Variance Estimation, Design Effects, and Sample Size Calculations for Respondent-Driven Sampling

Hidden populations, such as injection drug users and sex workers, are central to a number of public health problems. However, because of the nature of these groups, it is difficult to collect accurate information about them, and this difficulty complicates disease prevention efforts. A recently developed statistical approach called respondent-driven sampling improves our ability to study hidden populations by allowing researchers to make unbiased estimates of the prevalence of certain traits in these populations. Yet, not enough is known about the sample-to-sample variability of these prevalence estimates. In this paper, we present a bootstrap method for constructing confidence intervals around respondent-driven sampling estimates and demonstrate in simulations that it outperforms the naive method currently in use. We also use simulations and real data to estimate the design effects for respondent-driven sampling in a number of situations. We conclude with practical advice about the power calculations that are needed to determine the appropriate sample size for a study using respondent-driven sampling. In general, we recommend a sample size twice as large as would be needed under simple random sampling.
Introduction
To understand and control the spread of HIV, it is important to have accurate information about hidden populations such as injection drug users and sex workers.1 However, these populations are difficult to study with standard sampling methods because sampling frames do not exist. The need to gather information about such hidden populations is not limited to public health. Social scientists and policy-makers are interested in many other hidden populations such as undocumented immigrants, artists, and members of some social movements.
In response to the problem of studying hidden populations, a new statistical approach called respondent-driven sampling has been developed.2–4 Respondent-driven sampling data are collected via a link-tracing (snowball) design, where current sample members recruit future sample members. For many years, researchers thought it was impossible to make unbiased estimates from this type of sample. However, it was recently shown that if certain conditions are met and if the appropriate procedures are used, then the prevalence estimates from respondent-driven sampling are asymptotically unbiased.4 For example, respondent-driven sampling can be used to estimate the prevalence of HIV among drug injectors in New York City.
Despite the progress that has been made in making prevalence estimates, less is known about the sample-to-sample variability of these estimates. This gap in knowledge can lead researchers to construct inaccurate confidence intervals around estimates and to undertake studies with sample sizes that are too small to meet study goals. Filling this important gap in the respondent-driven sampling literature, this paper explores issues related to the sample-to-sample variability of estimates. The paper consists of four main parts. First, we briefly review the existing respondent-driven sampling methodology. Next, we develop and evaluate a bootstrap procedure for constructing confidence intervals around respondent-driven sampling estimates. Then, we estimate the design effect of the prevalence estimates in a number of simulated and real populations. The paper concludes with advice about the sample sizes needed for studies using respondent-driven sampling. In general, we recommend a sample size twice as large as would be needed under simple random sampling.
Review of Respondent-driven Sampling
A respondent-driven sample is collected with a link-tracing design, similar to a snowball sample.5–7 The sampling process begins with the selection of a set people in the target population who serve as seeds. After participating in the study, these seeds are each provided with a fixed number of unique recruitment coupons, which they use to recruit other people they know in the target population. After participating in the study, these new sample members are also provided with recruitment coupons, which they then use to recruit others. The sampling continues in this way, with subjects recruiting more subjects, until the desired sample size is reached.2–4 Experience has shown that this sample selection method is practical and it has already been used to study a number of different hidden populations, including jazz musicians,8 drug injectors,2 Latino gay men,9 and MDMA/Ecstasy users.10
In addition to collecting information that addresses the substantive focus of the study, a researcher using respondent-driven sampling must also collect two other pieces of information: the recruiter of each sample member and the number of relationships that each sample member has in the population of interest (sometime called degree of each person). This additional information is necessary because the estimation procedure is a variation of the traditional sampling and estimation process. Ordinarily, researchers take a sample and then use that sample to make inferences about a population (Figure 1a). However, when the data are collected with respondent-driven sampling, it is very difficult (and maybe even impossible) to make inferences from the sample directly to the population. Fortunately, such data can be used to make inferences about the social network connecting the hidden population, and this information about the social network can be used to estimate the prevalence a specific trait (Figure 1b).3 Within this new framework, unbiased estimation becomes possible.1 A more detail description of the estimation procedure and the conditions under which it is unbiased is available in the literature.4Figure 1Schematic of both traditional sampling and estimation and respondent-driven sampling. By not attempting to estimate directly from the sample to the population, respondent-driven sampling avoids many of the well-known problems with estimation from snowball samples.
While the ability to make unbiased prevalence estimates represented a step forward for the study of hidden populations, it was an incomplete one. In order for respondent-driven sampling to be practical as a methodology, a procedure is needed in order to put confidence intervals around these prevalence estimates.
Confidence Intervals
Before introducing the confidence interval procedure, we first need to introduce some language with which to describe the hidden population. In this paper we will consider the situation of a hidden population that is made up of two mutually exclusive and collectively exhaustive groups that, for the sake of generality, we will call group A and group B. The groups could be, for example, people with and without HIV. The proportion of the population in group A will be called PA. A point estimate of this prevalence is useful, but it is difficult to interpret without some measure of the precision of the estimate. One common way of describing this precision is with a confidence interval that provides a range within which the researcher expects to find the true population value with some level of certainty. Procedures to generate confidence intervals are well developed in the case of simple random sampling,12,13 but researchers using a complex sample design, where not all units have the same probability of selection, are often left without guidance. Despite numerous warnings,7,14 researchers often ignore the fact that their data were collected with a complex sample design and construct confidence intervals as if they had a random sample. This approach of ignoring the sampling design, which we will call the naive method, will generally cause researchers using respondent-driven sampling to produce confidence intervals that are too small. These incorrect confidence intervals are not just a technical concern; incorrect confidence intervals can lead to incorrect substantive conclusions.
In order to produce better confidence intervals, we will develop and evaluate a bootstrap method specifically designed for respondent-driven sampling.2 Although an analytic approach would be preferable,3 bootstrap methods are commonly used for variance estimation from complex sample designs because analytic solutions are often not possible.16,17 In the next sections, we will describe our proposed bootstrap procedure and then evaluate its performance using computer simulations.
Proposed Bootstrap Procedure
The general idea of the bootstrap procedure is to use the observed sample to generate a set of replicate samples. Then this set of replicate samples is used to produce a set of replicate estimates. By examining the variation in these replicate estimates, one can construct a confidence interval around the original point estimate. This three-step process can be seen in Figure 2.17Figure 2Schematic of the procedure for producing confidence intervals.
The first step in our procedure is the resampling step. In traditional bootstrapping, this resampling is done by randomly sampling with replacement from the original sample until the replicate sample is the same size as the original sample. This resampling procedure is well grounded theoretically for the case where the original sample is collected via simple random sampling.17 However, as described previously, in respondent-driven sampling there are dependencies in the sample selection process, and so we must use a modified resampling procedure which mimics these features. The modification of the resampling step is the main way that this approach deviates from traditional bootstrapping techniques.
Under our proposed procedure we divide the sample members into two sets based on how they were recruited: people recruited by someone in group A (which we will call Arec) and people recruited by someone in group B (which we will call Brec). For example, Arec could be the set of all sample members who were recruited by someone with HIV. Note that this set could include both people with and without HIV. In order to mimic the actual sampling process, the resampling begins when a seed is chosen with uniform probability from the entire sample. Then, based on the group membership of the seed, we draw with replacement from either Arec or Brec. For example, if the seed chosen for the replicate sample was a sample member with HIV, we draw from the set of sample members who were recruited by someone with HIV. Next, we examine the group membership of this newly chosen person and then draw again with replacement from either Arec or Brec.4 This process continues until the bootstrap sample is the same size as the original sample. Overall, this resampling scheme preserves some, but not all, of the dependencies that exist in the respondent-driven sampling data collection.5
Once the bootstrap samples are selected, we move to step 2 in Figure 2: the estimation step. Here we use the normal respondent-driven sampling estimation procedure on each of the R replicate samples to produce a set of R replicate estimates. Finally, in step 3 of the bootstrap procedure, the R replicate estimates are converted into a confidence interval. One way to do this would be to construct a 90% confidence interval based on the normal approximation,
where the estimated standard error, , is the standard deviation of the replicate estimates. While this approach is reasonable, it has two main disadvantages. First, it forces the confidence intervals to be symmetric, which can reduce accuracy, and second, it can produce intervals with endpoints outside of the range [0, 1].
Fortunately, there are several improvements over this standard error method, and in this paper we will use the percentile method.6 When using the percentile method, we define the endpoints of the 90% confidence interval to be the two replicate estimates, such that 5% of the replicate estimates fall below the interval, and 5% of the replicate estimates fall above the interval. For example, if a researcher generated 2,000 bootstrap replicates, a 90% confidence interval would be defined by the 100 and 1,900 ordered replicate estimates. As we shall see in the next section, the proposed resampling scheme combined with the percentile method produces confidence intervals that are generally good in an absolute sense and better than the naive method.7
Comparing the Naive and Bootstrap Methods
The quality of a confidence interval procedure can be measured by calculating φ, the percentage of proposed intervals that contain the true population value. For example, if we took 1,000 samples from the population and produced a 90% confidence interval from each of these samples, then 900 out of 1,000 of these confidence intervals should include the true population prevalence.8 Unfortunately, due to resource constraints, we cannot repeatedly sample from real hidden populations. However, using computer simulations, we can construct hypothetical hidden populations and then repeatedly sample from them to evaluate the coverage properties of the different confidence interval procedures. Further, in these computer simulations we can systematically vary the characteristics of the hidden population in order to understand the effects of population and network characteristics on the quality of the proposed confidence intervals.
