PII:

Journal of Dentistry, Vol. 26,No. 4, pp. 337-343,1998

so300-5712(97)00020-1

0 1998ElsevierScience Ltd. All rightsreserved Printedin GreatBritain 0300-5712/98 $19.00+0.00

ELSEVIER

The relationship between mandibular bone mineral density and panoramic radiographic measurements K. Horner and H. Devlin Turner Dental School,

University

of Manchester,

Manchester,

UK

ABSTRACT Objectives: To comparedensitometricand linear measurements (mandibularcortical thickness,MCT;

panoramicmandibularindex, PMI) madefrom dental panoramictomograms(DPTs) with bonemineral density (BMD) valuesobtainedusingdual energyX-ray absorptiometry(DXA) of the mandibleand to determinewhether measurements from DPTs have validity in predicting BMD. Methods: Forty edentulousfemalepatientswere examinedby a DPT incorporating a nickel stepwedge and by DXA of the mandible.In eachcasethe equivalentnickel thicknessof sitesin the mandibularbody, MCT and PM1 valueswere calculatedand their relationshipwith DXA measurements assessed. Results: Densitometricmeasurements of DPTs did not correlate with mandibular BMD. MCT significantly correlated with mandibular BMD (v=O.50,P=O.OOland v=O.36,P=O.O21for repeatedmeasurements) as did PM1 (~~0.37, PzO.019 and rz0.38, P=O.O16for repeated measurements).All three measurementsfrom DPTs had limited repeatability. MCT and PM1 had moderate sensitivity and specificityfor diagnosisof low mandibularBMD. Using ROC analysis,MCT and PM1 measurements of one observerwere significantly more valid than densitometryfor diagnosisof low mandibularBMD. Conclusions: It may be feasibleto useMCT and PM1 as diagnosticindicators of mandibular BMD, but further work is requiredto overcomeproblemswith repeatability and to provide a larger patient sample. 0 1998ElsevierScienceLtd. All rights reserved KEY WORDS: porosis J. Dent

1998;

Bone

densitometry,

26: 337-343

(Received

Dual-energy

18 November

X-ray

absorptiometty,

1996;

accepted

INTRODUCTION Osteoporosis, a generalized reduction in the amount of bone tissue, is a major health problem for middle-aged and elderly women. Bone loss occurs with age in men and women (age-related osteoporosis), but in the latter the rate of loss increasesat the time of the menopause (postmenopausal osteoporosis). This reduction in bone tissue is associated with an increased risk of fractures, pain and consequent morbidity for patients and high costs to the Health Service providersrS2. A considerable effort has been made to identify methods of Correspondence should be addressed to: K. Horner, Unit of Dental and Maxilla-facial Radiology, University Dental Hospital of Manchester, Higher Cambridge Street, Manchester, Ml5 6FH, UK. Tel: 0161 275 6690; Fax: 0161 275 6840.

Mandible,

23 March

Panoramic

radiology,

Osteo-

1997)

detecting individuals with osteoporosis at an early stage, as the institution of preventive therapy can limit the diseaseprocess. Bone mineral density (BMD) in the mandible has been shown, in a number of studies, to be positively correlated with that in the lumbar spine, femoral neck and forearm, important sites in osteoporosis3-*. Furthermore, osteoporosis has been associated in some studies with residual ridge resorptionv,rO and periodontal bone 10ss~‘,‘~, while ‘bone quality’ (of which bone mineral density is likely to be a determinant) is of relevance to the successof dental implants’3,‘4. BMD at specific sites can be measured using a variety of techniques, including single photon absorptiometry, dual photon or dual energy X-ray absorptiometry (DPA or DXA) and quantitative computed

