Growth References and Standards 383

Tim J. Cole

Annotated References 4 15 Index 4 19

Cnnvrlnhtftd Material


Department of Behavioral Sciences, University of Michigan—Dearborn

Professor of Human Biology, Department of Human Sciences, Loughborough University, Leicestershire, United Kingdom

William Cameron Chumlea, Ph.D.

Lifespan Health Research Center, Wright State University School of Medicine, Kettering, Ohio

Institute of Child Health, University College, London

Stefan a. czerwinski, Ph.D.

Lifespan Health Research Center, Wright State University School of Medicine, Kettering, Ohio

Ellen w. demerath, Ph.D.

Lifespan Health Research Center, Wright State University School of Medicine, Kettering, Ohio

Department of Anthropology, Peabody Museum, Harvard University, Boston

Shumei Sun Guo, Ph.D.

Lifespan Health Research Center, Wright State University School of Medicine, Kettering, Ohio

Roland c. Hauspie, Dr.Sc.

Professor, Laboratory of Anthropogenetics, Free University of Brussels, Belgium peter c. HINDMARSH, m.b., m.d., f.r.c.p.

Cobbold Laboratories, The Middlesex Hospital, University College, London

Department of Anthropology, University of Pennsylvania, Philadelphia

Kristen l. Knutsen, m.a.

Departments of Anthropology and Epidemiology, State University of New York at Albany

Associate Professor, Department of Anthropology, Emory University, Atlanta

Horacio Lejarraga, m.d., Ph.D.

Service of Growth and Development, Hospital Garrahan, Buenos Aires, Argentina

Michigan State University, East Lansing

Reader in Human Biology, Department of Human Sciences, Loughborough University, Leicestershire, United Kingdom

Department of Pediatrics/Endocrinology, Egleston Children's Hospital, Emory University, Atlanta

Biochemistry, Endocrinology and Metabolism Unit, Institute of Child Health, University College, London

Departments of Anthropology and Epidemiology, State University of New York at Albany

Bradford Towne, Ph.D.

Lifespan Health Research Center, Wright State University School of Medicine, Kettering, Ohio

Division of Gastroenterology and Nutrition, The Children's Hospital of Philadelphia


Noël Cameron

This book has its origins in my own lectures on human growth and development given to undergraduates attending British and South African universities over the last 25 years. In 1976, while studying for my doctoral degree under the supervision of James Tanner at London University's Institute of Child Health, I was asked to give an annual series of lectures to Biological Anthropology students at Cambridge University. The late William Marshall, who had been the "reader" in Tanner's department before taking the professorship and chair in Human Biology at Loughborough University, had previously given these lectures. At about the same time, the geneticist Alan Bittles, then a senior lecturer in Human Biology at Chelsea College, London University, asked me to provide a similar series of lectures to his students.

Faced with the prospect of two series of lectures, I searched the available literature to determine what I could use as sources to write the lectures and what I could recommend to students.

In the 1970s, there were a number of texts, almost exclusively from America, describing the growth and development of children. Ernest Watson and George Lowrey, pediatricians at the University of Michigan Medical School, had first written the Growth and Development of Children in 1951.1 Physical anthropologist and human biologist Stanley Garn, then chairman of the "Physical Growth Department" at the Fels Research Institute in Ohio, collaborated with Israeli pediatrician Zvi Shamir, from Jerusalem, to write Methods for Research in Human Growth in 1958.2 Donald Cheek of Johns Hopkins University wrote Human Growth: Body Composition, Cell Growth, Energy, and Intelligence, published in 19683; and the very useful Child Growth, by Wilton Krogman, recently retired from the University of Pennsylvania, was published in 1972.4 In 1966, a landmark work edited by Frank Falkner was destined to be the forerunner to a number of more recent texts in similar style. Called simply Human Development, it was, I think, the first volume to use different "authorities" (29 in this case) to provide the breadth and depth required to understand this most diverse of subjects.5 However, with some notable exceptions, almost all of these volumes had been written by pediatricians interested in the clinical aspects of the subject rather than the biology of growth. In addition to the usual descriptions of the pattern of human growth, they were replete with diagnostic criteria and assessment procedures. They had little in the way of discussion of broader topics and the biological and conceptual basis of growth and development.

