{{PAGE_1}} Unit A The Study of Physical Growth · The Nature of Craniofacial Growth · Theories of Craniofacial Growth
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Contents
- The Study of Physical Growth
- The Nature of Craniofacial Growth
- Theories of Craniofacial Growth
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1. The Study of Physical Growth
Growth vs. Development
Introduction
Before viewing this program, you should have looked at the short video introduction to this course, Level I in the Growth and Development sequence. As with this and all the computer teaching programs, it’s important to read the assigned material in Contemporary Orthodontics (5th edition, pages 33-40; 4th ed., 40-47;) as well as view the program. Then you will take the self-test, the last section of the teaching module, and use it to consolidate the information and to be sure that you really understand it. Remember, the test is a teaching tool. Its purpose isn’t to evaluate you and provide some sort of grade—that doesn’t happen. Its purpose is to help you master the material.
Learning Objectives
In this first computer teaching module, we will distinguish the somewhat overlapping terms of “growth” and “development” from each other, and provide an overview of methods used to study growth.
The general learning objectives of this module are to:
- Distinguish the somewhat overlapping terms of “growth” and “development” from each other
- Discuss the concepts of pattern, variability, and timing as they are applied to the study of growth and development
- Provide an overview of the methods for studying growth from which our current knowledge was derived
Growth
If you are not careful, the very word “growth” can cause some difficulties.
Growth certainly refers to an increase in size, but it’s more than that. More than anything else, growth indicates change—which is why it’s possible sometimes to speak of negative growth.
Development indicates new capabilities, often bigger and better, perhaps at some cost. In this course on growth and development, it’s important to distinguish these terms.
For our use: Growth, most of the time, will refer to a change, almost always an increase, in size or number, generally with an anatomic reference. Occasionally, however, it will be used to indicate more of an increase in complexity than size.
{{PAGE_4}} Development will be used primarily to refer to an increase in complexity—especially when this carries with it an overtone of specialization and loss of potential.
Growth / Development: Why?
As a dental student, why should you study growth and development?
There are two important reasons:
- You have to understand normal dental, facial and psychosocial growth and development to work with children. You can’t distinguish the abnormal from the normal if you don’t understand the normal pattern of development.
- The dentist can manipulate growth to some extent, and it is important to do so in treating developmental problems in children. For example, headgear devices, like the ones shown here often are used to treat problems like protruding upper teeth and the deficient lower jaw that often is a major part of the problem.
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{{PAGE_5}} Concepts of Pattern, Variability and Timing
Growth Pattern Let’s start with the important concept of growth pattern. Think about the pattern for an article of clothing. As the pattern increases in size, there are changes in some areas that are larger or smaller than changes in other areas—it isn’t just blown up like a balloon. In this way, the pattern reflects a complex set of proportional relationships. Pattern in growth is a higher level pattern, a step beyond the pattern that gets clothes to fit or describes body proportions at any one time. It refers to the predictable changes in body proportions over time as the individual grows.
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Pattern =
Growth Pattern: Proportion Changes
There are striking changes in body proportions over time.
Note that at the end of the second month in utero, the head and face comprise almost 50% of the total body length. In contrast, the limbs are still rudimentary and the trunk underdeveloped. It may seem strange that at one time your nose was as big as your hand, but that was the case in early life.
The proportion of total body size contributed by the head and face steadily decreases after the 3rd month of fetal life. By the time of birth, greater growth of the trunk and limbs has reduced the head to 25% of the entire body. This pattern continues, so that the head and face contribute proportionally less and less to the total body length. This relative reduction in head and face size is because the craniofacial structures developed earlier. In later growth, structures away from the head grow more to catch up. This is called the cephalocaudal gradient of growth, and it’s an important part of the growth pattern that you need to always keep in mind.
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{{PAGE_7}} Growth Pattern: Cephalocaudal Gradient
Even within the head and face, the cephalocaudal gradient of growth leads to changes in proportionality during growth. When the skull of a newborn is compared to that of an adult, it is easy to see that postnatally there’s relatively more growth of the face than the cranium. This reflects the early growth of the nervous system. The cranium, the part of the head that serves as a housing for the brain, must grow rapidly early on, and grows less later.
Within the face, structures closer to the brain grow more earlier and less later. Thus the mandible is less developed at an early point than the maxilla and grows more postnatally.
Variability
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{{PAGE_8}} Study of Physical Growth
Concepts: Pattern Variability Timing
Variability: Sample Size Effect
Normal variation leads to the well-known bell-shaped curve in the distribution of individuals within a group, so that most individuals cluster near a midpoint and few are found at the extremes. The bigger the group, the more obvious the clustering near the mean. Notice what happens when heights are plotted for these two groups.
An important concept: if you don’t see the bell-shaped curve with clustering around a mid-point, you’re not looking at a normal distribution. And then statistics based on the normal distribution no longer are appropriate.
{{PAGE_9}} Distribution #1 Range = 150 - 190 Mean = 168 Median = 170 SD = 13.26 Q1 = 160 Q3 = 170 Interquartile range (Q3 - Q1) = 10
Distribution #2 Range = 150 - 190 Mean = 168 Median = 170 SD = 13.26 Q1 = 160 Q3 = 180 Interquartile range (Q3 - Q1) = 20
Image 1, Distribution #1: This distribution and distribution 2 both are relatively normal, despite very different numbers of observations in each sample.
Image 2, Distribution #2: This distribution and distribution 1 both are relatively normal, despite very different numbers of observations in each sample.
Variability: Distribution Measures
There are several ways to express the distribution of values within a group:
- The range is from the smallest to the largest value.
- The mean is the arithmetic average.
- The standard deviation is calculated from a mathematical formula is a way to describe the variability.
One standard deviation (S.D.) encompasses 67% of the people in a normal distribution, two S.D. includes 95% and three S.D. includes 99%. A larger standard deviation implies greater variability—but the number of individuals in the group can affect the values. With only a few individuals, each one heavily influences the values, and the standard deviation for a small group is likely to be large. Larger samples give more reliable data for mean and S.D.
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{{PAGE_10}} Distribution #1 Range = 150 - 190 Q₁ = 160 Mean = 168 Median = 170 Q₃ = 170 SD = 13.26 Interquartile range (Q₃ - Q₁) = 10
Distribution #2 Range = 150 - 190 Q₁ = 160 Mean = 168 Median = 170 Q₃ = 180 SD = 13.26 Interquartile range (Q₃ - Q₁) = 20
Image 1, Distribution #1: The mean and standard deviation are most commonly reported to describe the central tendency and variation of a normal sample.
Image 2, Distribution #2: The mean and standard deviation are most commonly reported to describe the central tendency and variation of a normal sample.
Mean / Std. Deviation vs. Median / Percentiles Another way to describe the central tendency of a group is to use the median, or middle person in each distribution. The median value corresponds to the 2nd quartile (Q2), and the inter-quartile range (IQR) is the measure of variation reported with the median value - just as standard deviation is reported with the mean. Usually the median is less sensitive to one or two individuals at the extremes. Often it is a better descriptor of small samples.
Percentiles also can be used to note where an individual stands relative to his or her peers. The middle of a distribution is the 50th percentile. At the 25th percentile, 75% of the group are taller than that individual. At the 90th percentile, only 10% would be taller.
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{{PAGE_11}} Distribution #1 Range = 150 - 190 Q1 = 160 Mean = 168 Median = 170 SD = 13.26 Interquartile range (Q3 - Q1) = 10
Distribution #2 Range = 150 - 190 Q1 = 160 Mean = 168 Median = 170 Q3 = 180 SD = 13.26 Interquartile range (Q3 - Q1) = 20
Image 1, Distribution #1: The median and IQR (inter-quartile range) are most commonly reported to describe the central tendency and variation of a non-normal sample.
Image 2, Distribution #2: The median and IQR (inter-quartile range) are most commonly reported to describe the central tendency and variation of a non-normal sample.
Growth Charts Growth charts, expressed in percentiles, often are used to show how a patient compares to his or her peers in height and weight, and how that changes over time. The lines indicate the percentiles, the x axis is time and the y axis indicates height or weight. The charts for boys and girls are different (although the differences are surprisingly small prior to adolescence).
For this normal girl, height and weight values plot consistently near the 50th percentile, but normal variation is relatively large. As a general guideline, a child who is between the 3rd and 97th percentiles is considered within the normal range. Outside that, abnormality must be suspected.
To view this chart more clearly (it’s hard to make it large enough on the computer screen), look at Figure 2-4 in Contemporary Orthodontics (4th or 5th ed.).
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{{PAGE_12}} Growth Charts (cont.)
Normal growth is shown on a growth chart not so much by being at the 50th percentile, as by maintaining about the same percentile over time. A child who plots at the 20th percentile consistently is just a small but normal child.
Crossing the percentiles, particularly crossing several of them, usually indicates abnormal growth and some problem. In this respect, height is a more sensitive indicator than weight.
Here we see the plot for a boy who developed a medical problem that affected growth at age 10, with partial recovery at age 13, but a long-term growth deficit. To see it better, look at Figure 2-5 in Contemporary Orthodontics.
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{{PAGE_13}} Other Charts
Many body dimensions, not just height and weight, can be plotted against time to see if growth is normal.
This graph shows the change in the height of the face for boys and girls, based on measurements from radiographs.
You could check your patient’s face height, and its change over time, against a standard graph of this type. Note that there’s a different value for boys and girls, and the male-female difference gets larger as the children get older.
This is largely due to variations in timing, which is the next concept to be discussed.
