MRI at a Glance E-Book

Catherine Westbrook

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: At a Glance
• Sprache: Englisch

Seitenzahl: 306

Veröffentlichungsjahr: 2015

Beschreibung

Highly Commended at the British Medical Association Book Awards 2016

MRI at a Glance encapsulates essential MRI physics knowledge. Illustrated in full colour throughout, its concise text explains complex information, to provide the perfect revision aid. It includes topics ranging from magnetism to safety, K space to pulse sequences, and image contrast to artefacts.
This third edition has been fully updated, with revised diagrams and new pedagogy, including 55 key points, tables, scan tips, equations, and learning points. There is also an expanded glossary and new appendices on optimizing image quality, parameters and trade-offs.

A companion website is also available at www.ataglanceseries.com/mri featuring animations, interactive multiple choice questions, and scan tips to improve your own MRI technique.

MRI at a Glance is ideal for student radiographers and MRI technologists, especially those undertaking the American Registry of Radiation Technologist (ARRT) MRI examination, as well as other health professionals involved in MRI.

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Library of Congress Cataloging-in-Publication Data

Westbrook, Catherine.   MRI at a glance / Catherine Westbrook. — Third edition.     pages cm   Includes index.   ISBN 978-1-119-05355-2 (pbk.)  1. Magnetic resonance imaging.Outlines, syllabi, etc. 2. Medical physics.Outlines, syllabi, etc. I. Title.   RC78.7.N83W4795 2016 616.0-548.dc23

2015022541

A catalogue record for this book is available from the British Library.

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.

Cover image: © Getty Images/Yuji Sakai

CONTENTS

Preface

Acknowledgement

How to use your textbook

About the companion website

1 Magnetism and electromagnetism

Magnetic susceptibility

Paramagnetism

Diamagnetism

Ferromagnetism

Electromagnetism

2 Atomic structure

Introduction

Motion within the atom

MR active nuclei

3 Alignment

The classical theory

The quantum theory

What do the quantum and classical theories tell us?

4 Precession

Precessional (Larmor) frequency

Precessional phase

5 Resonance and signal generation

Energy absorption

Phase coherence

The MR signal

6 Contrast mechanisms

What is contrast?

Extrinsic contrast parameters

Intrinsic contrast mechanisms

The composition of fat and water

7 Relaxation mechanisms

Relaxation processes

Field inhomogeneities

8 T1 recovery

T1 recovery in fat

T1 recovery in water

Control of T1 recovery

9 T2 decay

T2 decay in fat

T2 decay in water

Control of T2 decay

10 T1 weighting

Typical values

11 T2 weighting

Typical values

12 PD weighting

Typical values

Other types of weighting

13 Conventional spin echo

Mechanisms of CSE

Contrast

Typical values

Uses

14 Fast or turbo spin echo – how it works

Mechanism

Contrast

15 Fast or turbo spin echo – how it is used

Typical values

Uses

16 Inversion recovery

Mechanism

Contrast

Uses

17 Gradient echo – how it works

Mechanism

18 Gradient echo – how it is used

Typical values

Uses

19 The steady state

Echo generation in the steady state

20 Coherent gradient echo

Mechanism

Typical values

Uses

21 Incoherent gradient echo

Mechanism

Typical values

Uses

22 Steady-state free precession

Mechanism

Typical values

Uses

23 Balanced gradient echo

Mechanism

Typical values

Uses

24 Ultrafast sequences

Turbo gradient echo

Echo planar imaging

Typical values

Uses

25 Diffusion and perfusion imaging

Diffusion weighted imaging

Perfusion imaging

26 Functional imaging techniques

Functional MR imaging (fMRI)

Spectroscopy

27 Gradient functions

How gradients work

28 Slice selection

Mechanism

Slice thickness

29 Phase encoding

Mechanism

30 Frequency encoding

Mechanism

31 K space – what is it?

32 K space – how is it filled?

33 K space and image quality

K space – signal and contrast

K space – spatial resolution

34 Data acquisition – frequency

Changing the receive bandwidth

Changing the frequency matrix

35 Data acquisition – phase

36 Data acquisition – scan time

TR

Phase matrix

Number of signal averages (NSA)

