Navigating the Brain

1. Navigating the Brain Mark P. Wachowiak, Ph.D. Department of Computer Science and Mathematics Nipissing University April 27, 2007

2. Outline • Basic brain anatomy • Brain imaging • Magnetic resonance imaging (MRI) • Computed tomography (CT) • Functional imaging • Brain navigation • Future directions

3. Mathematics Awareness Month

4. Interdisciplinary Nature of Brain Research • Neuroscientists • Physicians • Psychologists • Mathematicians • Biologists • Engineers • Computer scientists

5. Neurons • Electrically excitable cells in the nervous system. • Transmit and process information. • Dendrites • Conduct electrical impulses from other neurons or cells towards the cell body. • Axons • Conduct impulses away from the cell body to other neurons. http://faculty.uca.edu/~benw/biol1400/pictures/neuron.jpg

6. Hodgkin-Huxley Model of Neurons • First mathematical model of neurons (1952). • Models electrical characteristics of the cells • Based on systems of nonlinear ordinary differential equations. • Starting point for modern, advanced neuron models. Alan Lloyd Hodgkin Andrew Fielding Huxley www.nobel.org

7. Cerebrum • Largest part of the brain. • Higher brain functions: • Thought • Action • Vision • Memory http://serendip.brynmawr.edu/bb/kinser/Structure1.html#cerebrum

8. Cerebellum • Associated with the regulation and coordination of movement, posture, and balance.

9. Medulla Oblongata • Relays nerve signals between the brain and the spinal cord. • Involuntary functions: • Breathing • Blood pressure • Heart rate • Reflexes

10. Sulci and Gyri • Sing. sulcus, gyrus • Sulcus • Fissure in the brain tissue. • Interhemispheric fissure – divides the brain into left and right hemispheres. • Gyrus • Elevated “hill” areas between sulci. Gyrus Sulcus Atamai

11. White Matter • Found in the brain and spinal cord. • Consists of insulated (myelinated) nerve fibers (axons). • Responsible transmitting and conducting information. http://www.brainexplorer.org/brain-images/white_matter.jpg

12. Grey Matter • Consists of the bodies of neurons. • Responsible for information processing. • Generates responses to stimuli. http://www.brainexplorer.org/brain-images/white_matter.jpg

13. Neuroimaging

14. Types of Neuroimaging • Structural • Magnetic resonance imaging • Computed tomography • Ultrasound • Functional • Functional MRI • Positron emission tomography • Single photon emission computed tomography

15. Magnetic Resonance Imaging • Excellent for clearly visualizing structures in soft tissues, such as the brain. • Very commonly used in: • Diagnosis • Image-guided surgery and therapy • By adjusting scanning settings, specific features can be detected. • MRI images are 2D slices through the body at a specific location.

16. MRI Scanner http://psyphz.psych.wisc.edu/

17. Proton Precession Hydrogen protons precess about an axis, like a “wobbling” spinning top.

18. Proton Precession in Tissue Randomly-oriented hydrogen protons precess.

19. Application of Magnetic Field Magnetic field A strong magnetic field is applied in a specified direction. The protons align with the magnetic field.

20. Application of RF Pulse A strong, sudden RF (radiofrequency) pulse is applied in a direction orthogonal to the magnetic field. Magnetic field Protons are briefly placed into a high-energy state. RF pulse

21. RF Pulse is Turned Off Energy is released as the protons return to their low-energy orietation within the magnetic field. Magnetic field

22. MRI Image Formation • When the RF pulse is turned off, the hydrogen protons return to their natural alignment within the magnetic field. • Energy is released. • The coil detects this signal and sends it to a computer for processing. • The signal consists of complex values which have real and imaginary components.

23. Complex Numbers Imaginary number Complex number Magnitude

24. Fourier Transform • Determine the frequency components of a signal. • From a complex frequency representation, recover the original signal. • Involves calculus and integration of complex-valued functions. Jean Baptiste Joseph Fourier (1768-1830) ocw.mit.edu

25. Obtaining Frequency Information + Fourier Transform

26. Fast Fourier Transform • A very efficient method to compute the Fourier transform of a signal. • Developed in 1965 by J.W. Cooley and John Tukey (AT&T Labs). • One of the “top ten” algorithms of the 20th century. James W. Cooley John W. Tukey www.ieee.org, www.math.brown.edu

27. MRI Image Formation Fourier Transform Magnitude information from signal Phase information from signal

28. MRI Visualization • A series of 2D MRI images can be combined together to form a 3D volume. • This volume can then be used to generate realistic visualizations and models.

29. MS Lesions http://www.med.harvard.edu/AANLIB/cases/case5/mr2/035.html

30. Computed Tomography (CT) • Tomography • Imaging in sections, or slices. • Computed • Geometric processing used to reconstruct an image. • Computerized algorithms

31. Computed Tomography (2) • Uses X-rays • Dense tissue, like bone, blocks x-rays. • Gray matter weakens (attenuates) the x-rays. • Fluid attenuates even less. • A computerized algorithm (filtered backprojection) reconstructs an image of each slice.

32. CT Image Formation X-ray tube X-ray X-ray detector

33. Computed Tomography http://fitsweb.uchc.edu/student/selectives/TimHerbst/intro.htm

34. CT Image Formation Backprojection

35. CT Image Reconstruction – 6 Slices

36. CT Image Reconstruction – 12 Slices

37. CT Image Reconstruction – Final Image

38. fMRI • Functional MRI – used to investigate brain function. • Enables watching brain activity in vivo. • Measures haemodynamic response. • Changes in oxygen content of the blood occur as the result of neuronal activity.

39. Interdisciplinary Nature of fMRI • Physics • Hardware tools • Electrophysiology • Neuronal behaviour • Psychology • Cognitive psychology • Statistics • Making sense of observations • Neuroanatomy

40. Blood Oxygen Level Dependent fMRI (BOLD) Signal increase Signal decrease http://en.wikipedia.org/wiki/Neuroimaging

41. fMRI Active areas while subjects remembered information presented visually Active areas while subjects remembered information presented aurally Active areas for both types http://mednews.stanford.edu/stanmed/2005fall/brain-main.html

42. Complementary Imaging Techniques MRI CT fMRI http://www.med.harvard.edu/AANLIB/hms1.html

43. Brain Navigation

44. Mathematical Challenges in Neuroimaging • Segmentation • Identifying structures or abnormalities from 2D or 3D brain images. • Development of models to help plan surgery and therapy. • Concepts from computer graphics, geometry, topology, probability theory.

45. Mathematical Challenges in Brain Imaging • Registration • Aligning and combining images from the same or different type of image. • Useful in simulation, modeling, and in planning surgical procedures. • Employs concepts from probability theory, information theory, geometry, topology, optimization, parallel computing, and many other areas.

46. MRI Visualization and Segmentation Atamai

47. Segmentation – Differential Geometry Automatically computed network of 3D curves lying deep in the cortex (sulcal fundi), color-coded according to the curvature. G. Sapiro, SIAM News, Volume 40, Number 2, March 2007

48. Registration and Fusion MRI MRI Ultrasound PET Histology cryosection MRI + Ultrasound

49. CT-to-MRI Registration

50. Brain Warping • Nonlinear registration. • Used to match features in structurally different brains. • Uses: • Geometry • Topology • Probability • Calculus https://www.rad.upenn.edu/sbia/dgshen/HAMMER/brainWarping.htm