In the United Kingdom, Tanner's Growth at Adolescence, first published in 1959 and in a second edition in 1962,6 was, as it is now, the classic core text to be supplemented by a variety of scholarly scientific reviews and research papers to cover preadolescent growth and some other areas in greater depth. Later, his Foetus into Man (1978)7 partially made up for this deficit, but it was to some extent an introductory text and there was still the need for greater depth to be added through specific references. In the same year (1978), Frank Falkner collaborated with his friend and previous colleague Jim Tanner to edit the three volume series Human Growth: A Comprehensive Treatise,8 which was an excellent library resource but far too expensive for the undergraduate or graduate student. Clearly by the 1970s many of the earlier texts were becoming dated and my solution was to cite a variety of individual chapters from these various authorities and supplement them with more up to date research papers.

During my sojourn in South Africa, between 1984 and 1997, I lectured to large classes of 400 or more students studying medicine and the allied medical disciplines (dentistry, physiotherapy, occupational therapy, and nursing) in addition to smaller classes of medical science students. The large formal lecture classes presented a relatively restricted opportunity for discussion and the need to portray the biology of human growth in an immediate, vivid way in five or six lectures. The smaller medical science classes allowed me the freedom to "discuss" rather than "teach" human growth and development and to do so in an expansive series of 15 lectures covering half the academic year. By this time, I was invariably recommending Tanner's Growth at Adolescence and Foetus into Man in addition to specific contributions from Falkner and Tanner's "comprehensive treatise." Barry Bogin's Patterns of Human Growth became an accepted alternative text for this audience on its publication in 1988.9 However, like Foetus into Man, it suffered from being written from the perspective and knowledge of a single author and so lacked the breadth, and at times the depth, to be universally recommended.

Out of these experiences came the awareness that a course-work reference text was needed for undergraduate and graduate students but that no single scientist could hope to properly cover the different aspects of human growth and development with the breadth and depth required. Rather, what was needed was a team of lecturers and, if it was to be the best possible text, this team would have to be recognized international experts in their fields of interest. They would indeed be a "dream team" that would, in effect, be invited into the lecture theater to provide a one-hour discourse on their subject. The target audience was the senior undergraduate or immediate postgraduate student; that is, the American graduate stu dent. Therefore, a basic understanding of human biology was expected: human evolution, Mendelian genetics, anatomy, physiology, and descriptive statistics. The text would not only cover the important issues in human growth and development but allow the students the freedom to investigate the subject further through a good annotated reference list and a variety of recommended websites.

Thus, this particular volume was conceived. The contributors were requested to design their manuscript as a lecture that could be given in approximately 60 minutes. Each lecture is augmented by a list of appropriate reference material that the lecturer and students can use to extend any particular aspect of the lecture and provide both breadth and depth to the studies. Most, but not all, lecturers provided a summary or conclusion and some have annotated specific references that they feel contain core information. The limited time for each lecture is based on the duration of a normal university lecture of approximately 60 minutes and forces the lecturer to focus on the essential information. Through the reference list, the lecturer may guide the students toward extending their knowledge.

the lectures and lecturers

The first four lectures provide the core of a course on human growth in which the biological process of growth from birth to adulthood is described. My first chapter forms an introduction to the pattern and biology of human growth and development; the major areas that will be covered by the following 17 chapters.