338

J. Dent, 1998; 26: No. 4

tomography (QCT). DXA is well established as a means of bone densitometry in the spine and femoral neck, but with suitable software can be used in other anatomical areas. DXA is generally considered to be the technique of choice for assessment of BMD, but has only been used in the jaws in three studiess~i5~i6. Radiographic bone density can be assessed from simple radiographs in two main ways: by taking linear measurements (morphometric analysis) or by measuring optical density of bone and comparing it with a reference step wedge (densitometric analysis). Morphometric analysis has been limited to cortical thickness and calculation of measurements at various sitess,6,17-20 the panoramic mandibular index2’,22. Radiographic densitometry of the mandible has been performed in a number of studies, using both intra-ora15,6,‘8~‘9’23 and panoramic radiographs’9,24, but never related to mandibular BMD measured using DXA. Previous work has shown that the DPT, taken using a cassette fitted with a nickel step wedge, could be used to provide a quantitative measure of mandibular bone mineral content in vitro25. Subsequently in a clinical trial using DPTs~~, there was a significant difference in the densitometrically derived measurements of mandibular bone density between ‘osteoporotic’ and ‘non-osteoporotic’ groups of patients. Whilst not validating the technique as a diagnostic method, this study gave support for its further evaluation as a means of assessing BMD. The aims of this study were: (i) to assess the relationship between measurements (densitometric and morphometric) made from DPTs and mandibular BMD measured using DXA and (ii) to determine whether these radiographic measurements have validity in predicting BMD.

MATERIALS

AND METHODS

The participants in this study were healthy edentulous female patients attending a dental hospital for complete denture construction. Permission was sought from the patients to carry out bone densitometry as part of a study on osteoporosis. Local Ethics Committee approval was gained for the project and informed consent was obtained from the patients. Forty patients (44-79 years of age with a mean age of 65 years) agreed to take part. DXA examination DXA was performed using a Lunar DPX-L densitometer (Lunar Corporation, Madison, WI, USA) as described by Horner et ~1.‘. Briefly, patients were positioned semiprone, with superimposition of the contralateral sides of the mandible. To derive data for mandibular BMD, manual analysis was performed using a rectangular customized region of interest (ROI)

F/g. 7. A DXA scan from a patient in the study, showing a region of interest (ROI) box placed over the superimposed bodies of the mandible.

placed over the superimposed bodies of the mandible (Fig. 1). BMD measurements were recorded in g cmp2. Manual analysis of scans was carried out independently on two occasions, once by each author (one a radiologist and the other a hospital dental surgeon). The mean of these was taken as a ‘gold standard’ of mandibular bone mineral content. This was then compared with the panoramic radiographic measures of mandibular osteoporosis. DPT examination Each patient underwent DPT examination using a cassette fitted with a nickel step wedge as described previously24. Panoramic radiography was carried out using a Cranex dental panoramic tomographic unit (Soredex Orion Corporation, Helsinki) operated at 65 kVcp and 190 mAs. Images were recorded on Fuji HR-L 15 cm x 30 cm film in a standard cassette fitted with Fuji G-8 screens. Films were processed in a sensitometrically monitored Durr Medizin 430 automatic processor (Durr GmbH, Bietigheim-Bissingen, Germany). Radiographic Densitometty

DPT measurements of the mandible

Optical density of the nickel step wedge and test sites on the DPT were recorded using a hand-held densitometer (X-Ograph Ltd., Malmesbury, UK). The mandibular test site was situated below the mental foramen on each side of the mandible. The mean optical density measurement on both sites was recorded. The equivalent nickel thickness of the two test sites on each radiograph was then derived from the optical density data using the method of Devlin and Horner25 and the mean equivalent nickel thickness calculated for each patient. Mandibular

cortical

thickness

(MCT)

The thickness of the lower border cortex was measured on the right and left sides of the mandible. A line

Horner and Devlin: Mandibular

passing through the middle of the mental foramen and perpendicular to the tangent to the lower border was drawn on the radiograph. Measurements of the lower border cortical thickness were made along this line, using a clear plastic acetate sheet printed with millimetre gradations superimposed on the radiograph. Masking of radiographs and magnification ( x 2) was used. Measurements were estimated to the nearest 0.5 mm.