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{{PAGE_14}} L1NEAR MEASUREMENT Variable 160
Menton-Nasion ME=N 1-38
| Male | Female | ||||||
|---|---|---|---|---|---|---|---|
| Age | N | Mean mm | S.D. | Age | N | Mean mm | S.D. |
| 6 | 37 | 106.7 | 5.2 | 6 | 28 | 105.0 | 5.1 |
| 7 | 44 | 110.7 | 5.8 * | 7 | 31 | 107.8 | 5.3 |
| 8 | 44 | 113.6 | 5.6 ** | 8 | 36 | 109.5 | 5.4 |
| 9 | 46 | 115.9 | 5.4 ** | 9 | 31 | 112.1 | 5.7 |
| 10 | 45 | 118.7 | 5.7 ** | 10 | 35 | 115.1 | 6.7 |
| 11 | 43 | 121.5 | 6.0 ** | 11 | 30 | 116.2 | 6.4 |
| 12 | 44 | 123.3 | 6.3 ** | 12 | 27 | 118.2 | 6.0 |
| 13 | 42 | 126.8 | 7.0 ** | 13 | 28 | 120.7 | 5.8 |
| 14 | 39 | 130.3 | 7.9 ** | 14 | 25 | 122.3 | 5.9 |
| 15 | 32 | 133.8 | 7.8 ** | 15 | 19 | 122.7 | 6.4 |
| 16 | 23 | 136.8 | 7.9 ** | 16 | 9 | 123.2 | 5.1 |
Timing: Description Boys and girls get bigger over time, of course, but differences between individuals of the same age and gender, and differences between the sexes, are most notable near adolescence. That is because sexual maturation leads to an adolescent growth spurt. This happens at a different time in girls and boys and happens at different times in individuals of the same gender. On the average, girls have their adolescent growth spurt 2 years ahead of boys. That doesn’t mean that all girls mature faster than all boys—there’s too much individual variation for that to be true.
{{PAGE_15}} Study of Physical Growth
Concepts: Pattern Variability Timing
Timing: Description (cont.)
This diagram plots the increase in height each year for three girls, who experienced a growth spurt at different times because of a difference in timing of sexual maturation. M-1, M-2 and M-3 show for each girl the age (age range between measurements) at which menses began (called menarche). Note that the rate of growth for each girl was declining by then.
Sometimes differences in the timing of puberty, whether an individual matures unusually early or late, causes him or her to cross percentile lines during adolescence. This should not be considered an indication of a growth problem, especially if the plot for the early or late maturing preson returns toward the range where it was initially.
{{PAGE_16}} Chronologic vs. Biologic Age
Because of timing variability, chronologic age often is not a good indicator of an individual’s growth status. It is possible to measure age biologically, in terms of progress towards achievement of certain development markers.
For dentists and orthodontists, a good way to do this is to use the stages in maturation of cervical vertebrae, which are seen in the cephalometric radiographs that are obtained for most orthodontic patients. In these two radiographs of the same individual taken 2 years apart, you can see that the cervical vertebrae (within the box) look somewhat different. For now, you just need to understand the concept of biologic age—but soon you will be learning how to estimate a patient’s skeletal development age (one of many biologic ages that can be useful clinically in pediatric dentistry and orthodontics) from vertebral development seen in a radiograph.
{{PAGE_17}} Image 1, an individual at CVM 4: The yellow boxes surround the second, third, and fourth cervical vertebrae. The shape of these bones indicate this person is at stage 4 on the scale of Cervical Vertebral Maturation (CVM 4). Image 2, an individual at CVM 5: The yellow boxes surround the second, third, and fourth cervical vertebrae. The shape of these bones indicate this person is at stage 5 on the scale of Cervical Vertebral Maturation (CVM 5).
Chronologic vs. Biologic Age (cont.)
The stages in maturation of the cervical vertebrae correlate well with the adolescent growth spurt, which is the best time for most orthodontic treatment. Stage 2 indicates that peak growth at adolescence is still a year or so ahead. Stage 3 indicates that it is less than one year to peak growth, a good place to begin treatment. Stages 4, 5 and 6 are increasing distances beyond peak growth.
For now, you just need to understand the concept of evaluating growth using biologic markers instead of years. Later you will learn more about using both cervical vertebrae and hand-wrist bones to calculate skeletal age and how to use that knowledge to improve clinical decisions.
Timing: Biologic Age
These biologic ages also could be called developmental or maturation ages. Many different types of maturation, not just the skeletal age calculated from vertebrae or other skeletal indicators, can be determined and quantified in biologic terms. Dentists use dental age all the time, judging the state of development of the dentition against the usual chronologic markers. You will be learning about that in detail later in this course.
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{{PAGE_18}} For example, from the standard charts it would be possible to calculate a height age. When you’re the height of an average nine year old (just over 130 cms), your height age is 9, regardless of your chronologic age. Intellectual development can be calculated in the same way. Intellectual development relative to chronologic age usually is called IQ, for intelligence quotient, but it’s just another developmental age. It is interesting that the various developmental ages tend to be highly correlated. If you’re bigger than other children the same age, you’re probably also more developed mentally and socially. Correlated, of course, doesn’t mean that this is always the case, just that it’s more likely to be that way.
Timing: Biologic Age (cont.)
The use of biologic age is a way to control timing as a variable in growth studies. Look again at the growth curves for our three girls with early, average and late menarche (image 1). Now use menarche as a biologic marker and call that time zero and plot growth increments before and after (image 2). Note how similar the growth curves are for the group of girls after this simple transformation. They all had a very similar acceleration of growth leading up to menarche and decrease afterward. Using chronologic age instead of biologic age often can be misleading when developmental events are studied, as we will see when we consider cross-sectional vs longitudingal studies.
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Methods for Studying Growth
Introduction: Types of Growth Data
Growth studies may either be longitudinal or cross-sectional in design. When you look at growth data, it is important to know whether the study was longitudinal or cross-sectional.
In cross-sectional studies, rather than seeing the same individual at age 9,10,11, etc., data are taken for a group of 9 year olds, a different group of 10 year olds, another different group of 11 year olds, and so on. This is quicker and easier, but the amount of individual variation tends to be understated. The mean for the group (the dark line in this figure) when chronologic age is used as the time base gives a very misleading picture of what happens to any individual.
Longitudinal studies, in which the same individual is followed over time, provide more information about individual variation, but these studies take a long time and become quite expensive. Note that longitudinal data give a much better picture of what an individual would experience.
Now remember the effect of plotting the individual data with menarche as a base. Using biologic age in that way with cross-sectional data can make it easier to avoid distortions due to different timing in different individuals.
{{PAGE_20}} Longitudinal Growth, Distance
This graph shows the first published longitudinal study of growth, done by the French aristocrat De Montebillard in the 1700’s. He plotted the height of his son from birth to age 18, measuring the boy repeatedly over those 18 years. Many fathers or grandfathers still do this, often with marks on a door frame as a child grows. Did somebody do this for you?
You can see that the growth in height didn’t occur in a steady fashion. It was very rapid at first, trailed off after about age 2, then accelerated from ages 14 to 16 and was still continuing at age 18.
{{PAGE_21}} De Montebeillard’s son 1759-1777
Longitudinal Growth, Distance vs. Velocity
It’s easier to see changes in the rate of growth if the same data are plotted in a different way, showing the amount of change in each interval rather than the total height. In the plot of growth increments, note how the very rapid growth at first, slower rate in childhood prior to adolescence, and adolescent growth spurt stand out when the amount of change is plotted. The first curve is called a distance curve, the second a velocity curve.
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{{PAGE_22}} Other Data Transformations Various other mathematical transformations of data can make it easier to understand what is occurring during growth. In image 1, the graph showing the increase in weight of early embryos, you can see that there is an exponential acceleration in weight with increasing time.
In image 2, the same data are plotted after a logarithmic transformation. This shows a straight line, indicating that the rate of multiplication of individual cells remains almost constant. It’s not that cells are dividing faster as the embryo gets older, it’s that increasingly there are more cells to divide.
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Methods for Studying Growth: Growth Measurement Techniques
There are now four basic measurement techniques for physical growth:
- Craniometry
- Anthropometry
- Cephalometric radiography
- 3D radiography (computed tomography)
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Measurement Techniques
- Craniometry
- Anthropometry
- Cephalometric Radiography
- Cone Beam Computed Tomography (CBCT)
Craniometry
The science of physical anthropology began with craniometry, which is based on measurements of human skulls (or other bones, in which case it would be osteometry).
Although most craniometric studies have been done on the remains of populations from earlier times, study of contemporary skulls or other bones obviously would be possible. Distortions of the skull during growth can occur, and now are understood better after study of skeletal remains. A good example is the effect of premature fusion of sutures.
In the individual shown in image 1, the mid-sagittal suture fused prematurely and was entirely missing in adult life. Note the extremely narrow width of the cranium. In compensation, the brain and skull became abnormally long posteriorly. In image 2, note the effect of, premature fusion of sutures on the right side of the cranial base. This led to a marked asymmetry that affected both the cranium and cranial base. Once effects of this type have been noted in studies of skulls, the likely cause of similar asymmetries in living patients becomes apparent.
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{{PAGE_25}} Image 1: A photograph of a human skull showing premature fusion of the mid-sagittal suture, resulting in a narrow cranial vault. Image 2: A photograph of the base of a human skull showing premature fusion of sutures on the right side, leading to major asymmetry.
Anthropometry refers to measurements on living individuals. Various landmarks on the skull were established by investigators studying skeletal material, and the soft tissue points overlying those landmarks (or other soft tissue points that can be found repeatedly) can be used to study living individuals.
