in stress under constant strain.
  • Hysteresis: Energy loss during loading and unloading cycle.

Common Models:

  • Maxwell Model: Represents a spring and dashpot in series.
  • Kelvin-Voigt Model: Represents a spring and dashpot in parallel.

Fluid Mechanics

Reynolds Number (Re)

Predicts flow regime:
Re = (ρvL)/μ
Where:
ρ = Density (kg/m³)
v = Velocity (m/s)
L = Characteristic length (m)
μ = Dynamic viscosity (Pa·s)

Re < 2300: Laminar flow
Re > 4000: Turbulent flow

Viscosity (μ)

Measure of a fluid’s resistance to flow. Units: Pascal-seconds (Pa·s)

Poiseuille’s Law

Describes laminar flow in a cylindrical tube:
Q = (πr⁴ΔP)/(8μL)
Where:
Q = Flow rate (m³/s)
r = Radius of the tube (m)
ΔP = Pressure difference (Pa)
μ = Dynamic viscosity (Pa·s)
L = Length of the tube (m)

Biomaterials

Material Properties

Biocompatibility

The ability of a material to perform with an appropriate host response in a specific application.

Biodegradability

The ability of a material to degrade or be absorbed in the body.

Surface Properties

Surface energy, roughness, and chemical composition affect protein adsorption and cell adhesion.

Mechanical Properties

Tensile strength, compressive strength, Young’s modulus, and Poisson’s ratio determine structural integrity.

Types of Biomaterials

Metals:

  • Stainless steel, titanium alloys, cobalt-chromium alloys.
  • Used in implants, prosthetics, and surgical instruments.

Ceramics:

  • Alumina, zirconia, hydroxyapatite.
  • Used in bone grafts, dental implants, and coatings.

Polymers:

  • Polyethylene, polypropylene, silicone, poly(lactic acid) (PLA), poly(glycolic acid) (PGA).
  • Used in sutures, drug delivery systems, and tissue engineering scaffolds.

Composites:

  • Combination of two or more materials (e.g., carbon fiber reinforced polymers).
  • Used in load-bearing implants.

Biomaterial Degradation

Hydrolysis

Chemical breakdown of a material due to reaction with water.

Enzymatic Degradation

Breakdown of a material by enzymes present in the body.

Oxidation

Chemical degradation due to reaction with oxygen.

Corrosion

Electrochemical degradation of metals.

Bioinstrumentation

Sensors and Transducers

Strain Gauge

Measures strain by detecting changes in electrical resistance.

Thermistor

Measures temperature by detecting changes in electrical resistance.

Pressure Transducer

Measures pressure by converting it into an electrical signal.

Electrode

Measures electrical potential differences (e.g., ECG, EEG).

Signal Processing

Amplification

Filtering

Analog-to-Digital Conversion (ADC)

Digital Signal Processing (DSP)

Common Instruments

Electrocardiograph (ECG)

Records electrical activity of the heart.

Electroencephalograph (EEG)

Records electrical activity of the brain.

Electromyograph (EMG)

Records electrical activity of muscles.

Blood Pressure Monitor

Measures arterial blood pressure.

Bioimaging

Imaging Modalities

X-ray

Uses electromagnetic radiation to create images of bones and dense tissues.

Computed Tomography (CT)

Uses X-rays to create cross-sectional images of the body.

Magnetic Resonance Imaging (MRI)

Uses magnetic fields and radio waves to create detailed images of soft tissues.

Ultrasound

Uses sound waves to create real-time images of organs and tissues.

Positron Emission Tomography (PET)

Uses radioactive tracers to visualize metabolic activity in the body.

Image Processing

Image Enhancement

Image Segmentation

Image Registration

Image Reconstruction

Contrast Agents

Iodine-based

Used in CT scans to enhance the visibility of blood vessels and organs.

Gadolinium-based

Used in MRI to enhance the visibility of soft tissues and blood vessels.

Microbubbles

Used in ultrasound to enhance the visibility of blood flow and tissue perfusion.
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