Types of acquisition

Reducing scan time

37 K space traversal and pulse sequences

K space traversal in gradient echo

K space traversal in spin echo

K space traversal in single shot

K space traversal in spiral imaging

38 Alternative K space filling techniques

Partial or fractional averaging

Rectangular FOV

Anti-aliasing/over-sampling

Centric imaging

Keyhole imaging

Parallel imaging

39 Signal to noise ratio

Proton density

Coil type and position

TR

TE

Flip angle

Number of signal averages (NSA)

Receive bandwidth

40 Contrast to noise ratio

Administration of contrast

Magnetization transfer contrast

Chemical suppression techniques

Flow techniques

T2 weighting

41 Spatial resolution

Voxel volume and SNR

Voxel volume and resolution

42 Chemical shift artefacts

Appearance

Remedy

Appearance

Remedy

43 Phase mismapping

Appearance

Remedy

44 Aliasing

Frequency aliasing

Phase aliasing

45 Other artefacts

Magnetic susceptibility

Cross-talk

Truncation artefact

Zipper artefact

46 Flow phenomena

Time-of-flight phenomenon

Entry slice phenomenon

Intra-voxel dephasing

47 Time-of-flight MR angiography

Mechanism

Clinical applications

General advantages of TOF MRA

General disadvantages of TOF MRA

48 Phase contrast MR angiography

Mechanism

Clinical uses

49 Contrast-enhanced MR angiography

Mechanism

Administration

Image timing

50 Contrast agents

Gadolinium

Iron oxide

Other contrast agents

51 Magnets

Permanent magnets

Electromagnets

52 Radiofrequency coils

Transmit coils

Receiver coils

RF coil types

53 Gradients and other hardware

Gradients

The pulse control unit

The operator interface

Data storage

54 MR safety – bio-effects

Static magnetic field bio-effects

Time-varying field bio-effects

Site planning

55 MR safety – projectiles

Quenching

Metallic implants and prostheses

Appendix 1(a): The results of optimizing image quality

Appendix 1(b): Parameters and their associated trade-offs

Appendix 2: Artefacts and their remedies

Appendix 3: Main manufacturers’ acronyms

Glossary

Index

Eula

List of Tables

Chapter 1

Table 1.1

Table 1.2

Chapter 2

Table 2.1

Table 2.2

Chapter 3

Table 3.1

Table 3.2

Chapter 4

Table 4.1

Table 4.2

Table 4.3

Chapter 5

Table 5.1

Table 5.2

Chapter 6

Table 6.1

Table 6.2

Chapter 7

Table 7.1

Table 7.2

Table 7.3

Chapter 8

Table 8.1

Table 8.2

Table 8.3

Chapter 9

Table 9.1

Table 9.2

Table 9.3

Chapter 10

Table 10.1

Table 10.2

Chapter 11

Table 11.1

Table 11.2

Chapter 12

Table 12.1

Table 12.2

Chapter 13

Table 13.1

Table 13.2

Chapter 14

Table 14.1

Table 14.2

Table 14.3

Chapter 15

Table 15.1

Table 15.2

Table 15.3

Chapter 16

Table 16.1

Table 16.2

Chapter 17

Table 17.1

Chapter 18

Table 18.1

Table 18.2

Chapter 19

Table 19.1

Table 19.2

Table 19.3

Chapter 20

Table 20.1

Table 20.2

Table 20.3

Chapter 21

Table 21.1

Table 21.2

Table 21.3

Chapter 22

Table 22.1

Table 22.2

Table 22.3

Chapter 23

Table 23.1

Table 23.2

Table 23.3

Chapter 24

Table 24.1

Table 24.2

Table 24.3

Chapter 25

Table 25.1

Table 25.2

Table 25.3

Chapter 26

Table 26.1

Chapter 27

Table 27.1

Table 27.2

Table 27.3

Chapter 28

Table 28.1

Chapter 29

Table 29.1

Chapter 30

Table 30.1

Chapter 41

Table 41.1

Chapter 42

Table 42.1

Table 42.2

Chapter 43

Table 43.1

Chapter 44

Table 44.1

Chapter 45

Table 45.1

Chapter 51

Table 51.1

Chapter 52

Table 52.1

Chapter 53

Table 53.1

Chapter 54

Table 54.1

Table 54.2

Chapter 55

Table 55.1

List of Illustrations

Chapter 1

Figure 1.1

Paramagnetic properties.

