Prelim BPAD (old)

Math & Stats Foundations »
Single-Variable Calculus
Series Approximation: Taylor Expansions and Finite Differences
Scalars, Vectors, Matrices, and Tensors
Kinematics: Displacement, Velocity, and Acceleration
Polynomials, Exponentials, and Logarithms
Complex Numbers and Phasor Notation
Linear Systems, Convolution, and the Convolution Theorem
Fourier Series
The Fourier Transform
Sampling, Aliasing, and the Nyquist Criterion
Polar, Cylindrical, and Spherical Coordinates
Partial Derivatives, Vector Calculus, and PDEs
Ordinary Differential Equations in Biological Systems
Probability and Statistics
Noise Models, SNR, and CNR
Statistical Estimation, Error Propagation, and Inference
Linear Algebra: Systems, Eigenvalues, and the SVD
Dimensionality Reduction
Choosing the Right Tool

Optical & Thermal Methods »
Physical Foundations
Absorption-Based Methods
Scattering-Based Methods
Fluorescence-Based Imaging
Thermal Radiation and Infrared Thermography
Ultraviolet Radiation and Photobiology
Choosing the Right Optical Method

Ultrasound & Photoacoustic Imaging »
Fundamentals of Acoustic Wave Physics
Instrumentation and Signal Processing
Conventional Imaging Modes
Artifacts: When Assumptions Fail
Advanced Ultrasound Techniques
Acoustic Output, Bioeffects, and Safety
The Photoacoustic Effect
Multispectral Photoacoustic Tomography
Clinical and Disease Applications
Choosing a Method
Computational Lab

Nuclear Magnetic Resonance Imaging (MRI) »
Spin Physics: The Origin of the MR Signal
Relaxation and Tissue Contrast
Image Contrast: TR, TE, and Weighting
Spatial Encoding and k-Space
Pulse Sequences
Reconstruction, Resolution, and SNR
Artifacts and Corrections
Safety: SAR, Gradients, Projectiles, and Contrast Agents
From Images to Measurements
Advanced and Functional MRI
Contrast Agents and Angiography
Clinical and Disease Applications
Choosing a Sequence
Computational Lab

X-ray Photon Generation & CT Reconstruction »
X-ray Production
How X-rays Interact with Tissue
Attenuation and Radiographic Contrast
Beam Control, Detectors, and Noise
Radiation Dose, Risk, and Justification
From Radiography to CT
CT Data: Line Integrals, Sinograms, and the Radon Transform
The Central Slice Theorem
Reconstruction
Hounsfield Units and Windowing
CT Artifacts
Dual-Energy and Spectral CT
Resolution, Contrast, Noise, and Dose
Choosing the Acquisition
Computational Lab

X-ray Photon Generation & CT Reconstruction »
Emission versus Transmission
Radioactive Decay and Emission Physics
Radionuclide Production and Radiopharmaceuticals
Gamma Cameras, Collimators, and SPECT
Positron Emission Tomography
PET Resolution Limits and Time of Flight
Reconstruction in Emission Tomography
Attenuation Correction and Hybrid Imaging
Tracer Kinetics and Quantification
Partial-Volume Effects and Quantitative Accuracy
Internal Dosimetry, Risk, and Safety
Disease Applications
Choosing the Study
Computational Lab

Medical Image Processing, Quantitative Measurement & Uncertainty »
The general image-processing workflow
Image import and representation
Visualization and inspection
Preprocessing, normalization, and geometric transformation
Image filtering
Fourier analysis and spatial-frequency filtering
Registration and spatial alignment
Segmentation: from intensities to labeled structures
From segmentation to measurement: quantification and uncertainty
Feature extraction, radiomics, and modeling
Volumetric visualization and 3D rendering
Computational Lab: An end-to-end quantitative pipeline

(+RShiny Apps) Data Modeling, AI & Biomedical Applications »
(Part 1) Data Modeling, AI & Biomedical Applications »
(Part 2) Data Modeling, AI & Biomedical Applications »
From Physical Measurement to a Learning Problem
Mathematical Foundations of Statistical Learning
Running Case Study: the Real KiTS19 Kidney Cohort
From CT Volumes and Masks to Quantitative Features
Exploratory Structure, Preprocessing, and Representation
Supervised Learning: Classification and Regression
Time-to-Event and Longitudinal Modeling


Unsupervised Learning, Segmentation, and Spatial Structure
Deep Learning and Image-Native AI
Evaluation, Calibration, Uncertainty, and Clinical Utility
Translation: Shift, Fairness, Interpretability, Privacy, and Deployment
Reproducible Computational Practice and the Capstone