For example, to explore how network structure affects the quality of the confidence intervals, we constructed a series of hypothetical populations that were identical except for the amount of interconnectedness between the two groups. More specifically, we varied the ratio of the actual number of cross-group relationships to the number of possible cross-group relationship, and thus, our measure of interconnectedness, I, can vary from 0 (no connections between the groups) to 1 (maximal interconnection). All populations were constructed with 10,000 people, 30% of which were assigned a specific trait, for example HIV. Next, we began to construct the social network in the population by giving each person a number of relationships with other people in the population. The number of relationships that an individual has is called her degree. When assigning an individual’s degree we wanted to roughly match data collected in studies of drug injectors in Connecticut,2 so each person with HIV was assigned a degree drawn randomly from an exponential distribution with mean 20, and those without HIV were assigned a degree drawn from an exponential distribution with mean 10; later in this paper we will explore other degree distributions. Once the degrees were assigned, we insured that the population had the appropriate amount of interconnection between the groups.9
After each population was constructed, we took 1,000 samples of size 500, and for each of these 1,000 samples we constructed a confidence interval using both the naive method (i.e., ignoring the complex sample design and pretending to have a simple random sample) and the proposed bootstrap method. By seeing if each of these confidence intervals included the true population prevalence, we calculated  and . The results of these simulations are presented in Figure 3 and reveal two important features. First, the figure shows that, for the populations used in these simulations, the proposed bootstrap procedure outperforms the naive procedure. Second, it shows that the bootstrap procedure also performs well in an absolute sense, meaning .
Figure 3Coverage probabilities of the naive and bootstrap procedure. Results indicate that the proposed bootstrap procedure outperforms the naive procedure and performs well in an absolute sense.
To test the robustness of these findings, we explored the coverage properties in a larger portion of the possible parameter space by varying the sample size, the proportion of the population in the groups, and the average degree of the groups (results not shown). To summarize these findings, in a few unusual portions of the parameter space, the proposed bootstrap procedure did not perform well in an absolute sense, but in most portions of the parameter space, the proposed procedure performed well.10 Additionally, in all cases the proposed bootstrap procedure outperformed the naive procedure. To conclude, in the situations that we have examined, the proposed bootstrap procedure works well in an absolute sense and better than the naive procedure. Further, these results seem robust. Therefore, until some superior procedure is developed, we recommend this bootstrap procedure for future researchers who wish to construct confidence intervals around prevalence estimates from respondent-driven sampling.
Design Effects
Even though respondent-driven sampling produces unbiased prevalence estimates and allows researchers to produce approximate confidence intervals, respondent-driven sampling may not be appropriate for all situations. The unbiasedness of the estimates does not ensure that any particular estimate will be equal to the true population value. Rather, just like all other unbiased estimators, sometimes the estimate will be too low or too high; only on average will the estimate equal the true population value. If the respondent-driven sampling estimates are too variable, then, even if they are unbiased, they might not be useful in practice. For example, we constructed a population with 30% prevalence of a specific trait, for example HIV, and repeatedly sampled from that population using respondent-driven sampling. To provide a benchmark for interpreting the sample-to-sample variability, we also repeatedly sampled from the population using simple random sampling (even though this would not be possible in a real hidden population). Figure 4 shows the distribution of prevalence estimates from these two methods. Both distributions center around 0.30, the true value, so both sampling methods produced unbiased estimates. But, the distribution of respondent-driven sampling estimates was more variable than the distribution of estimates under simple random sampling. A common way to quantify this difference is the design effect,12 which measures the increased variation of the estimates under respondent-driven sampling.11 That is,
where  is the variance of under respondent-driven sampling and  is the variance of under simple random sampling. Because respondent-driven sampling generally provides less information, we expect that the design effect will generally, but not always, be greater than 1. For example, the results in Figure 4 show a design effect of 2.8. In the next section we will explore the design effects for a range of different network structures to better understand the situations in which respondent-driven sampling is likely to be precise enough to be useful.
Figure 4Distribution of estimates from respondent-driven sampling and simple random sampling. The respondent-driven sampling estimates center around the true population value, 0.30, but they are more variable than the estimates from simple random sampling. This extra variation corresponds to a design effect of 2.8.
Simulation Results on Design Effects
Estimating the design effect requires comparing the variance of the prevalence estimate under different sampling methods. While the variability of the prevalence estimate under simple random sampling can be derived from basic probability theory,12 we must use simulations to discover the variability under respondent-driven sampling. Thus, as when we evaluated the confidence interval procedure, we constructed a range of populations and simulated repeated sampling from them. We observed several general patterns that seem to occur in all portions of the parameter space. First, generally, but not always, the design effects from respondent-driven sampling were greater than 1, which indicates that respondent-driven sampling estimates were less precise than estimates from simple random sampling. This finding is consistent with the literature on complex sampling designs, which generally finds that departures from simple random sampling lead to increased variability of estimates. Second, as the interconnectedness, I, increased, that is, as the two groups became more closely connected, the design effect decreased (see Figure 5). Third, the minimum design effect for a given interconnectedness occurred not when the two groups had the same average degree (DA = DB), but when the two groups had the same total degree, (PADA = PBDB) (see Figure 6). Fourth, the design effects were sensitive to the degree distribution assumed in the simulations. Previously in this paper we assumed an exponential degree distribution, but for specific subpopulations, such as drug injectors, the true functional form of the degree distribution is unknown. When we assigned a Poisson degree distribution for both groups, we observed much lower design effects, including some design effects below 1 (Figure 7); the reason for this change is currently unknown.12 Overall, these observations should be viewed with some caution because they have not been verified analytically due to the previously mentioned inability to develop closed-form expressions for the variance of the prevalence estimate under respondent-driven sampling.
Figure 5Design effect as a function of interconnectedness I. In general, as the interconnectedness increases the design effect decreases. Results are based on 10,000 replicate samples.Figure 6Design effect as a function of DA for different DB. In general, the minimum design effect, for a given interconnectedness, occurs when the two groups have the same total degree (PADA = PBDB). So if PA = 0.3 and PB = 0.7, then when DB = 10 the minimum design effect occurs when DA ≈ 23 and when DB = 20 the minimum occurs when DA ≈ 46. Results are based on 10,000 replicate samples.Figure 7Design effect as a function of interconnectedness for different degree distributions. In general, the design effects are smaller when the degree distribution of the groups is Poisson rather than exponential. Results are based on 10,000 replicate samples.
Taken together, these simulation results suggest that the design effect is a complex function of the network structure in the population.13 The simulation results also suggest that in some cases respondent-driven sampling can be quite blunt, with design effects as large as 10, but that in other cases it can be extremely precise, sometimes even more precise than simple random sampling.
Estimated Design Effects in Real Studies
The simulation results indicate that a range of design effects are possible. Therefore, an important question becomes: What are the design effects in populations that people actually study? Our best attempt to answer that question is presented in Table 1, where we report the estimated design effects from all studies that are currently available.14 To produce the estimated design effects we took the published estimates of PA and used them to estimate the variability of the prevalence estimates (). This variability is then compared to the published estimates of the variability under respondent-driven sampling ().15 We report only one design effect because, due to the symmetry of the two-group system, .
Table 1Estimated design effects from real respondent-driven sampling data.8–10 Sample sizes vary within the same study due to missing dataStudy descriptionStudy resultsPopulationLocationnTraitLatino gay menChicago69HIV+0.170.00240.00211.1Latino gay menSan Francisco72HIV+0.490.00410.00351.2MDMA/Ecstasy usersOhio374Male0.580.00120.00071.7Jazz musiciansNew York City263Male0.760.00160.00072.3Jazz musiciansNew York City261Union member0.250.00100.00071.4Jazz musiciansNew York City253Received airplay0.750.00170.00072.4
Overall, Table 1 shows that the prevalence estimates from existing studies had design effects around 2, suggesting that respondent-driven sampling is reasonably precise in the situations in which it has been used so far.16 Based on this crude analysis of existing respondent-driven sampling data, we recommend that when planning a study using respondent-driven sampling researchers should assume a design effect of 2. This guideline should only be considered a preliminary rule-of-thumb and should be adjusted, if necessary, depending on pre-existing knowledge of the study population.
Sample Size Calculation
Information on design effects should be used when planning the sample size of a study using respondent-driven sampling, or else the sample size will not meet the goals of the study. Fortunately, once the researcher has an estimated design effect, it is rather straightforward to adjust the required sample size; the researcher need only to multiply the sample size needed under simple random sampling by the assumed design effect. Thus, for studies using respondent-driven sampling we recommend a sample size twice as large as would be needed under simple random sampling. However, calculating the appropriate sample size under simple random sampling is often difficult due to the overly general nature of the power analysis literature.20,21 Therefore, we will review the sample size calculations for two specific cases of most interest to researchers using respondent-driven sampling: estimating the prevalence of a trait with a given precision and detecting a change in prevalence over time.17
One common goal of studies is to estimate the prevalence of a characteristic with some pre-specified precision, for example, to estimate the proportion of sex workers in New York City that are HIV-positive with a standard error of no greater than 0.03. Since it is the case that,
we can solve for the required sample size, n, in terms of the desired standard error, which yields,
Therefore, if based on pre-existing knowledge we suspect that 20% of the sex workers have HIV and that the design effect is 2, we would need a sample size of at least 356 sex workers to estimate the HIV prevalence with a standard error no greater than 0.03. Notice that this calculation depends on our initial guess of the prevalence. If researchers do not have enough information to make such a guess, they should assume a value of 0.5 which is maximally conservative.