Figure 1.2

Diamagnetic properties.

Figure 1.3

Ferromagnetic properties.

Figure 1.4

The right-hand thumb rule.

Figure 1.5

A simple electromagnet.

Chapter 2

Figure 2.1

The atom.

Figure 2.2

The magnetic moment of the hydrogen 1 nucleus.

Chapter 3

Figure 3.1

Alignment: classical theory.

Figure 3.2

Alignment: quantum theory.

Figure 3.3

The net magnetization vector (NMV).

Chapter 4

Figure 4.1

Precession.

Figure 4.2

Precession of the spin-up and

Figure 4.3

The electromagnetic spectrum.

Figure 4.4

Coherent and incoherent phase positions.

Chapter 5

Figure 5.1

Energy transfer during excitation.

Figure 5.2

The flip angle. What flip angle gives maximum transverse magnetization?

Figure 5.3

Generation of the MR signal. Why would you expect it to be alternating?

Chapter 6

Figure 6.1

An axial image of the brain. Note the difference in contrast between CSF, fat, grey and white matter.

Figure 6.2

A basic pulse sequence showing TR and TE intervals.

Chapter 7

Figure 7.1

Relaxation mechanisms.

Chapter 8

Figure 8.1

The T1 recovery curve

Figure 8.2

T1 recovery in fat.

Figure 8.3

T1 recovery in water.

Figure 8.4

T1 recovery of fat and water.

Figure 8.5

T1 contrast generation.

Chapter 9

Figure 9.1

The T2 decay curve.

Figure 9.2

T2 decay in fat.

Figure 9.3

T2 decay in water.

Figure 9.4

T2 decay curves in fat and water.

Chapter 10

Figure 10.1

Axial T1 weighted image of the brain.

Figure 10.2

Coronal T1 weighted image of the knee.

Figure 10.3

Sagittal T1 weighted image of the lumbar spine.

Chapter 11

Figure 11.1

Axial T2 weighted image of the brain.

Figure 11.2

Axial T2 weighted image of the wrist.

Figure 11.3

Sagittal T2 weighted image of the thoracic spine.

Chapter 12

Figure 12.1

Axial proton density weighted image of the brain.

Figure 12.2

Axial proton density weighted image of the knee.

Figure 12.3

Sagittal proton density weighted image of the ankle.

Chapter 13

Figure 13.1

180° RF rephasing.

Figure 13.2

Single-echo spin echo sequence.

Figure 13.3

Dual-echo spin echo sequence.

Figure 13.4

Coronal T1 weighted SE image of the brachial plexus.

Figure 13.5

Axial T2 weighted SE image of the brain.

Chapter 14

Figure 14.1

The echo train in TSE.

Figure 14.2

Phase encoding versus signal amplitude.

Figure 14.3

K space filling and phase reordering.

Chapter 15

Figure 15.1

Axial T2 weighted TSE image of the abdomen.

Figure 15.2

Axial T1 weighted TSE image of the male pelvis.

Figure 15.3

The fast recovery or ‘DRIVE’ sequence.

Figure 15.4

Fast recovery or ‘DRIVE’ image of the internal auditory meatus.

Chapter 16

Figure 16.1

The inversion recovery sequence

Figure 16.2

T1 weighting in inversion recovery

Figure 16.3

How the use of short TI suppresses the signal from fat in a STIR sequence.

Figure 16.4

Axial T2 weighted FLAIR image of the brain

Figure 16.5

Coronal STIR of the knee.

Chapter 17

Figure 17.1

Flip angle vs signal amplitude.

Figure 17.2

How gradients alter field strength and frequency.

Figure 17.3

How gradients rephase.

Figure 17.4

A basic gradient echo sequence showing how a bipolar application of the frequency-encoding gradient produces a gradient echo.

Chapter 18

Figure 18.1

T1 weighting in gradient echo.

Figure 18.2

Sagittal T1 weighted gradient echo of the ankle.

Figure 18.3

T2* weighting in gradient echo.

Figure 18.4

T2* weighted gradient echo of the four chambers of the heart.

Chapter 19

Figure 19.1

The steady state.

Figure 19.2

Echo formation part 1.

Figure 19.3

Echo formation part 2.

Chapter 20

Figure 20.1

Coherent gradient echo sequence.