Varying soft tissue thickness introduces a source of error if the goal is to measure growth of the facial skeleton, but it is highly advantageous to follow the growth of an individual directly, making the same measurement repeatedly at different times.
This produces longitudinal rather than cross-sectional data and shows individual variation much more precisely. Much of what we know about cranial and facial growth was first deduced from anthropometric studies. Anthropometric measurements are still important in clinical examination of orthodontic patients. They are used now primarily to establish facial proportions—which are important in planning orthodontic treatment.
{{PAGE_26}} Image 1: Anthropometric measurement of bi-zygomatic width, which is important in clinical orthodontics because of its relationship to the width of the maxillary dental arch and in establishing face height-width proportions
Cephalometric Radiology
The third important measurement technique is cephalometric radiology. Using x-ray pictures of the head and face provides a way to combine the advantages of crainometry and anthropometry.
It allows direct measurement of the skeleton because the soft tissue thickness can be ignored—but the soft tissues also are imaged and can be measured if desired.
Proper positioning of the subject in a head holder is necessary, so that repeated x-rays can be made with the head positioned exactly the same. This allows longitudinal study of growth (or treatment) changes in an individual.
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{{PAGE_27}} Cephalometric Radiology (cont.)
The disadvantages of cephalometrics are that exposure to x-rays is required, and that the radiograph is a two-dimensional representation of three-dimensional structures. Some measurements are not possible and others are distorted in projection. The recent development of cone-beam computed tomography, which greatly reduces the radiation dose to obtain 3-D images of the head and face, means that this method is likely to replace traditional cephalometrics for many purposes.
But cephalometric radiographs give an excellent view of many skeletal and dental structures that aren’t accessible for anthropometric study, and these radiolographs are used routinely in dentistry to monitor growth and treatment of patients. A patient like this one, with too much growth of the lower jaw, has to be followed with serial cephalometric radiographs to determine the best time for treatment. You’ll be learning a lot more about how to use cephalograms for purposes like this.
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{{PAGE_28}} Newer Imaging: Computed Tomography (CT)
With newer imaging methods like computed tomography (CT), it is possible to reconstruct facial images in three dimensions.
Axial CT, which is used in most hospital applications, is very precise but has two problems for studies of growth: it is expensive and delivers a relatively large radiation dose.
The introduction of cone-beam CT (CBCT) for images of the head has offered a significant reduction in both cost and radiation, and CBCT is now an important tool in dentistry for improved diagnosis and treatment planning. CBCT is not quite as accurate as axial CT, but its precision is adequate for most applications in dentistry, including the study of growth.
This CBCT view of a patient with an impacted canine makes the position of the affected tooth clear (indicated by the yellow arrow), and the image can be rotated and manipulated to provide other perspectives.
{{PAGE_29}} CB-CT Superimpositions
For growth studies, it is important to see changes over time. This requires superimposition of images of the same individual that were taken at different times. With cephalometric radiographs, tracings based on identification of landmarks typically are used. That doesn’t work with 3-D images, but now it is possible to superimpose on surface contours, and changes between sequential 3-D images can be discerned by color maps. This allows you to look at the amount of change at thousands of points that can be viewed from any orientation, instead of being limited to tens of points seen from one orientation in a cephalometric radiograph. The superimposed images here show changes in the position of the jaws created in an adult by orthognathic surgery to reposition his maxilla and mandible, but the same approach can be used in growth studies, and such studies now are being undertaken.
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Experimental Methods in the Study of Growth
The second way to study growth is with marker techniques. These are classic experimental methods for studying growth. Using these methods, it is possible to follow either processes or physical changes by visualizing the marker. Most of these techniques are used in animal studies because the analysis may be destructive.
Those techniques include:
- Vital staining
- Autoradiography
- Cephalometric superimposition on Implants
- Molecular biology
{{PAGE_31}} Experimental Methods
- Vital Staining
- Autoradiography
- Implant Radiography
- Molecular Biology
Vital Staining
In vital staining, dyes that are incorporated into bone (or sometimes other tissues) are injected into animals. Bone that was growing at the time the dye was injected is stained, and the amount of growth between two injections or since the last injection can be seen.
The technique goes back to the famous English anatomist John Hunter, who observed that the dyes in textile wastes fed to pigs stained their bones in interesting ways. He experimented to find which dyes were best for staining bone. Alizarin proved to be best.
This young rat had four injections of alizarin dye at 2-week intervals, first red, then blue, then red again, then blue again. The dye is excreted rapidly, so the staining occurs during only a few hours after each injection.
As you look carefully at the mandible (image A, the condylar process is in the center), you can see the sequential bands of color. The white bone at the tip of the condylar process grew there since the last injection. Both the sites of growth and the rate of growth in various areas can be seen. The sites of growth are the areas where new bone is being formed, or removed by the remodeling that accompanies bone growth. The rate of growth is shown by the distance between bands of color that were deposited at known times when the dye was injected.
Image B shows the zygomatic arch. Note that new bone is being formed on the outside of the arch, while bone is being resorbed on the inside. The arch is growing outward by being constantly
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{{PAGE_32}} remodeled. In a view like this one, you can not only see where changes are occurring, you can tell how quickly if you know the timing of injections of the dye.
Autoradiography Autoradiography is based on causing tissues to take their own pictures. Radioactively labeled substances are injected, tissue specimens are prepared, and when photographic film is exposed by placing it over the tissue specimen in the dark, the location of radioactive materials in the tissue is revealed as radiation activates silver grains in the film layer.
This is an autoradiograph of a small bone that was growing in organ culture. Tritium-labelled thymidine was incorporated into the culture medium, and was taken up when DNA of new cells was formed at the time of cell division. The black dots are nuclei that contain the labeled thymidine, which means they must have been formed by cell division that occurred since the tritiated thymidine was added to the culture medium.
In this experiment, carbon 14-labelled proline also was added to the medium. Proline, an amino acid, is a major constituent of collagen, which in turn is the major component of connective tissues and bone matrix. The dark label away from the cell nuclei shows where proline is being incorporated into newly-formed collagen, and therefore shows where collagen formation is taking place. Note that it is most active in the area where maturing collagen is being replaced by bone spicules. With radioactive labeling, essentially any substance can be turned into the equivalent of a vital stain.
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{{PAGE_33}} Implant Radiology Implant radiology is based on visualizing metal pins placed in the skeleton. Perhaps you know that when bones are fractured, metal pins often are placed to hold them while they heal, and often the pins are left in place. A long time after the fracture has healed, the pin will still be visible on x-rays as a marker of the fracture site. It is possible experimentally to place small metallic implants in bones anywhere in the skeleton, including the face and jaws, as permanent markers.
This girl has small pieces of tantalum wire in her jaws, placed in areas where little growth occurs, as markers, so that the changes in jaw contours as she grows can be followed more precisely. The implants were placed from inside the mouth by anesthetizing the muscosa over the area where the implant is to be placed, then using small spring-loaded device to drive the implant through the soft tissue into the bone. It is a simple and painless procedure. When another cephalogram is taken later, one can superimpose on the markers, and then changes due to remodeling of the surfaces of the bone can be seen clearly.
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{{PAGE_34}} Implant Radiology (cont.)
Implants have been placed in a number of children whose growth pattern was followed longitudinally, using cephalometric x-rays to detect the location of the pins. Then the pins were used to superimpose the outline of the jaws, so that growth changes could be seen relative to the pins. This method was originated by Professor Bjork in Copenhagen, and has been responsible for much of our current understanding of jaw growth patterns. In this superimposition on pins in the mandible, you can see that bone was added to the posterior surface of the ramus and to the condylar and coronoid processes, but was removed from the gonial angle area. Note also that a great deal of remodeling of the condyles occurred. What was once the condyle at age 4 became a part of the ramus at age 10, and then was partially resorbed away as the condylar process continued to grow upward. Note also how the teeth erupted upward and forward relative to the pins in stable areas of the bone. Until cephalometric superimpositions on markers was done, the large amount of remodeling of the bone as the jaws grew had not been appreciated. You’ll be seeing more tracings of cephalometric radiographs superimposed on implants in the future, and you must understand the concept.
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{{PAGE_35}} 4 years 10 years 20 years
Molecular Techniques
It also is possible to use the techniques of molecular biology to study growth, and this holds great promise for the near future. An example of such methods is diagrammed on this slide. Genetic information carried by plasmids can be injected into the nucleus of a mouse egg, which is then implanted into a pseudopregnant mouse.
When the mouse gives birth, if the new genetic information is active and has been copied, the progeny have foreign DNA and are known as transgenic mice. These genetically-altered mice can be examined for morphologic differences, extracts can be made to test for inactivated hormones or enzymes, etc.
Molecular Techniques (cont.)
One of these mice strains was injected with a plasmid carrying genes coding for growth hormone. The impressively large size of the animal on the left confirms the activity of this genetic information in
{{PAGE_36}} these transgenic mice. Because normal growth patterns are so precise and specific, genetic control is obvious. Experiments of this type have great promise in explaining exactly how the control is mediated.