Panoramic

mandibular

index (PMI)

Benson et al.“’ described the panoramic mandibular index (PMI) as a measure of mandibular osteoporosis. The PM1 is the ratio of the thickness of the mandibular cortex to the distance between the mental foramen and the inferior mandibular cortex. Using the same line as described above for measuring cortical thickness, measurements between the lower border of the mandible and both the superior and inferior margins of the mental foramen were recorded, and the average of these two values calculated. Using this and the cortical thickness measurement, the PM1 for both the superior and inferior margins of the mental foramen were measured bilaterally, and the mean PM1 calculated for each subject. Relationship measurements

between

DXA and radiographic

The relationship between the mandibular BMD derived by DXA and the radiographic measurements (densitometry, MCT and PMI) was assessed by calculation of Pearson’s Correlation Coefficients using SPSS PC+26 with significance set at PcO.05 level. Diagnostic validity measurements

of radiographic

To illustrate the validity of the data obtained from the radiographs in detecting low mandibular bone mineral density, the sensitivities and specificities of densitometry, MCT and PM1 in diagnosis of ‘low’ mandibular BMD (< 1 s.d. below the mean mandibular BMD) were calculated at diagnostic thresholds based upon their respective means and standard deviations. These sensitivity and specificity data were used to derive receiver operating characteristic (ROC) curves by plotting sensitivity against (l-specificity). Areas and standard errors of ROC curves were calculated as described by Metz27. The significance of differences in areas of pairs of ROC curves was assessed as described by Hanley and McNei12* by taking into account the incresed sensitivity resulting from studying the same set of patients with different modalities. The ROC curve of each panoramic measurement (densitometry, MCT and PMI) was compared with the other for each observer in

bone density and PRM

339

this manner, followed by inter-observer comparisons of ROC curves for the same panoramic measurement.

Repeatability

of radiographic

measurements

To assess the repeatability of the mandibular radiographic measurements, in each case these were all performed on two occasions, once by each author. The strength of the relationship between repeated measurements was assessed by calculation of Pearson’s Correlation Coefficient, while the repeatability was examined using the method of Bland and Altman29, which derives a ‘coefficient of repeatability’ for repeated measurements which is twice the standard deviation of the differences between them.

RESULTS DXA examinations A typical mandibular DXA scan is shown in Fig. 1. The mean mandibular BMD of the 40 patients was 1.12 g cmp2 (s.d. 0.3 g cme2), with a range from 0.396 to 1.866 g cmp2.

Relationship measurements

between

DXA and radiographic

Densitometry

of the mandible

The mean optical density at the mandibular test site recorded bilaterally for each individual by both authors and averaged for each individual, was not significantly correlated with the mean DXA measurements (~0.01, PzO.93 and ~0.11, P=O.49 for separate measurements by the two observers). The mean equivalent mandibular nickel thickness derived from the optical density data was also not significantly correlated with DXA measurements (r=-0.25, P=O.13 and r=0.15, P=O.34 for separate measurements by the two observers).

Mandibular

cortical

thickness

(MCT)

Measurements of MCT for each patient, made by both experimenters, were independently, significantly correlated with mandibular DXA measurements (~0.50, P=O.OOl and r=0.36, P=O.O21).

Panoramic

mandibular

index (PMI)

The PM1 measurements of each patient, made by both experimenters, were independently, significantly

340 J. Dent. 1998; 26: No. 4 Tab/e 1. Areas (expressed as a fraction calculated using the method of Metzz9

1 1 1

Observer

Area

0.45 2 0.74 2 0.78 2

0.17 0.50 0.13 0.65 0.14 0.61

s.e.=standard PMI=panoramic

error; MCT=mandibular mandibular index.

of 1) under

the ROC

curves

SENSITIVITY

s.e.

0.18 0.12 0.12 cortical

thickness;

correlated with the respective DXA measurements (~0.37, P=O.O19 and r=0.38, P=O.O16).

Diagnostic validity of radiographic measurements ROC curves for the validity of densitometry, MCT and PM1 in the diagnosis of mandibular BMD are shown in Fig. 2(a-c). The areas of the ROC curves are shown in Table I. A perfect diagnostic test would be demonstrated by a line starting at the origin and extending up the y-axis to 1 and then running horizontally to a false positive rate (l-specificity) of 1, giving an area of 1.O. The diagonal line represents a test where the false positive rate is equal to the true positive test, giving an area of 0.50, i.e. a useless diagnostic test. The diagnostic validity (represented by the area of the ROC curve) of MCT and PM1 for observer 1 were significantly greater than densitometry in the diagnosis of mandibular BMD (PzO.04 and 0.02, respectively). The areas of all other pairs of ROC curves were not significantly different.