Figure 20.2

Echo generation in coherent gradient echo.

Figure 20.3

Axial coherent gradient echo image of the abdomen.

Figure 20.4

Sagittal coherent gradient echo image of the knee with tissue suppression.

Chapter 21

Figure 21.1

Incoherent gradient echo sequence.

Figure 21.2

Echo generation in incoherent gradient echo.

Figure 21.3

Coronal incoherent gradient echo from a 3D data set.

Figure 21.4

Coronal incoherent gradient echo acquired after gadolinium enhancement.

Chapter 22

Figure 22.1

SSFP sequence.

Figure 22.2

Echo generation in SSFP.

Figure 22.3

Axial SSFP image of the brain.

Figure 22.4

Perfusion imaging showing hyper-perfusion within oedema indicating recurrent tumour.

Chapter 23

Figure 23.1

Balanced gradient echo scheme in the balanced gradient echo sequence.

Figure 23.2

Alternating RF pulses balanced gradient echo.

Figure 23.3

Sagittal oblique balanced gradient echo of the cervical cord showing nerve roots and peripheral nerves.

Figure 23.4

Axial balanced gradient echo of the abdomen.

Chapter 24

Figure 24.1

Conventional versus ramped sampling.

Figure 24.2

GE-EPI sequence.

Figure 24.3

SE-EPI sequence.

Figure 24.4

Axial SE-EPI of the abdomen.

Chapter 25

Figure 25.1

Free and restricted diffusion.

Figure 25.2

Axial DWI of the brain showing a left-sided infarct.

Figure 25.3

DTI of the brain showing white matter tracts.

Figure 25.4

Set of perfusion images of the brain.

Chapter 26

Figure 26.1

BOLD images of the brain. Functional areas in red.

Figure 26.2

MR spectra of the brain.

Figure 26.3

Multivoxel MRS technique.

Chapter 27

Figure 27.1

A gradient coil.

Figure 27.2

Gradients and changing field strength.

Figure 27.3

How gradients change frequency and phase.

Figure 27.4

Gradient axes.

Chapter 28

Figure 28.1

Slice selection.

Figure 28.2

Using X, Y and Z gradients to select slices.

Figure 28.3

Transmit bandwidth, gradient slope and slice thickness

Figure 28.4

Timing of slice selection in a spin-echo pulse sequence.

Chapter 29

Figure 29.1

Phase encoding.

Figure 29.2

Steep and shallow phase encodings.

Figure 29.3

Timing of phase encoding in a spin echo pulse sequence.

Chapter 30

Figure 30.1

Frequency encoding.

Figure 30.2

Timing of frequency encoding in a spin echo pulse sequence.

Chapter 31

Figure 31.1

K space lines and numbering.

Figure 31.2

K space and the phase matrix.

Chapter 32

Figure 32.1

K space – the chest of drawers.

Figure 32.2

K space filling in spin echo.

Figure 32.3

Data points in K space.

Chapter 33

Figure 33.1

Phase gradient amplitude vs signal amplitude.

Figure 33.2

K space and signal and resolution data.

Figure 33.3

Image using central K space data points only.

Figure 33.4

K space and signal and resolution data.

Chapter 34

Figure 34.1

The Nyquist theorem.

Figure 34.2

Sampling time and the TE.

Chapter 35

Figure 35.1

Phase-encoding slope and phase shift.

Figure 35.2

The phase curve.

Figure 35.3

Fast Fourier transform.

Chapter 36

Figure 36.1

Data acquisition methods.

Figure 36.2

Encoding in a volume acquisition.

Figure 36.3

Axial T2 weighted image of the abdomen. The patient was unable to hold their breath for the duration of the selected scan time, and motion artefact has occurred.

Chapter 37

Figure 37.1

K space traversal in gradient echo.

Figure 37.2

Single-shot K space traversal.

Figure 37.3

Spiral K space traversal.

Chapter 38

Figure 38.1

Partial Fourier.

Figure 38.2

Centric K space filling.

Figure 38.3

Keyhole imaging.

Figure 38.4

Parallel imaging.

Chapter 39

Figure 39.1

Coil placement versus SNR.

Figure 39.2

TE versus SNR.

Figure 39.3

NSA versus SNR.

Figure 39.4

Receive bandwidth versus SNR.