Summary In studies of growth and development:
- growth (increase in size) and development (increase in complexity with specialization and loss of potential) are different concepts
- growth pattern refers to predictable changes in proportions with growth
- children outside the 3rd and 97th percentiles on standard growth charts may be beyond normal variation
- the timing of adolescence is a major contributor to variability in growth
- biologic ages based on physiologic events can be used to reduce variation related to timing
Summary (cont.) Important measurement techniques to know:
- Craniometry
- Anthropometry
- Cephalometric radiology
- Cone-beam CT Remember: the timing of adolescence is a major contributor to variability in growth Cross-sectional growth studies:
- quicker, less expensive, less precise in detecting typical timing fluctuations Longitudinal growth studies:
- slow, expensive and hard to maintain, very efficient and excellent in showing details Experimental marker techniques to know:
- vital staining
- autoradiography
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- implant superimposition Molecular biology techniques: The way of the future in growth studies.
Referral to Self-Test
The self-test section of this program is designed to help you be sure you have understood the material.
Now that you have gone through the module, do the assigned reading in Contemporary Orthodontics (pages 20–33 in the 5th ed.; pages 27–40, 4th ed.) Then take the self-test, and use it as a guide for further study and review. You should be sure you understand the correct answer to all questions that you didn’t get right on your first try.
Copyright 2013, UNC Dept. of Orthodontics
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2. The Nature of Craniofacial Growth
Introduction
Before viewing this program, you should have looked at “The Study of Physical Growth”, the first module in the series. In the following program we will go into craniofacial growth in more detail. As with this and all the computer teaching programs, it’s important to read the assigned material in Contemporary Orthodontics (5th edition, pages 33-40; 4th ed., 40-47;) as well as view the program, and then take the self-test at the end.
Learning Objectives
The general learning objectives for this module are to:
- Distinguish the various types of growth in the skeletal system, and understand important related concepts
- Describe the pattern of growth of the craniofacial skeleton in detail
To meet these educational objectives, be sure that you are able to:
- describe the cellular processes involved in physical growth and the differences in soft tissue and hard tissue growth
- describe the growth of the calvarium and cranial base in 3 planes of space, identifying the sites and mode of growth
- similarly describe the growth of the maxilla, identifying the chief sites of growth, the role of surface remodeling and the effect of secondary displacement
- describe the basic processes involved in growth of the mandible and the changes that occur in each area
- describe the growth of the dental arches and identify the chief sites of growth.
Types of Skeletal Growth
Bone Growth: Cellular Level
At the cellular level, there are only three possibilities when growth occurs:
- Hyperplasia - an increase in the number of cells
- Hypertrophy - an increase in size of the cells
- Secretion of extracellular material, which contributes to an increase in size independent of the number or size of the cells themselves.
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{{PAGE_39}} Skeletal Growth: Soft Tissues vs. Hard Tissues Calcification of extracellular material leads to a critical distinction between the soft or non-calcified tissues of the body and the hard calcified tissues.
Hard tissues are bones, teeth, and sometimes cartilages. Soft tissues are everything else. Most of the cartilage we will be talking about for craniofacial growth behaves like soft tissue and should be thought of in that way.
Growth of soft tissues occurs mostly by a combination of hyperplasia and hypertrophy. These processes go on within the tissues at all points, and the result is interstitial growth, which simply means growth inside the tissues. Secretion of extracellular material also can accompany interstitial growth, but hyperplasia primarily and hypertrophy secondarily are its characteristics.
Endochondral Ossification: Interstitial Growth Interstitial growth is shown well in this view of a growing area at the top of the mandibular condyle. This is endochondral ossification, in which cartilage is doing the growing and then is replaced by bone (a process we will review in detail later in this program).
{{PAGE_40}} Hyperplasia, formation of new cells, is occurring in the area below the fibrocartilage that covers the surface of the bone. Below that, note the enormous increase in the size of the maturing cartilage cells. This, of course, is hypertrophy. In addition, the cartilage cells are producing an extracellular material that lies between the cells and separates them. The hypertrophic changes are in preparation for the formation of new bone as it replaces the mature cartilage. Interstitial growth is a characteristic of uncalcified cartilage and other soft tissues.
Bone Growth: Growth of Hard Tissues In contrast, when calcification takes place so that hard tissue is formed, interstitial growth in the calcified area becomes impossible. Significant growth occurs only at surfaces, not within the calcified mass. The interior of the calcified material can and does remodel, but it can’t grow larger because it’s too hard and rigid to expand internally. Growth of hard tissue, therefore, occurs in two ways. The first is direct addition to the calcified tissue on its free surfaces. This occurs through the activity of cells in the periosteum, the soft tissue membrane covering the bone. Formation of new cells occurs in the periosteum, and extracellular material is secreted that then calcifies into bone. The second way is by replacement of soft tissue that grew before calcification occurred. Many bones are modeled in cartilage originally, and the cartilage model is replaced by bone, thus the term “endochondral ossification.” In this situation, the cartilage does the growing while the bone
{{PAGE_41}} Cartilage can grow interstitially, but bone cannot.
Growth of Long Bones: Endochondral Ossification Endochondral ossification of a typical long bone with a cartilaginous precursor begins with bone formation on the surface of the cartilage. This is followed by invasion of blood vessels that produce a hollowed-out center with bone formation in that area (A in the figure).
Ingrowth of blood vessels leads to an ossification center in the cartilaginous caps on either end (B), but a band of cartilage remains between what we can now call the diaphysis (the central part) and epiphyses. These cartilage bands are the epiphyseal plates.
The bone grows longer as the cartilage of the epiphyseal plates grows, matures, and is replaced by bone (C). Eventually, the rate of replacement of the cartilage with bone exceeds the rate of cartilage growth, all the cartilage is replaced—and the bone then is as long as it can get (D).
{{PAGE_42}} Bone Growth: Endochondral Ossification (cont.) A histologic view of endochondral ossification at an epiphyseal plate shows the areas of proliferating and maturing cartilage, then replacement of degenerating mature cartilage by spicules of bone. It is important to keep in mind that in addition to the endochondral replacement, periosteum is actively forming bone on the outer surfaces. The bone grows longer by endochondral ossification. It grows wider by direct formation of new bone on the surface.
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{{PAGE_43}} Bone Growth: Endochondral vs. Surface Ossification
The combination of surface apposition of bone and endochondral replacement can be seen in this drawing of a growing bone. Periosteal bone formation on the surface is different from the endochondral bone formation occurring beneath it.
For endochondral bone formation, a complex maturational pattern of the cartilage is required. In direct bone formation by the periosteum, osteoblasts secrete their matrix directly in connective tissue, and it calcifies there without any intermediate formation of cartilage.
The details of this process are a review of what you learned in histology and will not be emphasized further here, but you must understand it.
Bone Growth: Endochondral vs. Surface Ossification (cont.)
Growth at the epiphyseal plate requires corresponding changes in the surface of the bone. Not all the surface changes can be met by adding new bone. Because the contour of the long bones calls for a knob on the end, a continuous remodeling of the surface is required as endochondral growth occurs, meaning that bone must be added to the surface in some areas and removed in others.
The periosteum, therefore, must and does contain cells whose purpose is to remove bone as well as cells to make it, and there is a balance between apposition of bone in some areas and resorption in others. Addition of bone in some areas while old bone is removed in others is an essential component of the growth process.
{{PAGE_44}} Bone Growth: Internal Remodeling
We have said that growth within a calcified mass is impossible, but that doesn’t mean that metabolic change is impossible. In fact, osteocytes embedded in the bone are alive, and quite capable of producing internal remodeling of the bone. Calcified tissue in bones is turned over through a constant process of remodeling.
In this vital-stained section, you can see the live osteocyte with its processes extending out into the calcified bone around it. This makes it obvious how activity by a cell like this can affect calcified tissue at a distance from the cell body of the osteocyte.
Remodeling of the internal structure of bone has two major functions: it serves as a means of adapting the bone to mechanical stresses, and it also makes calcium and phosphate ions available for exchange with blood. Exchange of calcium and phosphate occurs near periosteal surfaces and around Haversian systems.
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{{PAGE_45}} Bone Growth: Internal Remodeling (cont.)
In this decalcifed section from a bone, the larger holes are where a blood vessel was, the smaller lacunae are where the cells were. Osteocytes cluster around vascular channels, as you can see. Ingrowth of blood vessels into an area of cartilage or connective tissue is essential for ossification. It also is essential for maintenance of the calcified tissue.
A complex like the one shown here, with osteocytes surrounding a blood vessel, is called a Haversian system, and it’s constantly remodeled during life. This internal remodeling, however, does not significantly contribute to growth or change the shape of the bone. The bone can’t get bigger through internal remodeling.
In this section of bone, you can see remnants of an old Haversian system (dotted yellow lines) being replaced by a smaller new one as the bone remodels. Bone is a dynamic tissue, constantly being rebuilt. It’s a mistake to think of it as just an inert scaffold on which the other tissues are suspended.
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{{PAGE_46}} Cranial and Maxillary Growth
Regions of the Cranium and Face
With the general principles of bone growth established, let’s look in more detail at growth of the cranium and face. For this discussion, it will be convenient to divide the cranium and face into two areas each:
For the cranium (labeled 1 in this image): The cranial vault and cranial base. For the face: The naso-maxillary complex (2) and the mandible(3).
The special features of growth of the dentoalveolar processes (4, 5) and eruption of the teeth will be considered later.
{{PAGE_47}} Skeletal Growth: Cranial Vault
Let’s begin by examining the cranial vault. It is made up of a number of flat bones that are formed directly by periosteum. Endochondral bone formation has no role here, and there’s never any cartilage in the vicinity. Instead, growth occurs entirely by periosteal activity at the surfaces of the bones, both at the flat inner and outer surfaces and the periosteum-lined spaces between them.
At birth, the bones are rather widely separated by connective tissues, and these open spaces are called fontanelles. The presence of the fontanelles allows considerable deformation at birth, which is important in getting the relatively large head through the birth canal.