This broad overview reflects my own breadth of experience and research in human growth and development. Doctoral study supervised by James Tanner at the Institute of Child Health at London University initiated my own background in human growth research. Concurrently, I acted as the clinical auxologist for Tanner's growth disorder clinics at the Hospital for Sick Children, Great Ormond Street, in which I assessed the growth and skeletal maturation of each child attending the clinics. With this dual role, I received probably the best available education and experience in the research techniques applied to both normal and abnormal growth. A lectureship in the same department followed the successful completion of my doctorate, and in time, I found myself being drawn toward the idea of working in a developing country. In this way, I felt that I could put my knowledge and experience to work in a demanding environment in which human growth was the clearest measure of the health and well-being of children.

Keen to put my theory into practice, I went to South Africa in 1984, a time when the black population of that country had experienced almost 40 years of active discrimination. The policy of apartheid had resulted in a society divided not only by color but by differential qualities of health care, access to education, living conditions, and economic empowerment. However, it was clear to those living in South Africa that the end of apartheid was drawing close, and with it, the need for knowledge of the health and well-being of children through information on their growth and development was of primary importance. I initiated two longitudinal studies of rural black children in 1985 and 1986. These set the baseline for comparisons to children in the notorious "township" of Soweto (in fact a city of about 1.5 million people called the "SOuth WEst TOwnship"; hence, Soweto). The national census of 1983 had identified the increasing migration of the black population into urban areas; 14 million were predicted to migrate to urban areas by 2000 and those areas were expected to double in size by 2010. With this realization, the need for relevant up-to-date information on the maternal and child health of these new urban dwellers was intensified; and with clinical and epidemiological colleagues, I initiated the Birth to Ten birth cohort study in 1990. Out of all the births in Soweto and Johannesburg over a 6-week period, over 4000 (74%) were voluntarily enrolled into what is now one of the largest and most detailed studies of child health and growth in the world. Thus, I bring to this book my broad and, I hope, profound experience of normal and abnormal growth in both developed and developing societies and my experience of the assessment of maturity.

Professor Horacio Lejarraga, from Buenos Aires, who provides the second lecture on growth in infancy and childhood, is a pediatric endocrinologist with an interest in child growth that extends over the last 40 years. Having qualified in medicine, he earned a Ph.D. under James Tanner's supervision in London before returning to Argentina to develop an awareness of the importance of human growth among the pediatric community. As president of Argentina's 10,000-strong Society of Paediatrics, he is responsible for Argentina's national growth studies and growth reference charts. Thus, while covering the basic pattern of growth in infancy and childhood, he also brings a clinical perspective to the area of preadolescent growth.

Chapter 3 is provided by Professor Roland Hauspie, from the Free University of Brussels. Hauspie is recognized as an international expert on the mathematical modeling of the human growth curve and plays a prominent role in European aux-ology. Knowledge of the pattern, magnitude, duration, and variability of adolescent growth was considerably enhanced by modeling techniques, and these are expertly described in Hauspie's lecture.

Peter Ellison, a professor at Harvard College and dean of the Graduate School of Arts and Sciences, is an anthropologist with an international reputation for research on reproductive biology. A spate of recent books (e.g., On Fertile Ground10) established him as the leading reproductive physiologist of his generation. His chapter on puberty reflects this research interest in addition to demonstrating his strong reputation as a communicator and teacher.

Chapters 5 and 6 address the control of the process of growth through the endocrine system and genetics. Peter Hindmarsh, coauthor of the core text on pae-diatric endocrinology,11 has for some time been the leading pediatric endocrinol-ogist at London University's Institute of Child Health. He brings both a biological and clinical approach to the endocrinology of growth. Brad Towne, Ellen Demerath, and Stefan Czerwinski work within America's leading center for human growth research at Wright State University and, in many respects, form the "rising stars" of our dream team. Brad Towne is a physical anthropologist by undergraduate training but an epidemiological and statistical geneticist by postgraduate experience and international reputation. Following a postdoctoral position in the early 1990s with Dr. John Blangero's team at the highly respected Southwest Foundation in Texas, he continues to be closely associated with their work. Ellen Demerath and Stefan Czerwinski are thoroughbred anthropologists, coming from excellent stables. The former is from Harvard and the University of Pennsylvania under the influence of Peter Ellison (Chapter 4) and Francis E. Johnston (Chapter 9), respectively; the latter is from the University of New York and the laboratory of Lawrence M. Schell (Chapter 8) in addition to a recent postdoctoral position at the Southwest Foundation. They provide an excellent and detailed chapter that thoroughly introduces the theory and methods of auxological genetics.