A second problem of interest to many researchers is comparing the prevalence of some behavior at two time points. For example, a researcher might want to test whether an outreach program was successful at getting drug injectors to stop sharing injection equipment. Assume that the researcher suspects that before the intervention 40% of drug injectors share injection equipment and that the researcher would like to choose the appropriate sample size to be able to detect a drop to 25% such that there is an 80% probability that a 95% confidence interval for the estimated difference will not include 0. Further, assume that the researcher suspects that each prevalence estimate will have a design effect of 2. Based on a derivation available in the literature,23 we can calculate that the required sample size is,
More generally, the required sample size for comparing prevalence in two populations is,
where Z1- and Z1−β are the appropriate values from the standard normal distribution and deff is the design effect.18
These sample size calculations are based on assumptions about the prevalence of the characteristics and the design effect. Therefore, the sample sizes produced by Eqs. 4 and 6 should be considered approximate.
Conclusions
This paper makes two main contributions to the literature on respondent-driven sampling. First, we introduce a bootstrap confidence interval procedure that in simulations outperforms the naive method currently in practice. Therefore, we recommend this bootstrap procedure be used in future analysis of respondent-driven sampling data. The procedure requires some custom computer programming to implement, but, fortunately, it is already included in RDSAT, a software package for organizing and analyzing respondent-driven sampling data.19
The second major contribution of this paper is the information on design effects. The simulation results suggest that the design effects can range from as high as 10 to less than 1. These findings imply that, because of the possibility of high design effects, respondent-driven sampling is not appropriate in all cases. In some extreme network structures, the prevalence estimates could be so variable that, even though they are unbiased, they might not be very useful. Fortunately, data from existing studies suggest that, so far, respondent-driven sampling has been used in situations where it is reasonably precise, yielding estimated design effects around 2 (see Table 1). Based on these data, we suggest that when using respondent-driven sampling, researchers collect a sample twice as large as would be needed under simple random sampling.
The sensitivity of the design effect to the functional form of the degree distribution further emphasizes the need for more research on methods to accurately measure the degree of each respondent. Currently, the estimated average degree depends on subjects' self-reported degree, and these reports may be inaccurate.26,27 In almost all cases, inaccuracy in the self-reported degree will introduce bias into the prevalence estimates.4 As far as we know, the best methods for estimating an individual’s degree are scale-up method and summation method.28 However, it is not clear that either of these approaches, which were designed for the general population, is appropriate for studying hidden populations.
Taken together, the results about the sample-to-sample variability presented in this paper add to the growing literature on respondent-driven sampling. By allowing researchers to obtain better information about key hidden populations, this research should allow public health professionals to monitor population dynamics more accurately, target resources more carefully, and intervene to slow the spread of disease more effectively.

variance estimation
design effects
sample size
respondent-driven sampling
hidden populations
snowball sampling
power analysis


Pediatric DXA: technique and interpretation

This article reviews dual X-ray absorptiometry (DXA) technique and interpretation with emphasis on the considerations unique to pediatrics. Specifically, the use of DXA in children requires the radiologist to be a “clinical pathologist” monitoring the technical aspects of the DXA acquisition, a “statistician” knowledgeable in the concepts of Z-scores and least significant changes, and a “bone specialist” providing the referring clinician a meaningful context for the numeric result generated by DXA. The patient factors that most significantly influence bone mineral density are discussed and are reviewed with respect to available normative databases. The effects the growing skeleton has on the DXA result are also presented. Most important, the need for the radiologist to be actively involved in the technical and interpretive aspects of DXA is stressed. Finally, the diagnosis of osteoporosis should not be made on DXA results alone but should take into account other patient factors.
Introduction
After its commercial introduction in 1987, dual energy X-ray absorptiometry (DXA) has become a widely available and clinically useful tool in the evaluation and management of adult bone diseases. More recently, its utilization in the pediatric population has rapidly increased. DXA presents unique challenges to pediatric radiologists, and the aim of this article is to review the technique and interpretation of DXA. Special focus is on the issues unique to pediatric DXA emphasizing the need for an expanded role for the pediatric radiologist in the performance and interpretation of DXA examinations.
Is the result of a DXA examination a number or a diagnosis? From the radiologist’s perspective, it is both, making it different from all other imaging studies. Like many laboratory tests, the DXA examination generates a numerical result. The radiologist, like the clinical pathologist, must be knowledgeable about the processes by which that number is obtained and must ensure that meticulous technique is used [1]. Additionally, the radiologist must be knowledgeable about the statistical limitations and uses of a numerical result. For example, he or she must be familiar with the precision and accuracy of the technique and be able to consult regarding the least significant change and be able to suggest appropriate follow-up intervals [2]. The radiologist must also interpret the study in terms of the relevant patient factors that influence the numeric result. These factors include gender, ethnicity, height, weight, body composition, and physiologic maturity, and they might be incorporated in the interpretation of the study. Therefore, the result of a DXA examination is both a number and a diagnosis, and radiologists should be expert in understanding and reporting both aspects in the DXA report. The diagnosis of osteoporosis should not be made on DXA results alone but should take into account other patient factors. Additionally, the radiologist needs to be aware of the limitations of DXA in children [3]: there are difficulties in scan interpretation because DXA is an areal rather than a volumetric density measurement; the growing skeleton has an impact on follow-up measurements; there is a lack of consensus regarding the patient demographic and physiologic factors that should be incorporated into normative databases; and there is yet to be determined a prognostic value of pediatric DXA with regard to fracture risk or peak bone mineral density (BMD) [4].
Areal vs. volumetric bone mineral density
As in all radiologic studies, DXA relies on the differential absorption of X-rays to differentiate tissues of different radiographic density. In addition, DXA can quantify (in grams) the bone mineral content (BMC) at various body sites. By selecting regions of interest, a bone area (BA) is selected with units of centimeters squared. (The abbreviation BA for bone area should not be mistaken for bone age.) BMD is measured directly for each pixel in the region of interest (ROI) by comparing the X-ray attenuation of that pixel to a reference standard. It has units of grams per centimeter squared. This value is multiplied by the pixel’s area to derive the BMC of that pixel with units of grams. The areas of all the pixels in the ROI are summed to give BA. Thus, BMD = BMC/BA.
Unlike other density measurements, the DXA-derived BMD is based on the two-dimensional projected area of a three-dimensional structure. The third dimension, depth, cannot be accounted for directly because it is in the same direction as the X-ray beam. Therefore, DXA-derived BMD is an areal (aBMD) rather than a true volumetric (vBMD) density. Because the third dimension is unaccounted for, problems with DXA-derived BMD can arise [5]. Specifically, smaller bones will be found to have lower aBMD than larger bones, even when the vBMD is the same (Fig. 1). For material of the same true density, a larger cube will be stronger than a smaller cube. Thus, in giving a lower aBMD for smaller bones when compared to larger bones with the same vBMD, an aBMD might give a more accurate indication of bone strength relative to size than a vBMD. Additionally, unlike adult patients in whom the bone volume does not change over time, a child’s bones grow over time and the growth of individual bones is not uniform in three dimensions. Thus, errors resulting from areal measurements of BMD might be introduced with DXA and can make comparison of follow-up and baseline studies more challenging to interpret in pediatric patients [4].
Fig. 1For two bones of known BMD=1g/cm2, the DXA-derived areal BMD will be higher in the larger bone because of the lack of accounting for the true volume of the measured bone. It should be noted that the larger cube will be stronger than the smaller cube (adapted from Carter et al. [5], with permission)
Technical aspects of DXA performance
Patient positioning and ROI selection as performed by the technologist require precision [6] and evaluation by the radiologist for each study. The lumbar spine should be straight and centered in the image, with visualization of the last rib pair and the upper sacrum. Artifacts, including enteric tubes, orthopedic hardware, and jewelry, should be excluded from the image, if possible. Vertebral segments with overlying artifacts should be excluded from BMD analysis. The ROIs are generated automatically using edge-detection software and are selected for the L1 to L4 vertebral bodies. These regions should include the entire vertebral body with a minimum of adjacent soft tissue (Fig. 2). For evaluation of the hip, the femoral shaft should be parallel to the long axis of the image with only a small amount of the lesser trochanter visualized. When using the manufacturer’s provided positioning device, there should be no overlap of the trochanters and the femoral neck or acetabulum. The ROIs include the femoral neck, trochanter, intertrochanteric, and total hip, (Fig. 2). The region of lowest femoral neck BMD, known as Ward’s triangle, is not used in pediatric DXA analysis, and, often, use of the total hip measurement is favored over the other subgroups in clinical practice because of its higher precision than the subgroups. Whole-body scanning provides total body BMC and BMD but also allows for subregions with appropriately drawn ROIs (Fig. 2). Because of the normally low BMD in young children, software analysis is modified for children to improve edge detection of lower-density bone. Such algorithms have been validated in healthy, obese, and chronically ill children for the assessment of lumbar BMD [7]. The adult algorithm significantly overestimates lumbar BMD when compared to the pediatric low-density algorithm (Table 1), because lower-density bone pixels will be excluded using the adult algorithm [8, 9]. It is suggested that normative pediatric data be collected using the low-density analysis routinely in children, thus allowing meaningful comparisons of patient data to normal data, and that the DXA report indicate which algorithm (adult or pediatric) was used [3].