Apposition of bone along the edges of the fontanelles eliminates these open spaces fairly quickly after birth, but the bones remain separated by thin periosteum-lined sutures for years.
Despite their small size, apposition of bone at the sutures is the major mechanism for growth of the cranial vault. In addition, there is a tendency for bone to be removed from the inner surface of each bone and added to the outer surface, especially in some areas where contours change. The magnitude of the remodeling changes, however, is much less than the growth at sutures.
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{{PAGE_48}} Skeletal Growth: Cranial Base
In contrast to the cranial vault, the bones of the cranial base (particularly in the midline) are formed initially in cartilage, then transformed into bone. At about 8 weeks in utero (image A), before any bone formation has begun, an essentially solid bar of cartilage extends beneath the brain from the nasal capsule anteriorly to the occipital area posteriorly. This cartilage is called the chondocranium.
At 12 weeks (image B), ossification centers have appeared in the midline cartilage structures. In addition, intramembranous bone formation has begun in the cranial vault (B in the Figure). From this point on, bone (dark blue color) replaces the original chondrocranium rapidly, but remnants of it persist as small cartilaginous synchondroses and remain between the developing occipital, sphenoid and ethmoid bones.
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Skeletal Growth: Cranial Base (cont.)
It should come as no surprise that the lengthening of the cranial base is largely due to endochondral replacement. As one moves laterally beneath the brain, growth at sutures and surface remodeling become more important, but the cranial base is essentially a midline structure, and the synchondroses are important growth sites. The most important ones are the spheno-occipital, inter-sphenoid and spheno-ethmoidal synchondroses.
Synchondrosis vs. Suture
Be sure you understand the difference between a suture and a synchondrosis. Both are thin soft tissue areas between adjacent bones, but the synchondrosis is filled with cartilage. A band of proliferating cartilage cells is located in the center of the synchondrosis, and a band of maturing cartilage extends in both directions away from the center. Endochondral ossification occurs at both margins.
{{PAGE_50}} Synchondrosis vs. Suture (cont.)
In contrast, a suture has only periosteum and connective tissue. At the synchondrosis, bone formation proceeds by cartilage replacement, while for sutures, there is no intermediate cartilage stage.
As you will see when we review growth control, the difference is significant: the cartilage at synchondroses is capable of active, independent growth while the connective tissue at sutures only reacts to what happens in its surroundings.
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Synchondrosis
Junction between adjacent bones Cartilage Endochondral ossification Active growth
Suture
Junction between adjacent bones Connective tissue Direct ossification Reactive growth
Skeletal Growth: Maxilla
Now let’s consider the maxilla and the associated smaller nasal and palatine bones. Postnatally, the face grows downward and forward from the cranium, and the maxilla must move a considerable distance. How this occurs, and what changes accompany the growth, are what we must focus on now. In the case of the maxilla, there is no pre-existing cartilage, so maxillary growth is a matter of sutures and surface remodeling.
In contrast to the cranial vault, however, surface remodeling changes are quite dramatic and important. In addition, as this figure shows, the naso-maxillary complex is affected indirectly by the endochondral growth of the cranial base, which pushes the maxilla forward and thereby contributes to its forward translation. How long would this mechanism of growth be effective? Only as long as the cranial base is growing—and that ends at about the time brain growth ends, at about age 6.
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{{PAGE_52}} Skeletal Growth: Maxilla (cont.) Let’s look in more detail at the right half of the maxilla in this figure. Note that it forms the floor of the orbit, the lateral wall of the nose, the roof of the mouth and the lateral aspects of the facial skeleton. There are sutures posteriorly along the maxillary tuberosity, superiorly at the end of the frontal process, and superiorly-laterally along the zygomatic process.
There’s also a suture in the midline down the middle of the palate, providing a mechanism for the midface and upper dental arch to become wider. Growth occurs by apposition at the sutures and by remodeling of the surfaces.
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Growth at Sutures and Surfaces of the Maxilla
It is apparent that the posterior and superior sutures of the maxilla are ideally situated to allow downward and forward repositioning. As the maxilla moves in that direction, new bone is added at the sutures to maintain its connection to the cranium.
The space that would otherwise open up at the sutures is filled in by proliferation of bone, so the sutures remain the same width but the various processes of the maxilla become longer. As the drawing illustrates, this requires moving the maxilla away from the structures above and behind it.
Part of the posterior border of the maxilla, in the tuberosity area, is a free surface. Bone is added to this area, creating additional space into which the molar teeth can erupt.
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Surface Resorption in Growth of Maxilla
As the maxilla grows down and forward, its front surfaces are remodeled, and bone is actually removed from most of the anterior surface.
In this three-quarter view (Image 1), areas of resorption are more darkly shaded. Note that almost the whole anterior surface is a resorptive area–which seems backward to what you might think it should be. If you look at it in profile (Image 2), there’s a little apposition at the anterior nasal spine and just below it, but all the other surfaces are resorptive.
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Translation and Remodeling
What takes place as the maxilla grows is represented by this cartoon. The whole bone is moving downward and forward relative to the cranium, being translated in space. This is exemplified in the cartoon by the platform on wheels.
At the same time, the front surface, represented in the cartoon by the wall, is being reduced on its anterior side and built up posteriorly, so that it moves in space opposite to the direction of overall growth.
How do we know this remodeling occurs? Vital staining shows this quite nicely, as you saw with the zygomatic arch in Module 1. How do we know that translation occurs? Superimposed tracings of cephalometric x-rays are a good way to show that.
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{{PAGE_56}} Translation and Remodeling (cont.)
It’s not always true that surface remodeling opposes the direction of translation. Depending on location, translation and remodeling may have an additive effect or may oppose each other. Look in more detail at what happens to surfaces in the palatal area during growth.
The maxilla is being translated downward and forward. At the same time the floor of the nose is resorbing and bone is being added to the roof of the mouth, so remodeling adds to the movement of those structures. But the front surface below the anterior nasal spine is resorbing, so the surface changes opposes the direction of translation there.
{{PAGE_57}} Translation and Remodeling: An Overall View
In this overall view of the movement of the dental portions of the maxilla during growth (using cephalometric tracings superimposed on the cranial base), you can see that the maxilla seems to be moving more downward than forward.
It looks like that because the direction of surface remodeling opposes forward translation of the maxilla but adds to the downward component.
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Summary: Overall Pattern of Maxillary Growth
The overall pattern of maxillary growth can be summarized as follows:
- As the bone moves downward and forward, new bone is added at the sutures and the tuberosity.
- Anterior surfaces resorb, while the roof of the mouth moves further down by remodeling.
- The remodeling of the roof of the mouth means, among other things, that you can’t judge how much a tooth has erupted by measuring how far it is from the height of the palatal vault.
If you understand that, you have grasped the concept of remodeling in relation to maxillary growth. If you don’t, go back and review this section and make some drawings.
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Mandibular and Dento-Alveolar Bone Growth
Skeletal Growth: Mandible
Growth of the mandible is different in many ways from growth of the maxilla. The difference begins with its relationship to the chondro-cranium. The mandible has a cartilage model, of sorts (Meckel’s cartilage, a cartilaginous bar in the mandibular arch whose proximal ends eventually ossify to form the malleus of the middle ear). But the mandible develops more in association with that cartilage than by replacing it.
Bone formation begins just lateral to Meckel’s cartilage and spreads posteriorly along it without any direct replacement of the cartilage by the newly forming bone. The two halves fuse very early, so for all practical purposes, a growing mandible, even in fetal life, is a single bone extending across the midline.
{{PAGE_60}} Meckel’s cartilage Inferior alveolar nerve Initial site of osteogenesis Mental branch
Origin and Growth of the Condylar Cartilage
There is some cartilage that covers the surface of the condyle at the temporomandibular (TM) joint, but it appears relatively late in embryonic life and is not derived from Meckel’s cartilage. It begins formation separately from the body of the mandible and fuses with the bone at about 4 months in utero, as shown in the figure.
This cartilage is not like the cartilage at an epiphyseal plate or synchondrosis, but hyperplasia, hypertrophy, and endochondral replacement do occur there. All other areas of the mandible are formed and grow by direct surface apposition and remodeling.
Pattern of Mandibular Growth
The overall pattern of growth of the mandible can be represented in two ways. Depending on your frame of reference, both are correct.
If you hold the cranium constant and look at mandibular growth relative to it (A), the chin moves downward and forward a long way relative to the cranium, so you might think that new bone was added anteriorly. But, if you look specifically at the sites of growth on the bone as revealed by vital staining and similar techniques, very little change occurs at the chin and most of the growth is posteriorly (B). Superimposing on the chin correctly shows that the body of the mandible grows
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{{PAGE_61}} longer by apposition of bone on the posterior surface, and the ramus grows higher by endochondral replacement at the condyle and by surface remodeling.
Pattern of Mandibular Growth (cont.) From cephalometric tracings superimposed on the cranial base, the overall growth pattern of the mandible looks like this: the bone moves downward and forward, taking the teeth with it (Image 1). The position of the TM joint can change because of changes in the posterior cranial base, but usually it remains about in the same place. If the x-ray tracings are superimposed at the chin so that the anterior mandible is held constant, then it appears that the mandible grows upward and backward (Image 2). In fact, this is where new bone is added, by a combination of endochondral replacement at the head of the condyle and surface apposition. Can you visualize the correctness of the statement that the mandible grows upward and backward, but the effect of this growth is a downward and forward translation of the chin? If that’s clear, you understand an important concept.