Chapters 7 through 9 examine factors that affect human growth through the environment: nutrition, the physical environment, and the socioeconomic environment. Nick Norgan, my colleague at Loughborough University, first taught me almost 30 years ago, as he began his postdoctoral academic career. He is a human biologist specializing in human energetics and body composition. His international reputation has been founded on population studies in the United Kingdom, Europe, India, Australia, and Papua, New Guinea, and surveys and studies of diet, nutritional status, anthropometry, physical activity, energy expenditure, and body composition. Currently he is the reader in Human Biology at Loughborough University, teaching courses on introductory physiology, the ecology of nutrition, and specialized courses in human energetics. Lawrence Schell has had a distinguished academic career in anthropology. His interest in human growth and, particularly, the effects of environmental stressors began almost 30 years ago, during his doctoral studies under the supervision of Francis E. Johnston at the University of Pennsylvania. At that time, the effect of aircraft noise on the growth, health, and well-being of infants living near airports was his primary concern. Now, he is recognized as the leading authority on the effect of environmental pollutants on human growth. Francis E. Johnston is a giant in the research and teaching on human growth. Falling under the academic influence of Wilton Krogman during his graduate studies, he has since had an enormous influence on the current generation of biologists and anthropologists interested in human growth and development. That influence is evidenced by the fact that five of his former doctoral students contributed to this volume (Bogin, Demerath, Lampl, Schell, and Zemel); and he continues to actively nurture and guide the science of auxology.

Chapters 10 and 11 are specifically aimed at preclinical and clinical students. John S. Parks is a professor of Pediatrics at Emory University and America's leading pediatric endocrinologist. He has a major interest in the genetics underlying and controlling the process of human growth and demonstrates his recognized ability as a teacher within his highly readable chapter. Michael A. Preece is a professor of Child Health and Growth at London University's Institute of Child Health, a position he occupied following the retirement of James M. Tanner. Thus, his academic history within human growth is distinguished. His early contributions were in endocrinology and statistics (particularly mathematical modeling), but later he moved toward molecular genetics and teaches within that theme in this volume.

Chapters 12 through 15 provide insight into specific topics within auxology that I believe should not be excluded from a thorough consideration of the science. The achievement of growth through the process of saltation and stasis was first demonstrated by Michelle Lampl in 1992.12 1 think this discovery is one of the most profound contributions to auxology in the latter part of the last century. It gives focus to the way in which we think about the control of human growth and answers many questions about the relationship between growth at the molecular, cellular, tissue, organ, and whole body levels. Babette Zemel, from the University of Pennsylvania, who writes about body composition and human growth, brings the expertise of both the anthropologist and clinical scientist to bear on this important area. Her early training in human growth was under the supervision of Francis Johnston. Following her doctoral studies in Papua, New Guinea, she became increasingly involved in the assessment of the growth and development of children with clinical disorders—much like my own training with Tanner as a clinical auxologist. Her contributions to our knowledge of the changes in the body composition of children compromised by disease and disorders are internationally recognized. Barry Bogin's Patterns of Human Growth was first published in 1988.9 In some respects, that volume was a vehicle for his evolutionary and biocultural approach to human growth and development and has rightly become a recognized inclusion in university reading lists. Here, he expands specifically on the evolution of the pattern of human growth and, in so doing, raises important questions about how this biological process is modified by evolutionary and environmental forces. Robert M. Malina holds two doctoral degrees, in Anthropology and Physical Education. It is not surprising therefore that his contribution to our knowledge of human growth and development has been in the relationship of exercise to the process of growth and maturation. Recognized as the world authority in this area, his contributions have spanned four decades and given rise to a global awareness of the central role played by exercise in maintaining normal growth.