Chapter 40

Figure 40.1

Sagittal (left) and coronal (right) T1 weighted image after contrast showing an ectopic posterior pituitary.

Figure 40.2

Axial slice of the knee from a 3D acquisition using chemical suppression.

Figure 40.3

Phase contrast MR venogram.

Figure 40.4

Axial T2 weighted image of the liver with chemical suppression. There is a good CNR between the liver lesions and normal liver using this technique, although the overall image quality is poor.

Chapter 41

Figure 41.1

Pixel size versus matrix size. Voxels are larger on the lower diagram, which results in a better SNR but poorer resolution than the upper diagram.

Figure 41.2

FOV versus SNR and resolution.

Figure 41.3

Sagittal image using a 10 mm slice thickness.

Figure 41.4

Sagittal image using a 3 mm slice thickness.

Chapter 42

Figure 42.1

Chemical shift and the receive bandwidth.

Figure 42.2

The periodicity of fat and water.

Figure 42.3

Out-of-phase artefact seen as a black line around the abdominal organs.

Chapter 43

Figure 43.1

The cause of phase mismapping from breathing during the acquisition.

Figure 43.2

An axial image of the abdomen during breathing showing phase mismapping.

Figure 43.3

Respiratory compensation and K space.

Figure 43.4

Pre-saturation to reduce flow artefact.

Chapter 44

Figure 44.1

Aliasing or phase wrap.

Figure 44.2

Coronal image of the chest showing aliasing.

Chapter 45

Figure 45.1

Sagittal GE imaging of the knee with metal screws in place. Magnetic susceptibility artefact is clearly seen.

Figure 45.2

Same patient as in Figure 45.1 using a spin echo sequence. The artefact is reduced because RF rephasing corrects for differences in susceptibility between structures.

Figure 45.3

Cross-talk.

Chapter 46

Figure 46.1

The different types of flow.

Figure 46.2

Time-of-flight flow phenomenon.

Figure 46.3

Co-and countercurrent flow.

Figure 46.4

Intra-voxel dephasing.

Chapter 47

Figure 47.1

Presaturation volume relative to the imaging stack.

Figure 47.2

Flow and the imaging volume.

Figure 47.3

3D TOF MRA of a 4-year-old child showing normal appearances.

Figure 47.4

Axial 3D TOF-MRA of the brain acquired at 3 T (left) and 1.5 T (right). Note the enhanced SNR and CNR of the 3 T image.

Chapter 48

Figure 48.1

Bipolar gradients in phase contrast MRA.

Figure 48.2

Flow-encoding axes in phase contrast MRA.

Figure 48.3

VENC settings.

Figure 48.4

PC venogram of the brain.

Chapter 49

Figure 49.1

Coronal CE MRA of the carotid and vertebral arteries.

Figure 49.2

Coronal CE MRA of the chest.

Figure 49.3

Coronal CE MRA of the abdominal vessels.

Figure 49.4

Coronal CE MRA of the iliac arteries showing an arteriovenous malformation.

Chapter 50

Figure 50.1

Tumbling of water molecules.

Figure 50.2

Axial arthrogram of the hip using gadolinium.

Figure 50.3

Coronal T1 weighted image of a small left acoustic neuroma after administration of gadolinium.

Figure 50.4

Axial T1 weighted image of the liver without (left) and with (right) manganese contrast. The enhanced image shows enhancement of normal A B liver so that the liver pathology is darker.

Chapter 51

Figure 51.1

A permanent magnet.

Figure 51.2

A simple electromagnet.

Figure 51.3

A superconducting system.

Figure 51.4

A high field open system.

Chapter 52

Figure 52.1

Spinal phased array coil.

Figure 52.2

Parallel imaging coils.

Chapter 53

Figure 53.1

The MR system.

Figure 53.2

A three-terminal electromagnet used in gradient coils.

Chapter 54

Figure 54.1

Static field in permanent and superconducting systems.

Figure 54.2

The fringe field.

Figure 54.3

The zoning recommended by the American College of Radiology White Paper on MRI safety. Note that there has to be locked access between Zones II and III.

Chapter 55

Figure 55.1

The pulling power of a pair of scissors in a 1.5 T system.

Figure 55.2

Standard labels associated with MR device testing.