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{{PAGE_62}} Image 1, superimposition of a growing patient, registered on the cranial base: Superimposed on the cranial base, the maxilla, mandible, and teeth all appear to have moved downward and forward with growth. The red tracing represents the second time point.
Image 2, superimposition registered on the chin: Superimposition on the chin shows the correct pattern of mandibular growth: growth is upward and backward at the condyle and ramus.
Remodeling Resorption
Nowhere is there a better example of remodeling resorption than in the backward movement of the ramus of the mandible. During growth, new bone is added on the posterior surface of the ramus. At the same time, bone is removed—large quantities of bone—from the anterior surface of the ramus. Bone from the tip of the condylar process early in life can be found at the anterior surface of the ramus some years later. The body of the mandible grows longer as the ramus moves away from the chin.
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Growth by Remodeling of the Mandible
How is this possible? Remember the previous cartoon: this movement occurs the same way as a wall could be moved by removing stones from the front side and adding them to the back.
Looking at mandibles at different ages, you might think there had to be a growth center somewhere under the teeth, so the chin could grow forward away from the ramus. But that is not possible, since interstitial bone growth is impossible. Instead, the ramus remodels. What was the posterior surface at one time becomes the center at a later date, and eventually may become the anterior surface and then disappear.
Removing bone from the posterior surface of the ramus also makes space available for the molar teeth to erupt.
{{PAGE_64}} Growth by Remodeling of the Mandible (cont.)
Looking down on top of the mandible, the effect of this remodeling can be seen clearly. This is the type of superimposition that metallic implants make possible. Note that surface remodeling also has made the bone wider.
There’s no midline suture like the one for the maxilla, so the ramus also is widened by surface remodeling. The old condyles are totally resorbed after a while, as the ramus widens by removing bone from the inside and adding it outside.
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{{PAGE_65}} Summary: Growth of the Mandible
Mandibular growth can be summarized like this:
- a large amount of bone is added on the posterior and superior surfaces of the ramus
- nearly as much bone is removed from the anterior surface of the ramus
- there are smaller remodeling changes elsewhere
- bone is added to some outer surfaces and removed from some inner surfaces, especially in the extensive remodeling of the ramus.
Skeletal Growth: Alveolar Processes of Maxilla and Mandible
In talking about craniofacial bone growth, we have made little mention of the alveolar processes of the maxilla and mandible. In both jaws, growth of the bone that supports the teeth is an important aspect of the overall growth process.
One way to think about it is that the mandible grows downward away from the maxilla, creating more space between the jaws. As the jaws grow, the teeth are actively erupting (they have to in order to maintain contact), and as they erupt they bring alveolar bone with them, so that the alveolar processes become taller. Note in this cephalometric superimposition how the teeth erupted to compensate for greater downward movement of the mandible than the maxilla. If new alveolar bone
{{PAGE_66}} didn’t form, the teeth would just grow right out of the bone. We’ll be looking more at what happens to the teeth during growth in the later part of this course.
Summary To summarize the important points: First, you certainly should understand that bone cannot grow interstitially, and the growth of the facial skeleton cannot be explained in that way. Where interstitial growth is important for the skeleton, a layer of cartilage in that area does the growing, and then bone replaces it. Second, with regard to the sites and types of growth in the cranium and cranial base:
- Growth of the cranium occurs largely at the sutures, with a little surface remodeling;
- The cranial base grows largely by endochondral replacement at the mid-line synchondroses, but also by apposition at sutures laterally; Additionally, with regard to the sites and types of growth in the jaws and face:
- Growth of the maxilla and associated structures is a combination of growth at sutures and surface remodeling. As the maxilla is translated downward and forward during growth, bone fills in at the superior and posterior sutures and is added at the tuberosity;
- The mandible grows largely by apposition and remodeling resorption of the ramus, and by endochondral replacement at the condyles;
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{{PAGE_67}}
- The alveolar processes of both jaws grow as the teeth erupt, bring bone with them.
Self-Test Referral Now take the self-test in the following section of this module to ensure that you understand what you have learned. Before you do, be sure you have read the assigned material in Contemporary Orthodontics (5th edition: pages 33-40; 4th edition: pages 40-47).
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3. Theories of Craniofacial Growth
Introduction
Introduction
Before viewing this program, you should have looked at the module entitled “The Nature of Craniofacial Growth,” which reviews the principles of skeletal growth and describes the sites and types of growth in the craniofacial skeleton.
This program focuses on the determinants of craniofacial growth, that is, why the bones of the cranium and face grow in the way they do. To take advantage of growth for clinical treatment and even manipulate it to our advantage, we must understand what controls or determines it.
Learning Objectives
The objective of this program is to review and put in perspective the three major theories of craniofacial growth:
- Theory 1 – Bone at sutures and surfaces is the primary determinant of its own growth
- Theory 2 – Cartilage is the primary determinant of skeletal growth, with bone and sutures reacting passively
- Theory 3 – The soft tissue matrix is the primary determinant of growth, while bone and cartilage both are secondary followers
After viewing the program and doing the reading (40-50 in the 5th ed or pages 47-58 in the 4th ed of Contemporary Orthodontics), be sure that you are able to:
- indicate the strengths and weaknesses of each theory
- describe the mechanism of growth for the cranium, cranial base, maxilla and mandible from a current perspective
- describe the growth of facial soft tissue
Definitions, Suture Theory
Definitions
Before we begin our review of growth theories and what they imply for growth control, some important terms must be defined:
Site of growth: Simply an area where growth is occurring
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{{PAGE_69}} Center of growth: A site of growth that has the ability to grow on its own, independently of its surroundings—it contains the information to control growth
All centers of growth are also sites, but not all sites are centers. Growth at some sites occurs only in response to growth in other areas. Growth at centers is internally stimulated and controlled.
Definitions (cont.)
Mode of growth: The way it occurs. In the case of skeletal growth, there are two possible modes: replacement of cartilage (endochondral ossification) or direct apposition of bone (intramembraneous ossification)
Mechanism: How growth changes occur at a higher level, such as downward and forward movement of the jaws or expansion of the cranial vault
Determinant: The cause of the observed growth changes (and therefore what controls them)
Suture Theory: Harry Sicher
The suture theory of craniofacial growth was popularized by Harry Sicher, an Austrian anatomist who came to the United States prior to World War II.
Dr. Sicher observed that new bone was formed at the synchondroses of the cranial base, at the mandibular condyle, and at the sutures of the cranial and facial bones. He theorized that pressures created by formation of new bone at these sites literally pushed the bones apart.
The theory says, therefore, that in the absence of cartilage, the intramembranous bones are able to determine their own growth. For example, Sicher believed that growth at the sutures of the maxilla caused it to be translated downward and forward.
{{PAGE_70}} Suture Theory: Sites vs. Centers
Let’s characterize the suture theory using the terms we just defined. Sicher’s theory was that sutures are both sites and centers of skeletal growth; and in his view, so were synchondroses, condylar cartilage, and at least to some extent, periosteal surfaces.
To him, the mode of growth was somewhat irrelevant, since there was no difference in how the two modes were controlled. The mechanism of growth movements was that the bones were pushed to a new position by growth at their points of attachment (the sutures of the cranium and maxilla, the synchondroses of the cranial base, the condyle of the mandible). The determinant was genetic information that operated at those areas.
{{PAGE_71}} Sicher Suture Theory
- Sites and Centers:
- sutures, synchondroses, condylar cartilage
- Mechanism:
- push by growth in these areas
- Determinant:
- genetic information operating locally
Suture Theory: Sites vs. Centers (cont.)
It is clear now that sutures and periosteal surfaces are not primary determinants of craniofacial growth and must be considered sites, but not centers, of growth. Growth at sutures does not push bones apart. Instead, when sutures are pulled apart, growth occurs to fill in the gaps.
Two lines of evidence lead to this conclusion. First, when sutures are transplanted to different locations, they fail to grow as centers would. Second, in both animal experiments and in humans with growth problems, it can be shown that sutures respond to outside influences. If the cranial or facial bones are pulled apart at the sutures, new bone will fill in and the bones end up bigger than they would have been otherwise. If the sutures are compressed, growth is inhibited. The sutures react rather than acting independently.
Why did Sicher, a highly intelligent and respected scientist, think as he did? At the time he proposed his theory (in the 1940s), the role of genetics in controlling growth was just becoming clearer, and it seemed obvious that direct genetic control was the explanation. The “sutural push” mechanism followed logically from that assumption.
{{PAGE_72}} Evidence Against Sutures as Growth Centers
- Transplantation experiments
- When sutures are transplanted to another location, they fail to grow.
- Reaction to manipulation
- When sutures are pulled or pushed, the pattern of growth is affected.
Cartilage Theory
James H. Scott
The second major theory, popularized by the Irish anatomist James H. Scott in the 1950s, is that the determinant of craniofacial growth, even in areas distant from the cartilage locations, is the growth of cartilages. Cartilage growth would push the bones to new positions; in response, bone would fill in at sutures and surface remodeling would occur.
The fact that in many areas cartilage does the growing while bone merely replaces it makes this theory attractive.
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Mandibular Growth
Scott accepted the evidence that sutures reacted rather than acted on their own, and so did not push bones apart by growing independently. He agreed with Sicher about “cartilage push” by the cartilages of the cranial base and the mandible as a major mechanism for cranial and facial growth, and he offered a clearer explanation of how growth at the mandibular condyle would control the growth of the mandible.