Finally, Chapters 16 through 19 describe the methodological basis of research in human growth and development: how we assess growth and maturation and how we convert these data to usable growth references and standards. Cameron Chumlea was a student of Robert M. Malina before taking up a position as research scientist at the Fels Research Institute, Wright State School of Medicine, in 1978. He was heavily involved in managing the day-to-day running of the Fels Longitudinal Study, involving anthropometry, body composition, and skeletal maturity assessments. As the Fels Professor in the Departments of Community Health and Pediatrics, his experience is broad and his contributions cover not only human growth but also measurement of the elderly. Tim J. Cole is Britain's leading expert in the statistical analysis of growth data. His LMS method for creating the cen-tiles required for growth reference charts has been accepted throughout the world, and he is in charge of producing the World Health Organization's new growth charts for global use.

using this book

The chapters or lectures within this volume have been designed so that a "core" course can be extracted that provides information on the most important issues. For example, assuming that the first introductory chapter is always included, a class of human biologists or anthropologists would also need the lectures on infancy and childhood, adolescence, and puberty to understand the underlying biology. To these could be added the environmental lectures and the methodological lectures to equip them with the skills for fieldwork. Preclinical or clinical students would need to understand the basic biology but also lectures on endocrinology, growth disorders, and assessment procedures. In this way, a series of lectures can be created to cater to the needs of a variety of audiences, such as medical, allied medical disciplines (physiotherapy, occupational therapy, nursing, etc.), dentistry, anthropology, human biology, education, sports science, sociology, psychology, and any other course dealing with children that will necessarily include information on human growth and development. Almost all the lectures carry their own reference list or bibliography but I have also grouped annotated texts into one section to allow the reader to browse, as if in a bookstore, and glean something of the essence of each book that may be useful.

Final-year students, graduates, and those who have wandered in the vale of academe for many years will appreciate the old adage that "organizing academics is like herding cats." Their very independence of thought and action is what makes them the free thinkers they are. Therefore, to get them all to conform to a specific style is not even a remote possibility. This results in a series of lectures that vary in format. Some lecturers have chosen to lecture as they would present a scholarly textbook chapter; others have been more expansive and less formal. In any case, I consider this variability to be a strength. The student will not be faced by a stereotyped series of lectures just as, in the university lecture theater, no two lecturers are the same.

As editor, I have had the mostly pleasurable experience of seeking some degree of rationality, of attempting to create an ordered series of lectures that would be of major benefit to students and lecturers alike. I thank all the contributors for their willingness to cooperate in this venture and appreciate that most have been under considerable pressure but have nevertheless been timely and gracious in their dealings with me. I thank my friends and colleagues within the science of auxology who have encouraged me to complete this task and hope that their confidence in my ability to produce a worthwhile volume has not been misplaced. Finally, I thank my partner, Anette, and my children Jamie and Beth for their forbearance of my ready willingness to leave them in search of new audiences for my research. This book is dedicated to them, for it would not have been possible without them.

I hope that students find within these pages a biological story that excites and fascinates them as it has me for the last three decades. The process of growth and maturation is one that every living thing in the history of our planet has experienced.

I do not think that the complexity of that process has reached or will reach an end point with Homo sapiens, because the process of human growth is constantly dynamic and constantly changing in response to the changes in the environment, both global and local, in which we live. For me, this plasticity, resulting in the wonderfully varied species we see around us, makes the process of human growth so fascinating.