0

0.1

of mandibular

0

3 1 -

0.4 0.5 SPECIFICITY

0.6

0.7

0.8

0.9

SENSITIVITY /’ 0

(b)

/’

9-

/’

,’ //

//

04

/

1’

0

Repeatability

0.2

/

_/’

/’

0.1

0.2

0.3

0.1

0.2

0.3 ‘I

0.4

0.5

1’

,/

‘-MCT

Observer

‘l

*-MCT

Observer

2

0 6

0

7

0.6

0.9

1

measurements

The mean values and standard deviations of data from the two observers are shown in Table II. The results of analysis of the inter-observer repeatability of mandibular measurements are shown in Table III.

SENSITIVITY

DISCUSSION This study used DXA as the ‘gold standard’ for in vivo measurement of bone mineral density. Although the only real ‘gold standard’ measure of mandibular BMD would be by bone biopsy, it is likely that DXA offers the best means of obtaining accurate information in vivo. Corten et al. l5 first suggested using DXA, already well-established as a means of measuring BMD in the spine and femoral neck, as a means of investigating bone density in the mandible. They carried out in vitro and in vivo studies, although the latter was limited to a trial involving just four patients. Hildebolt et al. I6 carried out mandibular DXA in cadavers and in nine patients in a study relating measurements of bone

0

-

0.4 0 5 SPECIFICITY

0.6

0.7

Fig, 2. ROC curves for (a) densitometry, (b) MCT diagnosis of mandibular BMD. Ni equiv=equivalent of the mandible determined by densitometry.

0.8

0.9

1

and (c) PMI in the nickel thickness

Horner and Devlin: Mandibular Table II. Mandibular

radiographic

Optical

Observer Observer

Mean 1.48 1.42

1 2

“Mean values MGmandibular

s.d. 0.27 0.28

of each measurement cortical thickness.

Tab/e 111. Analysis

Densitometry

Density

of interobserver

Optical Density Equivalent nickel thickness

MCT PMI r=Pearson’s correlation Altmar?‘. Inter-observer

measurements

of the 40 patients

Equivalent

Nickel

Thickness

Mean 0.22 0.23

deviations mandibular

(mm)

MCT Mean 4.11 4.39

PM/ (%)

(mm) s.d. 1 .oo 0.91

Mean 31.79 36.29

s.d. 12.29 11.35

(sd.) are given index.

repeatability

of mandibular

r

Mean difference

Standard Deviation of differences

Coefficient Repeatability

0.9326 0.6074

-0.05 -0.01

0.10 0.06

0.20 0.12

13.7% 53.3%

0.6419 0.77

-0.29 -4.49

0.81 8.07

1.62 16.14

38.0% 47.4%

measurements

coefficient. The coefficient of repeatability precision=coefficient of repeatability/mean

mineral density to bitewing radiographic measurements of alveolar bone. In a recent study’, mandibular DXA was found to have limited precision, but when the ranks of separate BMD measurements were compared they were highly correlated. Therefore relative, rather than absolute, mandibular BMD measurements are consistent. We used the mean BMD of the two analyses of the DXA scans in an attempt to increase the validity of the data, following the recommendation of Corten et ~1.‘~ who suggested that reproducibility might be improved by repeated measurements. We selected edentulous patients as this simplified the ROI placement on the DXA scans, with no risk of superimposition of teeth and an artificially high BMD measurement. Thus the results should be interpreted with some reservation about their validity in dentate patients. We assessed repeatability (Table 3) of mandibular measurements using both correlation coefficients and the method of Bland and Altman2’. Correlation coefficients are often used alone as a measure of repeatability, but this is erroneous as they demonstrate only the strength of a relationship. The coefficient of repeatability is useful as it is derived from the standard deviation of the differences: 95% of differences will lie within the range of rt 2 s.d. of the mean difference2’. As the magnitude of the coefficient has to be considered in relation to that of the measurement involved, we also derived a figure for inter-observer precision from the mean value of each. As can be seen from examination of Table 3, precision was best for optical density measurements. This was unsurprising as these were mainly dependent upon the optical densitometer while the linear measurements had greater observer dependency. MCT showed the best repeatability of the other measurements.