One way to visualize the mandible is by considering it as analogous to the diaphysis of a long bone, bent into a horseshoe and with the epiphyses removed. Then the condylar cartilage represents “half an epiphyseal plate” on each end of the bone. If this represents the true situation, then indeed the cartilage at the condyle should be a growth center, exactly analogous to epiphyseal cartilage except that there was bone only on one side.
{{PAGE_74}} Maxillary Growth
Growth of the maxilla, however, would be much harder to explain as determined by cartilage. How could cartilage determine maxillary growth when there is no endochondral replacement involved in the growth of this bone?
There is cartilage in the nasal septum, however, and in the 1950s Scott hypothesized that the cartilaginous nasal septum serves as a “pacemaker” for other aspects of maxillary growth.
This diagram from Scott’s work shows the septal cartilage (yellow) at a fetal stage. Note that it is located so that its growth could pull the maxilla downward and forward. If the sutures on the maxilla served as reactive areas, they would respond by forming new bone as they were pulled apart by the forces created by the growing cartilage. Although the amount of cartilage in the septum decreases as growth continues, enough remains even into adult life to make the pacemaker role potentially possible.
{{PAGE_75}} Experimental Support
Two types of experiments have been used to clarify whether specific cartilages are true growth centers: (1) transplanting it to see if it still grows and removing it to see whether that area then fails to grow, and (2) removing it surgically to see what the effect on growth would be.
If transplanted cartilage continues to grow, it must have innate growth potential and can be considered an independent growth center. If doesn’t grow in its new location, it probably doesn’t have innate growth potential and can’t be an independent growth center.
Similarly, if a cartilage is removed surgically and that area no longer grows, it may be a growth center (but damage from the surgery could be another explanation). But if the area grows just as well without the cartilage, it definitely wasn’t a growth center.
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Experiments:
Cartilage as a Growth Center
- Transplantation experiments
- Some transplanted cartilage grows well
- Epiphyseal plate – grows well
- Cranial base synchondrosis – grows well?
- Nasal septum – grows sometimes
- Mandibular condyle – doesn’t grow
- Some transplanted cartilage grows well
- Surgical removal experiments
- Removing cartilage affects growth, but why?
Experimental Support (cont.) When cartilage from an epiphyseal plate is transplanted, it grows very nicely—so the epiphyseal plates meet the criteria for a growth center.
Cartilage from cranial base synchondroses is difficult to get at in order to transplant it, and transplantation experiments have not given a clear picture. This cartilage, like the cartilage of the epiphyseal plates, is a remnant of the original skeletal cartilage. It seems reasonable then to consider it a growth center, especially in light of what happens in patients with a genetic mutation that prevents its growth (discussed later).
Transplanting cartilage from the nasal septum gives equivocal results. Sometimes it grows reasonably well, sometimes it doesn’t.
When mandibular condyles are transplanted, they hardly grow at all.
Based on this evidence, we have to doubt that the mandibular condylar cartilage could possibly act as a growth center, and we would have some doubts about the nasal septum.
Surgical Removal of the Nasal Septum Removing the presumed growth center for a craniofacial structure ought to seriously affect growth of that structure.
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{{PAGE_77}} The impact of removing a segment of the cartilagenous nasal septum from a rabbit is shown here. The lower rabbit (image 2) had a piece of the septum removed at an early age, while his brother, shown above (image 1), did not. Obviously, losing that little piece of cartilage cost a great deal of growth in the midface. It can be argued that the surgery itself, not the loss of the cartilage, caused the deficient growth, but removing the cartilage decreases growth so much that it looks to most observers as if growth potential was lost along with it.
Loss of Nasal Cartilage after Trauma When this man sought treatment for his midface deficiency, we were intrigued to learn that following an accident at age 7, all of his nasal cartilage was removed. He certainly looks like a human analog of the experimental rabbit, doesn’t he? Remember that the lack of growth in the area could be due to the original injury or the surgery rather than to the loss of the cartilage growth center, but in humans also there is decreased forward growth of the maxilla when the nasal cartilage is removed. Is the nasal septum a growth center, and if so, does it determine maxillary growth? At least in part, perhaps it does.
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{{PAGE_78}} Maxillary Growth and Achondroplasia
The maxilla is affected by cartilage growth in another way: because it is attached to the cranial base, the maxilla is pushed forward as lengthening of the cranial base occurs. Is this evidence of “cartilage push” from growth at the synchondroses? An interesting “experiment of nature” sheds some light on this.
This girl has moderately severe achondroplasia, a condition in which the primary growth cartilages fail to grow because of a genetic mutation. She has short arms and legs because of lack of growth at the epiphyseal plates. Note the midface deficiency. The maxilla has not been pushed forward because of lack of growth at the synchondroses of the cranial base, which are affected in the same way as the epiphyseal plates. It looks as if the cranial base lengthening is due to, or at least greatly affected by, a push from growth at the synchondroses.
That kind of push is important in midface development, and Scott cited it in support of the cartilage theory, but the push doesn’t open space at the sutures of the maxilla. Some kind of pull is necessary for that, and Scott’s theory was that growth of the septal cartilage pulled the maxilla forward and opened space at the sutures.
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{{PAGE_79}} Mandibular Growth and Achondroplasia
Take a good look at the mandible in this achondroplasia patient. You can see that the midface wasn’t pushed forward by lack of growth at the synchondroses and the nose is small and underdeveloped—but the mandible seems to have grown almost normally.
What does that imply about the condyle as a growth center, with its growth determined by its internal genetic information? It doesn’t look as if the condyle was affected by the genetic mutation in the same way as the other cartilaginous growth centers.
Remember what you learned earlier about the origin of the cartilage of the mandibular condyles. It isn’t part of the chondocranium, the primary cartilage that is the origin of the cranial base. When does the cartilage that becomes the condylar cartilage first appear? That’s right, weeks after the primary cartilage. Where does it arise? Yes, in mesenchyme rather far away from the primary cartilage. So a mutation affecting primary cartilage might well not affect it.
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Condylar Fracture
The effect of removing the mandibular condyle can be observed in inadvertent human experiments, because the condyle, cartilage and all, gets removed rather frequently in growing children through trauma. The neck of the condyle is a fragile area, and when the jaw is struck sharply on one side, the condylar process on the other side often fractures. Usually when this happens, the condyle fragment is retracted well away from its previous location by the pull of the lateral pterygoid muscle, and it resorbs over a period of time.
The condyle literally has been removed when this happens, and the cartilage is gone. If this occurred at an early age and the cartilage was an important growth center, severe growth impairment would occur. As recently as the 1960s, standard texts stated that early fracture of the mandibular condyle was a devastating injury because of the growth problems that would follow.
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Condylar Fracture (cont.)
Two studies in Scandinavia in the 1960s disproved the idea that early condylar fracture always produced a growth problem. The studies showed that after fracture of the condylar process in children, there was about a 75% chance that the condyle would regenerate and the mandible would grow normally.
In experimental animals, the condyle resorbs after a fracture, but a new one regenerates directly from the periosteum at the fracture site, complete with a new layer of cartilage. Presumably the same thing happens in human children. The human observations of lost condyles lend no support to the idea that the condyle is a growth center. We’ll come back to the 25% of children with a later growth problem shortly.
{{PAGE_82}} 75%: condyle regenerates, no growth deficit
25%: altered growth after injury, growth problem occurs (usually growth deficit)
Functional Matrix Theory
Melvin Moss
If neither bone nor cartilage is the determinant for skeletal growth, what does determine it? The “functional matrix” theory was offered as an alternative in the 1960s by Melvin Moss, a dentist-anatomist at Columbia University. It became the subject of much debate in orthodontics in the 1970s because its implications changed clinical practice.
In its simplest form, Moss’s theory says that growth in the cranium and face occurs as a response to functional needs and is mediated by the soft tissue adjacent to the skeletal units. In this conceptual view, the external soft tissues grow, and both bone and cartilage merely react.
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{{PAGE_83}} Natural Experiments
Growth of the cranial vault illustrates this view of skeletal growth very well. There can be little question that under normal circumstances the brain case grows in direct response to the growth of the brain. The pressure exerted by the growing brain separates the bones at the sutures, and new bone passively fills in so that the brain case fits (and protects) the brain.
Two “experiments of nature” illustrate this very well. First, when the brain is very small or does not grow, the cranial vault also is very small, and the condition of microcephaly (small head) results. In this case, the size of the head is an accurate representation of the size of the brain.
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Normal # Microcephaly
Natural Experiments (cont.)
The second natural experiment is the condition called hydrocephaly. When reabsorption of cerebrospinal fluid is impeded, the fluid accumulates and intra-cranial pressure builds up. The increased pressure impedes development of the brain, so the hydrocephalic person may have a small brain and be mentally retarded, but it also leads to enormous growth of the cranial vault.
Uncontrolled hydrocephaly may result in a cranium the size of a basketball due to pressure separating the sutures where bone then fills in.
Another example is that an enlarged or small eye will cause a corresponding change in the size of the orbit by the same mechanism: pressure from within the orbital cavity shapes the bone around it.
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{{PAGE_85}} No Cartilage Growth Centers?
Professor Moss theorized that the determinant of growth of the nasal and oral structures is similar to that of the cranial vault, and that they grow because of functional demands from the nasal and oral cavities.
The theory does not make it clear how functional needs are transmitted to the tissues of the mouth and nose, but it does say that the cartilages of the cranial base, nasal septum and mandibular condyles are unimportant as determinants of growth and are not growth centers. To Moss, the cartilages of the cranium and face merely react to outside influences, just as sutures react. He argued strongly that the synchondroses of the cranial base respond to the growth of the brain and behave like sutures, and that when the nasal cartilage is removed, any growth deficit is just due to the surgery.