1. Watson EH, Lowrey GH. Growth and Development of Children. Chicago: Year Book Publishers, 1951.

2. Garn SM, Shamir Z. Methods for Research in Human Growth. Springfield, IL: Charles C Thomas, 1958.

3. Cheek DB. Human Growth: Body Composition, Cell Growth, Energy, and Intelligence. Philadelphia: Lea & Febiger, 1968.

4. Krogman WM. Child Growth. Ann Arbor: University of Michigan Press, 1972.

5. Falkner F (ed). Human Development. Philadelphia: W. B. Saunders Co., 1966.

6. Tanner JM. Growth at Adolescence, 2nd ed. Oxford: Blackwell Scientific Publications, 1962.

7. Tanner JM. Foetus into Man. London: Open Books, 1978.

8. Falkner F, Tanner JM. Human Growth: A Comprehensive Treatise. New York: Plenum, 1978.

9. Bogin B. Patterns of Human Growth. Cambridge: Cambridge University Press, 1988.

10. Ellison PT. On Fertile Ground. Cambridge, MA: Harvard University Press, 2001.

11. Brook CGD, Hindmarsh P. Clinical Paediatric Endocrinology, 4th ed. Oxford: Blackwell Scientific Publications, 2001.

12. Lampl M, Veldhuis JD, Johnson ML. Saltation and stasis: A model of human growth. Science. 1992;158:801-803.

Human Growth Curve, Canalization, and Catch-Up Growth

Professor of Human Biology, Department of Human Sciences, Loughborough University, Leicestershire, United Kingdom historical background

This introduction to the curve of human growth and development begins in the Age of Enlightenment in eighteenth century France. Between the death of Louis XIV in 1715, and the coup d'état of November 9, 1799, which brought Napoleon Bonaparte to power, philosophy, science, and art were dominated by a movement away from monarchial authority and dogma and toward a more liberal and empirical attitude.1 Its philosophers and scientists believed that people's habits of thinking were based on irrationality, polluted by religious dogma, superstition, and overadherence to historical precedent and irrelevant tradition. The way to escape from this, to move forward, was to seek for true knowledge in every sphere of life, to establish the truth and build on it. People's minds were, literally, to be "enlightened."2 Its prime impulse was in pre-Revolutionary France within a group of mostly aristocratic and bourgeois natural scientists and philosophers, who included Rousseau, Voltaire, Diderot (whose Encyclopedia was the first literary monument to the Enlightenment), and the Compte de Buffon. Georges Louis LeClerc (Figure 1-1), the Compte de Buffon, was a core member of this group, often known collectively as the Encyclopedists, because of their contributions to Diderot's work.

Buffon was born on September 7, 1707, at Montbard in Bourgogne, the provincial capital of Dijon in southwest France. His father, described by the biographer

Franck Bourdier as "un homme sans grand charactère," was a minor parliamentary official married to an older woman, Anne-Christian Martin.3 She died of tuberculosis when Buffon was only 7 years old. However, an extremely wealthy uncle, Georges Blaisot, had financially favored his niece Anne-Christian, and on her death she left her husband and son with a considerable fortune. Monsieur Leclerc used these funds in 1717 to buy the land of Buffon and the "châtellenie" of Montbard at Dijon. Georges Louis was educated by the Jesuits at the Colleges de Godran, where he demonstrated an aptitude for mathematics. In 1728, he moved to the University of Angers and thence suddenly to England following a duel with an officer of the Royal-Croates over "une intrigue d'amour." He traveled in Switzerland, France, and Italy during the next 4 years, returning to Dijon in 1732 to reach a financial settlement with his father, with whom he had long argued following the latter's remarriage. He inherited his maternal ancestral estate at Montbard and divided his time between Paris and the country, pursuing his interests in mathematics, natural science, and sylviculture. By the age of 32, he was recognized as the premier horticulturist and arborealist in France and was appointed by King Louise XV as the director of the Jardin du Roi in 1739. This position was the equivalent of being the chief curator of the Smithsonian Institution or the British Museum of Natural History—it was the most prestigious governmental scientific position in the "natural sciences" that Buffon could have obtained. During the next few years, Buffon started to work on an immense project that was to include all that was known of natural history. Histoire Naturelle, Générale et Particulière would be a vast undertaking, but one that Buffon, who from all accounts was a man of no small ego, appears to relish and that, by his death, was composed of 36 volumes. There were 15 volumes on quadrupeds (1749-1767), 9 on birds (1770-1783), 5 on minerals (1783-1788), and 7 "supplementary volumes." Eight further volumes prepared by E. de Lacepede were added posthumously between 1788 and 1804 and included two volumes on reptiles (1788-1789), five on fish (1798-1803), and one on Cetacea (1804). However, the supplement to volume 14, published in 1778, is particularly interesting to us.

