Paul Lauterbur and the Invention of MRI

Appendix A: The Notebook, September 1971

Appendix A: The Notebook, September 1971 Appendix A 203 Page 1 Spatially Resolved Nuclear Magnetic Resonance Experiments The distribution of magnetic nuclei, such as protons, and their relaxation times and diffusion coefficients, may be obtained by imposing magnetic field gradients (ideally, a complete set of orthogonal spherical harmonies) on a sample, such as an organism or a manufactured object, and measuring the intensities and relaxation behavior of the resonances as functions of the applied magnetic field. Additional spatial discrimination may be achieved by the application of time-dependent gradient patterns so as to distinguish, (Signature of Paul C. Lauterbur, Sept. 2, 1971) (Signature of Donald Vickers, Sept. 3, 1971) Page 2 for example, protons that lie at the intersection of the zero-field (relative to the main static field) lines of three linear gradients. The experiments proposed above can be done most conveniently and accurately by measurements of the Fourier transforms of the pulse response of the system. They should be capable of providing a detailed three-dimensional map of the distributions of particular classes of nuclei (classified by nuclear species and relaxation times) within a living organism . For example, the distribution of mobile protons in (Signature of Paul C. Lauterbur, Sept. 2, 1971) (Signature of Donald Vickers, Sept. 3, 1971) Page 3 tissues, and the differences in relaxation times that appear to be characteristic of malignant tumors [R. Damadian, Science, 171, 1151 (1971)], should be measurable in an intact organism. (Signature of Paul C. Lauterbur, Sept. 2, 1971) (Signature of Donald Vickers, Sept. 3, 1971) 204 Appendix A Page 4 Classification of Spatially Resolved Nuclear Magnetic Resonance Experiments 1. Time-independent methods: based upon the combination of independently measured spectra in a distinct set of field gradients. A) Orthogonal gradients: in two dimensions, a pair of orthogonal first-order gradients acting on a set of n elements can produce as many as n2 images. The degree to which an image of the whole array free from significant false elements can be generated by a particular truncated set of gradients is not yet known. (Signature of Paul C. Lauterbur, Sept. 6, 1971) Page 5 B) non-orthogonal gradients: examination of simple test cases suggests that additional linear gradients quickly eliminate many false aspects of the two-dimensional image generated by a pair of orthogonal gradients. No vigorous evaluation of the efficiency or limits of such a process has yet been carried out. 2. Pulsed gradient methods: the rapid application of a sequence of gradients provides a unique history and modulation pattern for each point in the sample volume. Cross-correlation of the resonance response with a function derived (Signature of Paul C. Lauterbur, Sept. 6, 1971) Page 6 from the modulation sequences could generate an image. Appendix A 205 206 Appendix A Appendix A 207 208 Appendix A Appendix A 209 210 Appendix A ...