The cartilage of the mandibular condyle was viewed in the same way, as reacting to growth of the mandible rather than controlling it. The functional matrix theory predicts that if proper function could be maintained, loss of the condylar cartilage in a child would have no effect on growth of the mandible.
Loss of Condylar Cartilage
We have already seen that in 75% of the children who suffer a condylar fracture, there is no problem with subsequent mandibular growth. What about the other 25%? Could some interference with
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{{PAGE_86}} function be the cause of their growth problem?
The answer is yes. It has been known for many years that mandibular growth is greatly impeded by ankylosis of the mandible. Ankylosis of a joint is defined as fusion across it (by scar tissue in most cases) so that motion is prevented or extremely limited. Don’t confuse this with what happens with an ankylosed tooth. The tooth is fused to the alveolar bone and can’t move at all; the ankylosed joint can’t move normally but often does have some degree of motion.
This boy’s pediatrician noticed that his facial asymmetry appeared to be increasing and referred him for further evaluation. From the history and routine x-ray examination it did not appear that there was anything unusual about the left mandibular condyle.
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{{PAGE_87}} Image 1, ¾ view: Note the mandibular asymmetry.
Image 2, frontal view: Note the mandibular asymmetry.
{{PAGE_88}} Image 3, smiling view: Note the mandibular asymmetry. Image 4, profile view: Note the mandibular deficiency.
Loss of Condylar Cartilage: Radiographic View
When special laminagraphic x-rays were made, an old fracture of the left condylar neck was observed. In this instance, the condyle was not retracted by the muscles, but instead was bent over and partially locked in the joint area. Although the boy could open his mouth, translation of the condyle down to articular eminence was limited and the affected side did not grow normally.
{{PAGE_89}} Loss of Condylar Cartilage: Surgical Repair
In this case the damaged condyle was removed surgically, and a section of rib taken at the costo-chondral junction (image 1) was used as a graft to replace it. It can be seen wired in place in image 2.
The piece of rib was chosen because when it was grafted in place, there would be cartilage covering the joint between the graft and the tempormandibular fossa. Why the cartilage on the new “condylar process”? Not because it would be necessary for future growth, but because if raw bone were placed into the joint, the bone of the graft probably would unite with the bone of the fossa, producing an even worse ankylosis. Some material to separate the bony areas is needed. The surgeon could have used a sheet of Teflon or other inert material, but Mother Nature uses cartilage, and in this case the surgeon did too.
Image 1, costo-chondral graft: Material from the rib is used because is includes cartilage to prevent bony union with the temporal bone, not because cartilage is necessary for growth.
Image 2, intra-operative view of costo-chondral graft: An extra-oral approach is necessary to graft bone from the rib to the ramus.
Loss of Condylar Cartilage: Post-Repair Growth
The facial asymmetry was greatly improved, and the mandibular ramus continued to grow after the damaged condyle had been removed and replaced with the rib graft. In the profile view (image 4) you can detect the scar from the extra-oral surgical approach, but already it’s hardly visible.
Both the growth deficit when motion was limited following the fracture, and the excellent growth after the ankylosis was released by removing the condyle, support the functional matrix view that the soft tissue environment, not the cartilage of the condyle, is the determinant of mandibular growth.
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{{PAGE_90}} Image 1, ¾ view: Note the improved symmetry. Image 2, frontal view: Note the improved symmetry.
{{PAGE_91}} “Functional Matrix”
The term “functional matrix” can be misunderstood easily, because in order to grow normally, the mandible really doesn’t have to be doing anything except opening a reasonable amount.
Remember that when opening, the mandible first rotates in a hinge motion and then translates down the articular eminence. In order to grow normally, it’s not enough to be able to open just on a hinge. The condyle has to be able to translate. Scarring of the capsule around the condyle can impede translation, and it’s the extent of the soft tissue injury that accompanies a condylar fracture, not the extent of injury to the bone, that determines how well it will grow later.
Why did normal growth occur after a condylar fracture in 75% of the children, and growth problems develop in 25%? In the fortunate 75%, the soft tissues around the TM joint were uninjured or minimally injured, and no scarring to restrict translation occurred. The unfortunate 25% had more extensive soft tissue injury and subsequent scarring.
{{PAGE_92}} So what was the functional matrix that controlled mandibular growth? It was the soft tissues that surround the bone. What determines the growth of the soft tissues? At this point we have to say that it’s largely genetically determined.
This leads to another term that you must understand: epigenetic, which means genetic control at a distance. The bone of the mandible (and the condylar cartilage) reacts to the soft tissue growth around it, and the ultimate determinant appears to be the genetically-controlled soft tissue itself.
But the soft tissues can be affected by environmental influences, trauma being an excellent example. We have seen how scarring of soft tissues can impede mandibular growth. What would happen to growth of the maxilla if the facial soft tissues over it were scarred by trauma, as in this boy injured in an automobile accident? You should be thinking that the maxilla would not grow downward and forward as it normally would because the growth of the soft tissue surrounding it would be affected.
Absence of Nasal Cartilage
As you think about the importance of soft tissue in craniofacial growth, keep in mind that like bone and cartilage not all soft tissues are created equal with regard to their ability to grow independently.
This girl was born with cebocephaly, characterized by total absence of all the nasal structures and the areas of the brain to which they project. Almost all such children die at birth, but this one survived for several years and it was possible to study her facial growth.
{{PAGE_93}} With the absence of the nasal structures, including the cartilage, there was an obvious severe deficiency in midface growth, more severe than just the absence of the nose. This is another experiment of nature that suggests a role for the nasal cartilage in determining maxillary growth.
Achondroplasia
Look again at achondroplasia. In this condition that we considered previously, the primary growth cartilages (those formed first in embryonic life) do not grow normally. Such individuals are characterized by extremely short arms and legs, as you would expect—and also by severe midface deficiency.
This occurs because the cranial base does not lengthen as it should (although growth of the brain is normal) and so the maxilla is not pushed forward. This is, of course, evidence that the cartilage of the cranial base is an important determinant of growth in that area. In achondroplasia, however, the mandible is not affected at all—note its normal size. The nose is small, but it’s hard to tell whether the midface deficiency also relates to diminished activity of the nasal septal cartilage.
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Summary
Growth of the Cranial Vault
Let’s summarize. What determines growth of the cranial and facial units? Consider first the cranial vault, in the context of our descriptive terms:
Sites of growth: primarily sutures, some remodeling of surfaces Centers of growth: none Mode: intramembraneous ossification Mechanism: separation of sutures → growth to fill in the gaps Determinant: growth of brain → pressure to separate the sutures
Growth of the Cranial Vault (cont.)
What’s the best evidence? The experiments of nature with decreased growth of the brain (microcephaly) and increased intracranial pressure (hydrocephaly).
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Growth of the Cranial Base
For the cranial base: Sites of growth: primarily synchondroses, some apposition at sutures and remodeling of surfaces away from the midline Centers of growth: synchondroses Mode: primarily endochondral ossification Mechanism: interstitial growth of cartilage → pressure to separate the bones Determinant: expression of genetic information at the synchondroses
Growth of the Cranial Base (cont.)
What’s the best evidence? The natural experiment of achondroplasia, in which failure of growth at the synchondroses occurs, as it also does at the epiphyseal plates of the long bones.
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{{PAGE_96}} Clinical photo showing a young patient’s face in frontal and profile views, illustrating the subject of naso-maxillary complex growth.
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{{PAGE_97}} Image 1, a girl with achondroplasia: Her midface deficiency is the result of inadequate growth at the synchondroses of the cranial base. Image 2, a boy with an injury to the soft tissue of the midface: As a result of impeded soft tissue growth, the maxilla has not grown down and forward.
Growth of the Mandible
For the mandible: Sites of growth: surfaces of bone, especially remodeling of ramus; condylar cartilage Centers of growth: none Mode: primarily intramembraneous ossification; endochondral ossification at condyle Mechanism: soft tissue pull → reactive growth at condyle and surfaces Determinant: epigenetic at soft tissues
Growth of the Mandible (cont.)
What’s the best evidence for mechanism and determinant? Growth (or growth distortion) after condylar fracture. Remember, 75% of children who had a condylar fracture grew normally afterward, while 25% had a growth problem—because of more severe soft tissue injury near the condyle.
{{PAGE_98}} Image 1, ¾ view: Note the mandibular asymmetry. Image 2, frontal view: Note the mandibular asymmetry.
{{PAGE_99}} Image 3, smiling view: Note the mandibular asymmetry.
Image 4, profile view: Note the mandibular deficiency.
Theories of Craniofacial Growth
Sometimes students think learning about theories is a waste of time. It’s hard to realize that even the questions one asks are based on some level of theoretical understanding. For many years nobody tried to modify facial growth—because they “knew” that the sites of growth were genetically controlled and therefore growth could not be modified. The new understanding of how and why jaws grow has led quite directly to clinical advances in treating growth problems.
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{{PAGE_100}} You should not be surprised, either, if current understanding proves to be inadequate long before you finish a clinical career. You’ll have to understand the theories of the early 21st century to keep up with early 21st century practice. But to follow the further development of concepts, you have to know something of the background—so what you have learned at this point will stand you in good stead even if new theories are developed.
Now, be sure that you have read pages 40-50 in the 5th ed or 47-58 in the 4th ed of Contemporary Orthodontics, then take the self-test in the following section to consolidate what you have learned and to be sure that you have understood the material.
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