On page 77 of this supplement is the record of the growth of a boy known simply as De Montbeillard's son. The friendship between Philibert Geuneau De Mont-beillard and Buffon had been secured by a common interest in the natural sciences. Between 1770 and 1783, De Montbeillard coauthored the nine volumes of Histoire Naturelle devoted to birds. He was also a correspondent of Diderot and clearly recognized as one of the Encyclopedists. Given the desire of these central scientific figures of the Enlightenment to measure and describe the natural world as it is and to find the truth, it is not too surprising that De Montbeillard would take an empirical interest in the growth of his own son. Nor is it inconceivable that his friend and colleague Buffon would wish to include this primary evidence of the course of human growth within his opus magnum.

De Montbeillard had been measuring the height of his son about every 6 months from his birth in 1759 until he was 18 years of age in 1777. The boy's measurements of height were reported in the French units of the time: pieds, pouces, and lignes, which correspond roughly to present day units as a foot, inch, and 12th part of an inch. (Tanner,4 p. 470, notes that, "The Parisian pied, or foot, divided into 12 pouces, or inches, each divided into 12 lignes, was longer than the English foot. Isaac Newton . . . found 1 pied equal to 12.785 inches, but the later official conversion, on the introduction of the metre, gave it as 12.7789 inches. The pouce, then, equals 2.71 cm whereas the English inch equals 2.54 cm.")

Not until an American anatomist, R. E. Scammon, at the University of Minnesota, translated these measurements into centimeters and his results were published in the American Journal of Physical Anthropology under the title "The First Seriatim Study of Human Growth," could we look on the growth of De Mont-beillard's son in the form of a chart.5

the distance curve of growth

By joining together the data points at each age, Scammon produced a curve that described the height achieved at any age, which became known as a height distance or height-for-age curve (Figure 1-2). We use the term distance to describe height achieved, because it is easy to visualize and understand that a child's height at any particular age is a reflection of how far that child has progressed toward adulthood. It embodies the sense of an ongoing journey that we are, as it were, interrupting to take a "snapshot." The resulting curve is interesting for a number of reasons. First, when growth is measured at intervals of 6 months or a year, the resultant curve is a relatively smooth and continuous process. It is not characterized by periods of no growth and then by dramatic increases in stature. Second, growth is not a linear process. We do not gain the same amount of height during each calendar year. Third, the curve of growth has four distinct phases (or five if we include the mid-growth spurt, see later), corresponding to relatively rapid growth in infancy, steady growth in childhood, rapid growth during adolescence, and very slow growth as the individual approaches adulthood. Fourth, growth represents a most dramatic increase in size. De Montbeillard's son, for instance, grew from about 60 cm at birth to over 180 cm at adulthood. The majority of that growth occurs during infancy and childhood, but perhaps the most important physical changes occur during adolescence. Fifth, we cease growing, or reach adult height, during our late teenage years, at 18 or 19 years of age.

The pattern of growth that we see from this curve is a function of the frequency of data acquisition. For instance, if we were to measure a child only at birth and at 18 years, we might believe, by joining up these two data points, that growth was a linear process. Clearly, the more frequently we collect data, the more we can understand about the actual pattern of growth on a yearly, monthly, weekly, or even daily basis. Naturally, such high-frequency studies are logistically very difficult, and therefore only a very few are in existence. The most important is probably that of Lampl, Veldhuis, and Johnson, who were able to assess growth in length,

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