Fig. 2DXA images. a AP image of the lumbar spine shows regions of interest from L1 to L4. The bone area and mineral content are used to derive the bone mineral density at each level. The areal density is based on the bone area; the depth dimension is not directly assessed with DXA. Note transitional lumbosacral vertebral body. b AP image of the lumbar spine shows regions of interest from L1 to L4. AP DXA image of the left hip shows regions of interest of the femoral neck, greater trochanter, and total hip. c Total body scan with sub-regions of interests for trunk, extremities, and headTable 1Effect of pediatric vs. adult software analysis on bone area and BMC results. Total body DXA from a 13-year-old patient processed using pediatric and adult software. Note decreased BA (1315 cm2) and BMC (1149 g) but increased BMD (0.874 g/cm2) with the adult technique. Low-density portions of the bone are included using the pediatric technique and thus a larger BA (1810 cm2) with a greater BMC (1375 g) are obtained but the BMD (0.759 g/cm2) is lower because of the inclusion of low-density bone pixelsRegionPediatricAdultBA (cm2)BMC (g)BMD (g/cm2)BA (cm2)BMC (g)BMD (g/cm2)Left arm201930.465114710.622Right arm196970.497116760.655Left ribs79400.50775390.511Right ribs98510.52592480.525Thoracic spine85480.56983480.524Lumbar spine49280.5033200.599Pelvis1791360.760115950.829Left leg3532690.762281990.873Right leg3382450.7242261870.829Subtotal157710080.63910817820.723Head2333671.5722333671.572Total181013750.759131511490.874
The sites selected for BMD analysis should provide a robust evaluation of the patient bone density status. If technically feasible, the pediatric DXA examination should measure lumbar spine and total body BMD [3]. The manufacturers’ normative data for the hip in preadolescents are limited, and evaluation of the hip is not recommended in these young children. There are normative DXA data for the adolescent hip, especially in girls [10], and for these patients this site might be a useful addition to the standard examination. When evaluating group data of normal children, there is usually close correlation of BMD between the lumbar spine and hip [11]. For individuals, when the DXA results deviate from normal, there is less concordance between these two sites. For example, if the hip Z- score is between +1 and −1, the lumbar Z-score will vary an average of less than 0.5 SD from the hip score. As the hip Z-score decreases to −3, the lumbar score varies on average 1.7 SD from the hip Z-score. For example, immobilized or paraplegic children might have preserved lumbar BMD but low hip BMD. If evaluation of the spine and hip is not feasible because of extensive orthopedic hardware or patient positioning issues, DXA of the forearm can be performed. However, there are few normative data for pediatric forearm studies, and the value obtained might be useful only when compared to subsequent studies. Because of its reproducibility and lack of areal density-related errors, the total body BMC is preferred for the assessment of bone status by some clinicians and researchers [12].
The DXA lumbar ROI will not include the thoracic spine. However, the identification of a thoracic body compression deformity in patients with osteoporosis has significant prognostic value, indicating a higher risk of subsequent vertebral compression fractures. Evaluation of thoracic and lumbar vertebral bodies can be achieved with modern DXA scanners (Fig. 3) and can identify thoracic compression fractures that would have been otherwise undiagnosed. Makitie et al. [13] found compressive thoracic deformities in 11 of 32 children suspected of having secondary osteoporosis who were studied with DXA. Of these 11 children, 8 had normal lumbar DXA, and the demonstration of a thoracic compressive deformity was thought to be an important diagnostic and prognostic finding. The addition of vertebral morphologic assessment might be an important adjunct in the diagnosis of pediatric osteoporosis.
Fig. 3Lateral thoracic and lumbar spine image from DXA study for vertebral morphology. Note compressive deformities at T-7 and T-9, and a Schmorl’s node at L1, with otherwise normal vertebral morphology of the lumbar spine
DXA requires remarkably low radiation doses. Using manufacturers’ data, the effective dose for lumbar spine and whole-body DXA is reported to be 1−5 μSv [14]. This is less than the dose of a standard PA chest radiograph. Scanning times are now less than 2 min for the spine, hip or forearm, and less than 3 min for the total body.
Accuracy, precision, and least significant change
DXA provides both accurate and precise bone mineral data. Accuracy refers to how close a measured value is to the true value as determined by a gold-standard technique. For BMC, the gold standard is the laboratory assessment of ashed bones, and DXA measurements of BMC are within 7–9% of ashed bone measurements [15, 16]. Precision is a measure of reproducibility of a measurement and can be expressed in terms of coefficients of variation (%CV). Both short- and long-term precision are important in performing DXA examinations. Short-term precision reflects both the imprecision of the equipment (manufacturers report this to be less than 1%) and the imprecision resulting from variation in patient positioning and motion effects (typical values are less than 2–3% for the spine, up to 5% for the hip, and 1–2% for the whole body) [14, 17, 18]. This component varies with each technologist and should be calculated with a repeated measures procedure [2]. Long-term precision is a measure of machine drift. It is normally well below 1%, and the radiologist should review the daily quality control scans of phantoms graphed over a period of weeks in order to detect this [15].
Because the DXA result is a number, the radiologist must be aware that the magnitude of change required to be statistically significant varies with the precision of the measurement technique. This is expressed in terms of the least significant change (LSC), and is equal to 2.8×%CV for the 95% confidence limit [2]. If the %CV was 1.5, then a change from the baseline measurement of 4.2% would be required for it to be considered statistically significant. The LSC can also be used to suggest the timing of follow-up measurements, i.e. if the LSC is 4.2% and the expected annual rate of change in the BMC or BMD is 2%, a follow-up study before 2 years would likely result in a value not statistically significantly different from the baseline. The annual rates of change in BMC and BMD vary considerably during childhood, with dramatic acceleration of bone accrual during the early pubertal years [19–21], especially in females [22]. The annual rates of change for early-stage and late-stage adolescents are approximately 25% and 10% for BMC and 10% and 3% for BMD [23]. For most pediatric conditions, follow-up examinations are obtained between 6 and 12 months.
DXA in newborns
DXA has been used to evaluate bone mineralization in newborns and young infants since its inception as a clinical tool, and numerous investigators have established its precision and accuracy [24–28]. The technique has a high degree of accuracy, even in preterm low-birth-weight neonates, with a slight underestimation of BMC of approximately 7% [26, 28]. The high precision of DXA has been shown in neonates with %CV of 2.4% [25] for measurements of the lumbar spine and of the total body BMC when assessed in piglets [26]. The absorbed dose is extremely low, and most neonates and infants can be imaged with gentle immobilization without the need for sedation.
Normative data for neonates indicate a very close relationship of total body BMC and BA with weight; height is also strongly correlated with BMC in the newborn [25]. Koo et al. [29] found weight and, to a lesser extent, body length but not gender or race to predict total body BMC, BA and BMD in newborns. Additionally, body mass was more closely correlated with BMC and BA than BMD. This may be because of DXA-derived BMD is areal rather than volumetric. Last, the proportional contribution to total body BMC from each subregion (head, trunk, and upper and lower extremities) is maintained across gestational ages (27–42 weeks) and birth weights (1–4 kg) with only slight variation [29].
Indications for pediatric DXA
Despite many potential uses of DXA, there has been relatively little written regarding the indications for DXA in children. The International Society for Clinical Densitometry has suggested that any child being treated or considered for treatment of osteoporosis should undergo a DXA examination [3]. The National Osteoporosis Foundation lists the following indications for DXA in children: systemic long-term steroids, chronic inflammatory conditions, hypogonadism, prolonged immobilization, osteogenesis imperfecta, idiopathic juvenile osteoporosis, recurrent low trauma fractures, and apparent osteopenia on radiographs [14]. It is important to note that DXA would be inappropriate for skeletal pain, chronic disease and traumatic fractures without any of the additional risk factors listed above [14]. The National Institutes of Health recommend a baseline DXA examination for patients for whom systemic corticosteroids will be used for more than 2 months or who are at significant risk of osteoporotic fracture [30]. These guidelines are also suggested by the American College of Rheumatology [31]. The American College of Radiology has listed DXA of the lumbar spine and hip as highly appropriate for pediatric patients with a significant risk factor for osteoporosis [32]. Recommendations from other subspecialty societies have been slow in coming. Neither the Society for Pediatric Radiology nor the American Academy of Pediatrics has made recommendations regarding pediatric DXA.