Figure 55.3

Patient with an intracranial vascular clip using spin echo (left) and gradient echo MRI (right). Magnetic susceptibility artefact is clearly seen on the gradient echo image.

Guide

Cover

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Preface

MRI at a Glance is one of a series of books that presents complex information in an easily accessible format. This series has become famous for its concise text and clear diagrams, which are laid out with text on one page and diagrams relating to the text on the opposite page. In this way all the information on a particular topic is summarized so that the reader has the essential points at their fingertips.

The third edition has been updated with a new companion website that includes some exciting new features. In the book, some chapters have been streamlined and reorganized and there are some updated images and diagrams. Each topic is presented on two pages for easy reference and large subjects have been broken down into smaller sections. In the book and companion website I have included simple explanations and animations, analogies, bulleted lists, simple tables, key points, equations (but only for those who like them), scan tips, ‘Did You Know’ learning points, some questions and answers and plenty of images to aid the understanding of each topic. There are appendices on tradeoffs, acronyms, abbreviations and artefacts. The glossary has also been expanded.

This book is intended to provide a concise overview of essential facts for revision purposes and for those very new to MRI. For more detailed explanations the reader is directed to MRI in Practice and Handbook of MRI Technique. Indeed, the diagrams and images in this book are taken from these other texts and MRI at a Glance is intended to complement them.

Learning MRI physics can be hard work. I hope that this book helps to demystify it!

Acknowledgements

Once again I thank my friend and colleague John Talbot for his beautiful diagrams and for his support. We make a great team and long may it continue! Thanks again to Philips Medical Systems and GE for supplying the images, and to all my friends and family in Brighton, London, Paris, Witney, Leeds, St Augustine, Atlanta and New York.

CW

How to use your textbook

Features contained within your textbook

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The website icon indicates that you can find accompanying resources on the book's companion website.

About the companion website

Atomic structure

Figure 2.1 The atom.

Figure 2.2 The magnetic moment of the hydrogen 1 nucleus.

Introduction

Atoms make up all matter in the universe and also therefore in the human body. There are approximately 7 octillion (7 × 1027) atoms in the average 70 kg person. Most of the human body (96%) is made up of just four elements. These are hydrogen, oxygen, carbon and nitrogen. Hydrogen is the most common element in the universe and in humans.

The atom consists of the following particles:

Protons

in the nucleus

are positively charged

Neutrons

in the nucleus

have no charge

Electrons

orbit the nucleus

are negatively charged (

Figure 2.1

).

The following terms are used to characterize an atom:

Atomic number:

number of protons in the nucleus and determines the type of element the atoms make up.

Mass number:

sum of the neutrons and protons in the nucleus.

Atoms of the same element having a different mass number are called isotopes. In a stable atom the number of negatively charged electrons equals the number of positively charged protons. Atoms with a deficit or excess number of electrons are called ions and the process of removing electrons from the atom is called ionization. Only certain types of atoms are available to us in Magnetic Resonance Imaging (MRI). These are atoms whose charged nuclei move or spin. This is because a moving electrical charge produces a magnetic field (see Chapter 1).

Motion within the atom

There are three types of motion of particles in the atom:

Negatively charged electrons spinning on their own axis.

Negatively charged electrons orbiting the nucleus.

Particles within the nucleus spinning on their own axes (

Figure 2.1

).

Each type of motion produces a magnetic field (see Chapter 1). In MRI we are concerned with the motion of particles within the nucleus and the nucleus itself.

MR active nuclei

Protons and neutrons spin about their own axis within the nucleus. The direction of spin is random, so that some particles spin clockwise and others anticlockwise.

When a nucleus has an even mass number, the spins cancel each other out so the nucleus has no net spin.

When a nucleus has an odd mass number, the spins do not cancel each other out and the nucleus spins.

As protons have charge, a nucleus with an odd mass number has a net charge as well as a net spin. Due to the laws of electromagnetic induction (see Chapter 1), a moving unbalanced charge induces a magnetic field around itself. The direction and size of the magnetic field are denoted by a magnetic moment (Figure 2.2). The total magnetic moment of the nucleus is the vector sum of all the magnetic moments of protons in the nucleus. The length of the arrow represents the magnitude of the magnetic moment. The direction of the arrow denotes the direction of alignment of the magnetic moment.

Nuclei with an odd number of protons are said to be