Pediatric DXA interpretation
As with other laboratory tests, the numeric value reported is meaningless without comparison to the appropriate normal controls. After comparison is made, the reported value is given as a percentile or a standard deviation score, the Z-score. A Z-score of zero is equivalent to the mean, and Z-scores of −1 and +1.5 are equivalent to values one standard deviation below and 1.5 standard deviations above the mean, respectively. The T-score (comparison of the current Z-score with peak adult BMD) is used in adult interpretation of DXA but should not be included in the pediatric DXA report [3]. Because the T-score is a measure of bone density loss since early adulthood, its use in children whose BMD has yet to peak will always yield a low result. Because the World Health Organization’s DXA-based definitions of osteopenia and osteoporosis are in terms of T-scores, T<−1.0 and T<−2.5, respectively [3], a different terminology is needed for pediatric patients. It is recommended that the phrase “low bone density” be used in DXA reports [3]. Some clinicians and researchers use the terms osteopenia and osteoporosis in children when Z-scores are less than −1.0 and −2.5, respectively. It is important to note that the diagnosis of osteoporosis should not be made on DXA results alone but should take into account other patient factors.
Much of the research in pediatric DXA has focused on determining which factors most influence BMD and should be accounted for in the development of normative pediatric datasets. The factors age, gender, ethnicity, and physiologic maturity level have been extensively studied and are included in most current normative datasets provided by the major DXA manufacturers. Some of the earliest reports indicate the influence of age on BMD values, and several authors have presented normal data accounting for age [10, 19–21, 33]. The effect that age has on BMD is largely related to the increase in frame size that occurs with increasing chronologic age. Increasing height and weight strongly correlate with increasing BMC and BMD. The changes in height and weight are most pronounced during the pubertal growth spurt. BMD increases rapidly during early puberty [21, 34], but because the age of pubertal onset is quite variable, physiologic maturity has a stronger influence on BMD than age. Several authors have included Tanner stage or gynecologic age as a primary factor in their normative datasets [21, 34–37]. Weight is an important factor influencing BMD for multiple reasons [4, 19, 20, 32, 38, 39] and has been included in normal datasets [10, 34]. Ethnicity has been determined to be important in the analysis of BMD results, with black children showing significantly higher BMD values than non-black children [10, 20, 36, 39–41]. Multiple factors are thought to account for this, including increased cross-sectional area in the axial skeleton and thicker trabecula in cancellous bone [36]. Lifestyle and anthropometric factors might also play a role [42].
There are numerous published pediatric normative datasets, many of which are summarized in Table 2. These datasets have been developed using a variety of scanners and processing software and are based on various combinations of demographic and physiologic patient variables. Rather than simplifying pediatric DXA interpretation, the sheer number of available normal databases has made DXA interpretation complex, confusing, and at times erroneous [43]. To report the numeric result generated from the manufacturer’s automated processing without consideration of factors specific to the patient being studied is unacceptable. This often will lead to misdiagnoses and can result in inappropriate therapy [44]. In fact, the diagnosis of osteoporosis in a child based on a DXA result is often a misinterpretation of the scan data. Gafni and Baron [45] found this to be the case in more than half of the pediatric patients referred to them with the diagnosis of osteoporosis. The most common causes for misdiagnosis were the use of T-scores, inappropriate normative datasets, inadequate ROIs, and inattention to short stature.
Table 2Normative pediatric DXA databases (C/B/H/A/O Caucasian/black/Hispanic/Asian/other, GA gestational age, (L) longitudinal study, SA surface area)ReferenceYearScannerNo. of patients (M/F)Age rangeEthnicity (C/B/H/A/O)InputOutput251992Hologic 1000 PB29/28NewbornGA + weight + height + SALumbar BMD and BMC251992Hologic 1000 PB22 total1–24 monthsGA + weight + height + SALumbar BMD and BMC291996Hologic 1000 PB82/68GA 27–42 weeksWeightTotal BMD, BMC and BA351991Hologic 1000 PB84/1342–17 years162/56/0/0/0Weight + Tanner stageLumbar BMD561990Lunar DP-3184 total5–11 yearsWeightLumbar BMD571993Norland XR-2686/685–18 yearsGender + Tanner stageTotal BMC and % fat461997Hologic 1000 PB142/2014–19 years (L)343/0/0/0/0Gender + Tanner stageTotal BMD, BMC and BA58, 592002Lunar DPXL/PED188/2564–20 years (L)444/0/0/0/0Gender + ageLumbar BMD and apparent BMD or total BMC, % fat and lean body massGender + Tanner stageLumbar BMD and apparent BMD or total BMD and BMC622002Hologic 4500 FB107/1245–22 years226/0/0/3/2Gender + ageTotal BMC and BAGender + heightTotal BAGender + total BMCTotal BMD612005Hologic 4500 FBup to 19483–20 yearsGender + age Lumbar, total hip and total BMD211991Hologic 1000 PB109/989–18 years207/0/0/0/0Gender + Tanner stage or age Lumbar BMC, BA and BMD, femoral neck BMD22, 331996Hologic 2000 FB110/1248–17 years (L)220/0/0/0/0Gender + ageLumbar and total BMC and BMDFemoral neck BMC and BMD40a1999Hologic 1000 PB193/2309–25 years (L)103/114/103/103Gender + age + ethnicityLumbar, femoral neck, and total hip BMD and BMADTotal BMD and BMC/Ht102004Hologic 4500 FB0/42212–18 years153/264/0/0/5Age + weight + ethnicity Lumbar and femoral neck BMD, femoral neck apparent BMD60b2001Hologic 2000 PB0/1519–14 years (L)151/0/0/0/0Breast stage + age Lumbar, femoral neck, trochanter and forearm BMC and BMD542003Lunar DPX PB210/2493–30 years459/0/0/0/0Gender + height or ageTotal lean body mass and total BMC/lean body massaFurther data available at http://www.stat-class.stanford.edu/pediatric-bonesbFurther data available at http://www.bcm.edu/bodycomplab
As with any other radiologic study, a methodical evaluation of the results should be undertaken in order to minimize the risk of misdiagnosis. The radiologist needs to review all input data, including patient age, gender, ethnicity, weight, height, and Tanner stage (if provided). Patient positioning should be evaluated, and the ROIs need to be analyzed for artifact and appropriateness. Comparison should be made with previous studies to ensure consistency of positioning and ROI selection. In addition, changes in patient height, weight, and Tanner stage should be noted. After these steps have been taken, interpretation of the numeric result is performed. An appropriate database for comparison purposes is selected. Ideally, this is based on data generated locally using the same equipment and technologists, but this is rarely possible. Normative data provided by the DXA manufacturers can be used, but historically these datasets do not include the parameters currently thought to be most important for interpretation. At a minimum, patient body size (height and weight) and physiologic maturity (Tanner stage, gynecologic or bone age) should be factors included in the normative dataset. Ethnicity and gender are also frequently included in the generation of normative data and are generally thought to affect BMD significantly. Table 2 summarizes a large number of normal databases that can be used to best match the patient scan to be analyzed.
More complex and scientifically rigorous analyses of the BMD result have been suggested. Molgaard et al. [46] described a three-step analysis of BMD. Bone length is categorized as short or long by assessing the patient’s height for age. Height is highly correlated with BMC [12] and thus needs to be accounted for, especially when BMD Z-score is abnormal (Z=±2). Bone width is categorized as thin or thick by assessing BMC for height. Last, bone mineralization is categorized with assessment of BMC for BA. The first step takes into account height because of its profound effect on BMC; taller children will have a higher bone content. However, bone width is also important in determining bone content, thus the second step accounts for this. The last step is often the only step performed by many radiologists with reporting of BMC for BA which, by definition, is BMD. Height for age can be assessed using standard growth charts corrected for age, gender, and ethnicity. Percentile rankings can be easily converted to a Z-score [47]. Bone area for height tables are available for select groups, but normative data for all pediatric patients need to be developed. Using this three-step analysis, Molgaard and Michaelsen [48] found that the causes for low BMC might be various combinations of factors such as short stature and thin bones, as in children with cystic fibrosis, or short stature and reduced mineralization, as in children with milk allergy. BMC might be normal despite short stature in the presence of wide bones, as in children with previously treated leukemia.
In summary, an abnormal BMD Z-score should lead to evaluation of confounding patient factors that influence BMD, including height, weight, and physiologic maturity, before a diagnosis of low bone density is made. Until the manufacturers’ databases sufficiently account for the physiologic factors that most impact BMD results, normative data derived locally or from the medical literature should be used in pediatric DXA interpretation. The report should include the DXA equipment and software algorithm used (pediatric or adult, low bone density or standard), the source of the normative reference data, the Z-score (not the T-score), and an impression giving a clinical context for the result. The diagnosis of “low bone density” does not rest solely on the DXA numeric result, and the report should indicate which patient factors were incorporated into the final impression. A specimen DXA report and the examination protocol from Columbus Children’s Hospital are given in Appendix.
Bone growth over time and changes in BMD
As mentioned previously, bone size affects the DXA aBMD result. Changes in bone size over time, as occur in normal pediatric development, confound DXA interpretation. This is one of the major limitations in the use of pediatric DXA. On both follow-up studies, when the child’s data are compared to prior results, as well as when the child’s DXA values are compared to normative values, the effect of bone size needs to be accounted for. These problems could be avoided, at least in part, if a true volumetric BMD were available with DXA. As this is not possible with current DXA technology, investigators have attempted to account for the effect of bone volume on the DXA result and minimize the effect the growing skeleton has on the BMD value [49]. Katzman et al. [50] estimated the volume of the lumbar vertebral bodies, assuming it to be a cube, using this formula: apparent lumbar BMD (BMAD) = BMC/BA1.5. Kroger et al. [51] suggested a volumetric correction based on the assumption that the vertebral body is a cylinder using this formula: BMAD=(BMC)(4/[π{bone width}]). This correction can also be applied to the femoral shaft and neck [52]. These corrections do not fully account for changes over time in lumbar BMD but do eliminate age and height dependence of BMD at the hip. A different approach has been to not evaluate BMD at all, but to measure BMC only, because it is determined with greater accuracy and precision than BMD [53]. In an effort to incorporate the fundamental relationship between the mechanical stress a bone experiences through muscle action and its mineral content, Hogler et al. [54] and Crabtree et al. [55] used DXA to assess BMC and proposed algorithms that focus on the evaluation of lean total body mass (LTM) with respect to height and BMC. They found LTM explains greater than 95% of the variation in total body BMC in boys and girls. By incorporating LTM/height and height/age into the DXA interpretation, patients could be grouped as being normal or having a primary, secondary or mixed bone defect. For example, the diagnosis of low BMD for age might be a result of smaller bones and not osteopenia. Hogler et al. [54] found children with growth hormone deficiency to be short for their age (low height/age ratio) but to have a normal amount of bone adaptation (BMC) for the muscle force (LTM). The BMC/LTM ratio for these children is normal. In contrast, children with anorexia nervosa with normal height had low LTM and also low BMC/LTM ratios. Their low BMD for age was a result of decreased muscle loading on bone (a secondary bone defect with low LTM/height) and decreased mineralization for the level of muscle loading present (a primary defect with low BMC/LTM). This indicated that a mixed defect caused their low BMD for their age.
In summary, smaller bones will have lower aBMD than larger bones as measured with DXA, even when the vBMD is the same because of limitations of the areal bone density technique. Attempts to correct for or to circumvent this limitation have been proposed and show promise in improving DXA interpretation and our understanding of bone physiology.
Clinical case studies
The following case studies are examples of common clinical indications for DXA in pediatrics and illustrate the principles used at Columbus Children’s Hospital in DXA interpretation.
Patient 1 was a 4-year-old white female with nutritional rickets and multiple fractures following minimal trauma. She presented for a baseline study and was Tanner stage 1 and weighed 19 kg. Her lumbar BMD was 0.399 g/cm2. Using our normal database that corrects for Tanner stage and weight [35], the patient’s lumbar BMD was far below the first percentile (Z-score was much less than −2.3). The manufacturer’s database (which is based in part on the data from reference 35) yielded a Z-score of −2.1. The total body BMC was 543 g with a Z-score of −2.3 [43]. The patient was reported as having markedly reduced lumbar bone density and reduced total body BMC.
Patient 2 was a 13-year-old black female with lupus. On baseline DXA the lumbar BMD was 0.719 g/cm2, equivalent to a Z-score of 1.6 using our local database and was considered to be a high normal value for a 33-kg and Tanner stage 1 patient. The total body BMC was 1280 g, equivalent to a Z-score of 1.5 [43], and was also thought to be a high normal value. During the next 15 months, she was treated with corticosteroids and gained 15 kg and progressed to Tanner stage 2. On follow-up DXA the lumbar BMD was 0.723 g/cm2. This value corresponds to the 25th percentile and a Z-score of −0.67 [35]. Thus, she had a slight decrease in her lumbar BMD value at a time when rapid bone mineral accrual would be expected [21]. This was made evident by the rather marked decrease in her Z-score, from 1.5 to −0.67. Her total body BMC was unchanged, but the Z-scores also decreased substantially.
Patient 3 was a 16-year-old white female with Turner syndrome and of small stature (150 cm, first percentile, Z-score −2.3). Her lumbar BMD was 0.641 g/cm2, equivalent to the eighth percentile (Z-score −1.3) for Tanner stage 3 and weight 50 kg [43]. It should be noted that the manufacturer’s normal database yielded a lumbar BMD Z-score of −3.0, but it did not take into account height or weight. The low lumbar BMD Z-score was likely a result of the patient’s short stature (low height Z-score). The weight correction in our normal database partially accounted for her short stature and gave a more meaningful interpretation of the numeric DXA result. This patient’s bone age was 13 years (Z-score −2.3), and using this rather than her chronologic age (16 years) with the manufacturer’s normal database would result in a Z-score of −1.0. This value would better reflect the patient’s actual bone status. Because our database corrects for weight and Tanner stage, each patient is weighed and has a Tanner stage determination made by the referring clinician prior to the DXA study. Thus, we do not use the patient’s bone age in DXA interpretation.
Final recommendations
Pediatric radiologists need to assume a more prominent role in DXA performance, interpretation and research. They require expertise with DXA as a laboratory procedure, a numeric result, and a clinical diagnostic examination. The radiologist must be a “clinical pathologist” closely supervising the acquisition of the DXA study with assessment of quality control data as well as the clinical images. The radiologist must be a “statistician” understanding the principles of least significant change and the relationship of standard deviation scores and percentile rankings. The radiologist must also be a “bone specialist” providing a meaningful context for DXA, translating the numeric value to a clinically useful result. As always, pediatric radiologists must be children’s health advocates by ensuring the appropriate clinical use of DXA as well as actively participating in research efforts.

pediatric dxa
osteoporosis
technique interpretation


The Lymphatic Anatomy of the Breast and its Implications for Sentinel Lymph Node Biopsy: A Human Cadaver Study

Background Current understanding of the lymphatic system of the breast is derived mainly from the work of the anatomist Sappey in the 1850s, with many observations made during the development and introduction of breast lymphatic mapping and sentinel node biopsy contributing to our knowledge.
Management of the lymph nodes has been an important part of breast cancer treatment since the time of Halsted’s radical mastectomy.1 Until the 1970s it was based on the perceived need to remove cancer cells before they spread via the lymphatics beyond the reach of the surgeon. The national surgical adjuvant breast and bowel project B04 study questioned the therapeutic benefit of axillary clearance, however it remained part of the treatment of invasive breast cancer because of the prognostic significance of the axillary lymph nodes status.
Sentinel node biopsy (SNB) has replaced axillary dissection in clinically node negative patients,2–4 with trials confirming a false negative rate of 5–10%. While it is agreed that SNB is appropriate, the optimal injection sites of dye and/or colloid has not been defined.5–7 There are advocates of peritumoral,8–9 dermal and subdermal10–12 or subareolar and periareolar injection13–14 of the tracers. These recommendations regarding injection sites are derived from clinical experience rather than from anatomical studies.
The anatomical basis of axillary clearance was derived from the publications of Sappey in the 1870s15 who showed the breast lymphatics as separate from those of the underlying torso, with a subareolar plexus of lymphatics, and a small number of large lymphatic vessels draining into axillary lymph nodes (Fig. 1). Despite the revolution in the surgical approach, there has been no advance in the underlying anatomical knowledge of the breast lymphatics.
Fig. 1.Sappey’s drawing of the superficial lymphatics of the upper torso (left) and female breast (right) in 1874.15
The lymphatics start as an avalvular lymph capillary network. In the skin they commence in the superficial dermis with diameters of 20–70 μm.16 They drain to precollectors that are up to 300 μm diameter, contain valves, have some smooth muscle cells in their wall,17 and drain this network to subcutaneous lymph collecting vessels (Fig. 2). The lymph collecting vessels (lymph collectors) have a smooth muscle layer18 and are the vessels commonly identified as lymphatics. The breast develops as a modified skin gland appendage and expands into the subcutaneous tissues.19Fig. 2.Schematic diagram of the relationship between the lymph capillaries, precollectors, and lymph collecting vessels.
Progress in microsurgery has enabled new methods for investigating the lymphatic system. We developed a protocol for injecting radio-opaque contrast medium into lymph vessels of <0.3 mm diameter in cadavers. The contrast agent fills the draining lymph vessels, which are then radiographed.20,21We have previously published detailed investigations of the lymphatics of the upper limb.22–24
This study addresses the lymphatic anatomy of the breast and anterior upper torso. Our findings may explain the clinical experience in lymphatic mapping and sentinel node biopsy, and also the persistence of a false-negative rate of 5–10% irrespective of the experience of the surgeon.
Materials And Methods
Bilateral anterior upper torso specimens, which included both breasts, were harvested from 10 cadavers (4 male and 6 female) with incisions across the root of the neck, down the posterior axillary line and across the abdominal wall, just above the umbilicus. Another four unilateral studies were obtained from separate cadavers (1 male and 3 females) by a midline incision of the sternum, thus resulting in a total of 24 sides. Protocol refinements at the beginning of the study limited early results and there were always time limits to complete the work, especially on the contralateral side of bilateral subjects, before the specimen became putrefied. The injection and dissection for each side of a specimen took 4–5 weeks. The specimens were stored at −20°C prior to dissection and at 4°C during the dissection.
The lymphatic mapping technique has been described previously.20–21 Briefly 6% hydrogen peroxide was injected into the tissue being examined. Bubbles appear in the tissue and the lymphatic collectors and an operating microscope (Stemi 2000, Carl Zeiss Pty. Ltd. Germany) is used to identify and cannulate the lymphatic vessels with a 30-gauge needle (Precision glide needle: Becton Dickinson & Co., USA.) or an extruded glass cannula for very small vessels. Radio-opaque contrast medium containing lead oxide (P3O4 Red lead, AJAX Chemicals, Australia) was injected antegrade with a micromanipulator (UM-3C, Narishige Co., Japan). The contrast stopped after a variable distance because of coagulation requiring further cannulation and injection. This was repeated until the first lymph node for each collector was reached (sentinel node).
The procedure was performed: around the entire periphery of the specimens in the subcutaneous plane; around the internal thoracic artery on the inner aspect of the chest; and in the vicinity of the perforating branches of the internal thoracic artery to identify superficial lymphatics, internal mammary lymphatics, and perforating lymphatics respectively.
Indocyanine Green dye (Pulsion Co., Germany) was injected into the internal mammary artery to demonstrate the artery and its perforating branches, which supply blood to the medial aspect of the breast, thus facilitating the identification of associated deep perforating lymphatics.
A mixture of blue dye (Ultamarine, Educational Colours Pty Ltd., Melbourne) and hydrogen peroxide was used to stain the lymph collecting vessels originating from the nipple and areolar region. In previous studies of the upper limb we have first injected this blue dye into the dermis before injecting hydrogen peroxide into the subcutaneous tissues to help identify the collecting lymphatics.22 This was helpful in identifying lymphatics in the fingertips, where they exist at high concentration. This dye was injected also into the dermis over the breast mound but was only helpful in the nipple areolar area where again the lymphatics were concentrated.
The specimen was radiographed after completion of all injections to give the two-dimensional views of the lymph vessel anatomy. To provide the three-dimensional views, the female specimens were sliced parallel to the lymph vessels as they passed towards the axilla. These slices were then placed on their sides and radiographed to show the position of the lymphatic collectors with respect to the skin and the breast tissue.
Radiographs were photographed (Nikon D100, Nikon Co., Japan) and transferred to the computer, then each lymphatic collector was traced (Adobe Photoshop CS, Adobe System Inc.) to its first-tier node and color coded. All collectors draining to the same first-tier node were assigned the same color after tracing them retrogradely from the sentinel nodes.
Results
Superficial Lymphatic System
Lymphatic collectors were identified in the subcutaneous tissues near the peripheral cut edges of the specimens and the lateral border of the sternum. The collectors often branched in the peripheral region then combined to form larger collectors that remained approximately uniform in diameter until they reached the first lymph node (Figs. 3 and 4). Some collecting lymph vessels joined with others within the same sentinel node territory, rarely with others, before reaching the lymph node. All superficial lymph vessels in these dissections entered a lymph node in the axilla, which was always close to the lateral edge of the pectoralis minor muscle. The findings were similar in both sexes (Fig. 4). In all of the specimens we examined, many of the lymphatic collectors that passed over or through the breast ended by draining into the same first-tier lymph node. In some, almost the entire breast drained to one sentinel node. In others however, there was at least one other node that was the first-tier node for a collecting lymphatic that passed through part of the breast.
Fig. 3.Radiographs in antero-posterior views of a male (left) and female (right) specimen after completing injections with the lead oxide mixture. Note that the torso lymph vessels radiate centripetally towards the axilla.Fig. 4.Tracing distally of lymphatics of both hemi upper torsos (male: A and C, female: B and D) from each first-tier lymph node colour coded; pectoral node (green, orange, black and yellow), subclavicular node (light blue), and internal mammary node (red). Note (i) that the lymph collecting vessels from the nipple and areolar region on each specimen drain into the green-colored lymph node; (ii) the similar pattern of chest and breast drainage between the male and female studies; (iii) that the breast lies in the pathway of collecting lymphatics that start peripherally and (iv) that, although the majority of the breast drains to one sentinel node in D, every breast area is drained by more than one first-tier node in each study.
The lymphatics deep to the nipple and areola area were different from those of the other areas we examined. Microscope-assisted dissection of the areolar region revealed a dense network of lymph capillaries and precollectors in the dermis. This structure is presumably the subareolar plexus identified by Sappey. In most areas, dye injected subcutaneously over the breast mound was not taken up by the lymphatics. Dye injected in the nipple and areolar region was taken up by 2 or 3 superficial lymph collecting vessels via lymph capillaries and precollectors (Fig. 5) each side of the areola and these drained into a first tier node in the pectoral group of axillary nodes (shown green in Fig. 4).
Fig. 5.Photograph of dissection in the areolar region after injecting the mixture of dye and hydrogen peroxide into the nipple. Lymph capillaries and precollectors (black arrows), and lymph collecting vessels (white arrow) were stained with the blue dye.
The radiograph of the cross-sectioned female specimen showed that the lymphatics have a “wavy” path through the superficial part of the subcutaneous tissue of the chest (Fig. 6). In the breast region most of the lymph collectors ran between the dermis and the breast tissue. However, some passed through the breast tissue itself. After traversing the breast all of the collectors passed deeply to reach axillary lymph nodes.
Fig. 6.The diagram (above) shows how the breast of Fig. 4B was sectioned to provide cross-section radiographs (middle of the breast and its lymphatic drainage (below). Note that some lymph collectors originating from the lower torso run through the breast tissue in both A and B sections.
Internal Mammary Lymphatic System
The internal mammary lymphatic vessels were identified alongside the internal mammary artery and vein, deep to the parietal pleura, with lymph nodes present in the intercostals spaces. Collecting lymphatics were identified beside the perforating branches of the internal mammary arteries that were found in the deep medial aspect of the breast tissue (Fig. 7). A single collector passed though the intercostal fascia and muscle beside each perforating artery to join the internal mammary lymphatic system.
Fig. 7.The appearance of the perforating lymphatics (orange) along the branch from the internal mammary artery (green) in the right lateral sternal region of the female specimen.
There was no apparent connection between the collecting lymphatics accompanying the branches of the internal mammary artery and the superficial collecting lymphatics. Contrast injected into the superficial collecting lymphatics never flowed into the perforating collecting lymphatics. Even in the subcutaneous tissues overlying the lateral edge of the sternum, the superficial collecting lymphatics passed laterally towards the axilla. We found no evidence of direct anastomosis between the superficial collecting lymphatics and the collectors associated with perforating arterial branches, at the size of the collecting vessels. However, this does not exclude a connection at either the precollector or lymphatic capillary network as we were unable to demonstrate them radiologically.
Discussion
Cruikshank was the first to report the lymphatics of the breast in his book published in 1787.25 He used the cadaver of a pregnant woman injecting mercury into the mammary duct from the nipple. He reported seeing by chance mercury-filled lymphatics but did not make any diagrams of his findings.
In 1874, Sappey applied the same method,15 injecting mercury into the dermis of a semiputrefied cadaver to identify the superficial lymph vessels. A very thin adult cadaver was used and he described the superficial lymphatic drainage of the torso, dividing it into four territories by a sagittal midline and a horizontal line at the L2 level. The upper torso lymphatics always drained into the ipsilateral axilla (Fig. 1). Sappey reported that the lymphatics of the breast collected in a subareolar plexus and then drained towards the axilla via lymph collecting vessels. Sappey’s description of the breast lymphatics was adopted by anatomists and became the theoretical basis for the subareolar injection of dye and/or isotope for lymphatic mapping as part of the sentinel node biopsy for breast cancer more than one century later.13–14
In 1903, Poirer and Cuneo summarized Sappey’s results.26 They added their results from foetal studies using with Gerota’s method27 using oil painting dye to stain the lymphatics, they reviewed other people’s studies and published a comprehensive anatomy book of the lymphatic system. Poirer and Cuneo’s famous picture of the lymphatics of the breast (Fig. 8) was redrawn and is still being used in Gray’s Anatomy.28Fig. 8.Poirier and Cuneo’s summary diagram of the breast lymph drainage.26 This diagram was composed based on the anatomical and clinical findings of several people, including Sappey.
In 1959, Turner-Warwick performed photographic and radiographic studies of the collecting lymphatics injecting them with iron Prussian blue or radioisotope gold (Au198) during surgery in breast cancer patients.29 He demonstrated lymphatic pathways that passed direct from the tumor injection site in the breast to the axillary lymph nodes that bypassed the subareolar plexus. He found that all quadrants of the breast drained to the axilla and either the internal mammary or posterior intercostal nodes. He suggested that Sappey had mistaken the mammary duct for a lymphatic vessel, thereby overemphasizing the importance of the subareolar plexus.
The more recent users of lymphoscintigraphy examinations of the breast are also skeptics of the centripetal lymphatic route towards the subareolar plexus. Tanis30 and Uren (Uren RF: personal communication, May 2007) stated that there is no constant route via the subareolar plexus.
Our current anatomical knowledge of the breast lymphatics still depends on Sappey and Poierer and Cuneo’s diagrams. Since Sappey used thin adult cadavers and Poirer and Cuneo used infant cadavers, the relationship between the superficial lymphatics and the adult breast tissue, and also the relationship of the lymphatic drainage of the breast tissue with that of the surrounding superficial tissues, has not been adequately described. Controversy still exists over the role of the subareolar plexus in the lymphatic drainage of the breast. There has been no concrete evidence of a centripetal anatomical lymphatic pathway that drains the breast tissue towards the subareolar plexus and then, via this plexus, towards the sentinel node.
Our direct injection technique, however, gives a comprehensive image of the lymphatic system in individual specimens. Each lymph vessel that enters a lymph node can be traced retrogradely to provide an accurate map of the tissue for which that lymph node is “sentinel.” We have photographed, radiographed, and recorded actual lymphatic pathways. In addition, cross-sectional studies have been performed to obtain three-dimensional images of these lymph collecting vessels.
We have shown that some of the torso vessels pass from the periphery through the breast tissue on their way towards the axilla. This is discordant with the conventional understanding that they run just underneath the skin.
We compared the torso lymphatic vessel pathways and breast tissue lymphatic vessel pathways in adult female cadavers. Although our results do not show conclusively that the lymph drainage of the breast tissue is via the collecting lymphatics that pass through or immediately superficial to the breast substance, this is likely to be the case since (i) the lymph collecting vessel has a microporous nature and drains surrounding tissue fluid along its entire course31 and (ii) lymphoscintigraphy in breast cancer patients after peritumoral injection, coupled with similar studies with radioactive gold by Turner-Warwick, usually reveals a direct pathway from the injection site to the axillary lymph node,29–30 not via a subareolar plexus. Therefore we conclude that the lymph collecting vessels that pass through the breast contribute to breast lymph drainage and must be the same vessels shown in lymphoscintigraphy examinations.
Embryologically, the development of the human peripheral lymphatics is poorly understood. However, the lymphatics of the foetus represent similar arrangements to those of adults.32–33 We assume that some of the lymph vessels are trapped inside the mammary gland as the breast develops around preexisting superficial lymph collectors. We have color coded a diagram of our dissection to simulate various injection sites in lymphatic mapping and sentinel node biopsy for breast cancer. Figure 4 shows that, if the tracer is injected deep around the purple-colored vessel (lower outer quadrant), it reaches both the green and orange lymph node in the pectoral group. However, if the tracer is injected into the subareolar region or into the lower outer quadrant intradermaly near the tumor, it reaches only the green node. This anatomical analysis suggests a mechanism for false negative sentinel node biopsy since more than one sentinel node drains the breast in this example.
False-negative results following sentinel node biopsy are of the order of 5–10% in different series.34–37 Reasons given to this have been technical; either related to:The surgeons’ experience with the technique orThe size of the radioactive tracer which may not reach the lymph node, especially if sited in a peritumoral position.
Our results now offer an anatomical explanation for these false negative results as a distinct third possibility.
Perforating lymphatics that pierce the deep fascia are critical when discussing breast lymph drainage. The lymphatic system is classified conventionally into the superficial system and the deep system because of their relationship to the deep fascia. However, we subdivided the system draining the tissues above the deep fascia into the superficial system and the perforating system (Fig. 9). The perforating system is connected to the deep lymphatic system and these collecting vessels have the same appearance as the superficial lymphatics as they course with the internal thoracic blood vessels. Variations of the blood supply to the breast have been reported.38–42 Therefore, we hypothesize that the perforating lymphatics may have the same variations. This helps explain the fact that in all quadrants of the breast, cancer has the potential to metastasize via the internal mammary lymphatics especially if the tumor is medial or deep in the breast parenchyma.43–44 It is accepted that intradermal injection of tracer rarely demonstrates the internal mammary lymphatics.10–12 The variable contribution of perforating lymphatics along the branches of the internal mammary artery to lymphatic drainage of the breast cannot be predicted clinically and therefore the likelihood of sentinel nodes being located along the internal mammary artery is also unpredictable. Our anatomical analysis suggests that accurate lymphatic mapping requires peritumoral injection.
Fig. 9.Our concept of the breast lymph drainage, drained by both the perforating lymphatic system and the conventional horizontal superficial lymphatic system with their relationship to the lymphatic system beneath the deep fascia.
Conclusions
Current anatomical knowledge of the breast lymphatics is derived from the work of Sappey, Poirier, and Cuneo. Our anatomical cadaver study of the relationship of the lymphatics of the torso and the adult breast goes a step further and provides additional information which has special significance for sentinel lymph node biopsy. We have used a refined protocol to accurately record the anterior upper torso lymphatics in adult male and female cadavers. The patterns of the superficial lymphatics were no different between sexes and frequently more than one sentinel node drained the breast. The cross-sectional studies of the female breast showed some lymph vessels of the torso coursing through the breast tissue. We found also perforating lymphatics coursing with similar branches of the internal mammary artery and vein.
This anatomical analysis suggests that (i) peritumoral injection is preferable for identification of the sentinel lymph node for breast cancer treatment and (ii) may help explain the incidence of negative sentinel node studies where only the subareolar plexus is injected with the radioisotope tracer.

sentinel lymph node biopsy
cadaver study
subareolar injection
lymphoscintigraphy
peritumoral injection
dermal injection


Hemangiopericytoma of the Greater Omentum

A 41-year-old Chinese woman was admitted to our hospital with epigastric pain. Computed tomography detected a heterogeneous enhancement tumor fed by the left gastroepiploic artery in the left lower quadrant and cholelithiasis. Excision of the tumor in the greater omentum and cholecystectomy were performed laparoscopically. Histological findings confirmed a diagnosis of hemangiopericytoma with low-grade malignancy. To our knowledge, hemangiopericytoma of the greater omentum is very rare, and only 12 cases were reported in English literature. We report a case of hemangiopericytoma arising in the greater omentum and review the literature.
Introduction
Hemangiopericytoma is a rare tumor of the Zimmermann’s pericyte, which was first described by Murray and Stout1 in 1942. Pericytes are rudimentary cells that have contractile properties and regulate the blood flow through capillaries. Although hemangiopericytoma may arise anywhere, the musculature of the lower extremities, the pelvic fossa, and the retroperitoneum are the predominant sites of origin2. The development of hemangiopericytoma in the greater omentum is rare; to our knowledge, only 12 cases were reported in the English literature until the end of 20033–11. We report a patient with hemangiopericytoma originating in the greater omentum.
Case Report
A 41-year-old Chinese woman was admitted to our hospital with epigastric pain of 6-months in duration. On physical examination, the abdomen was flat and no tumor was palpable. Enhanced computed tomography detected a well-defined tumor with heterogeneous contrast enhancement and no calcifications in the left lower quadrant whose arterial blood supply came from the left gastroepiploic artery (Fig. 1). Cholecystolithiasis was an incidental finding. With a preoperative diagnosis of abdominal stromal tumor of the greater omentum, laparoscopic surgery was performed; a solitary tumor arose with a vascular pedicle originating from the greater omentum, which was free from adjacent organs and structures (Fig. 2). There was no evidence of peritoneal or liver metastases. The tumor was excised with 10 cm of the vascular pedicle to secure sufficient surgical margin, and cholecystectomy was also performed. The resected tumor was a solid tumor with the largest diameter of 55 mm, measured 55 × 45 × 40 mm, weighed 68.5 g, and was encapsulated without central necrosis or hemorrhage (Fig. 3). On histological examination, hematoxylin–eosin staining demonstrated that spindle cells grew around the vascular endothelial cells, and no mitoses were found in high power fields. Immunohistochemical examination exhibited that the tumor was positive for CD34, factor-XIIIa, and HLA-DR. These findings confirmed a diagnosis of hemangiopericytoma with low-grade malignancy, and the resection margin was clear. The resected gallbladder demonstrated chronic cholecystitis with gallstones. The patient made a satisfactory recovery and was discharged on the fifth postoperative day. Histological findings and absence of mitoses suggests hemangiopericytoma with low-grade malignancy. Therefore, adjuvant chemotherapy was not given. She remains well with no evidence of tumor recurrence 6 months after resection.
Figure 1Enhanced computed tomography exhibited a well-defined heterogeneous tumor with contrast enhancement in the left lower quadrant of the abdomen, and demonstrated that the left gastroepiploic artery (arrow) was feeding the tumor.Figure 2A solitary tumor arose in the greater omentum and was connected with the greater omentum by a vascular pedicle.Figure 3The resected tumor measured 55 × 45 × 40 mm, weighed 68.5 g, and was solid and encapsulated without central necrosis or hemorrhage.
Discussion
Hemangiopericytoma arising in the greater omentum is extremely rare and only 12 cases were reported in the English literature3–11. A review of the reported cases revealed that three patients died of recurrence. Therefore, evaluation of the malignant potential seems important. Recent reports proposed that malignant hemangiopericytoma is suspected for tumor size of more than 5 cm, a high mitotic index with more than four mitoses per ten high power fields, and necrosis and hemorrhage within the tumor12. According to the 13 reported cases3–11, tumor size and mitotic index related to tumor recurrence after resection.
Because most recurrences developed at distant sites, i.e., the liver, lung, and peritoneum, systemic chemotherapy may be an additional treatment for hemangiopericytoma with high malignant potential after resection and for recurrence. However, effective chemotherapeutic regimens and molecular targeting therapy have not been established to date. Because three of the four patients who underwent omentectomy in the literature had peritoneal recurrences, the significance of omentectomy is questionable, especially for these with low-grade malignancy like in our patient. Therefore, surgical resection provides the only opportunity of cure for patients with hemangiopericytoma arising in the greater omentum. For pedunculated tumors like in our patient, laparoscopic excision is feasible.

hemangiopericytoma
greater omentum
laparoscopic surgery