341

by the two observers*

s.d. 0.08 0.05

and standard PMI=panoramic

bone density and PRM

was derived measurement

of Precision

by the method of Bland and in the 40 patients xl 00 (%).

Despite the good repeatability of mandibular optical density measurements, the equivalent nickel thickness data showed poor repeatability and no significant correlation with mandibular BMD. This was disappointing, particularly when previous work24,25 had given encouraging results. The equivalent nickel thickness of mandibular test sites was derived from regression analysis of the optical density values of the step wedge. In this study there were problems because of shadows of the hyoid bone, cervical spine and pharyngeal air shadow overlying the image of the nickel step wedge. These anatomical superimpositions were not present in the in vitro study25 where only mandibles were examined and where overlying soft tissues had been mimicked by immersing the mandibles in a water bath. Most previous work in which radiographic densitometry has been used to measure in vivo mandibular bone density has used intra-oral radiographs5~6~‘8~1g~23. This method is likely to provide more reproducible information because the problem of complicating shadows of bone and air are absent, while soft tissue shadows are of a more consistent thickness over the image on an intra-oral film. One other studylg has employed panoramic radiographs for densitometry, but found similar problems to us in finding a place on the panoramic image free of superimpositions. The results from this study do not support the validity of using panoramic radiographic densitiometric measurements as a means of measuring mandibular BMD. MCT has been used previously as a morphometric tool for assessing osteoporosis status by a number of workers5%6”7-20, but in only three studies5a6,17has cortical width been directly related to mandibular BMD. In all of these, cortical thickness was measured at the

342

J. Dent. 1998; 26: No. 4

gonion. Bras et al. l7 noted that gonial cortical thickness remained relatively constant except in postmenopausal women of 60 years and older, where it was distinctly thinner. They suggested that cortical thickness at this site might be a useful tool in evaluating metabolic bone loss, although their study can be criticized for lack of a thorough statistical analysis. Kribbs et ~1.“~ found that while cortical thickness at the gonion correlated with forearm and spinal BMDs, there was none with mandibular BMD as assessed by radiographic densitometry. Our study is the first to relate the inferior mandibular cortical thickness directly to mandibular BMD, although similar data were available to, but not presented by, Klemetti et al.22. PM1 was first proposed by Benson et a1.21 as a radiomorphometric index of adult cortical bone mass. Although it has subsequently been employed in two studies assessing its relationship with bone mass in important skeletal sites20,22, only one of these directly related PM1 to mandibular BMD. Klemetti et aZ.22, who assessed mandibular BMD by QCT, found that PM1 correlated (rz0.37) with buccal cortical BMD. Our study gives almost identical correlations between PM1 and mandibular BMD (integral cortical and trabecular bone). Our study suggests that PM1 has no significant advantage over MCT as a measure of mandibular BMD. There were greater problems of repeatability with PM1 than with MCT, which appeared to be due to problems in identification of the mental foramen in some patients, resulting in marked differences in measurements between the two observers. This problem of confident identification of the mental foramen has been noted previously22. Furthermore, it has been shown30a3’ that the mental foramen may sometimes be multiple, compounding the identification problem. Although it is possible that identification of the mental foramen may be improved by observer calibration, or by averaging repeated measurements, the results here suggest that PM1 is unlikely to offer any advantages over MCT as a tool for general osteoporosis assessment or as a means of assessing mandibular BMD prior to implantology. In order to assessthe prediction of mandibular BMD by the various radiographic measurements, we calculated sensitivities and specificities at a number of thresholds to prepare ROC curves. On ROC curves, the diagonal line indicates a combination of sensitivity and specificity for a diagnostic test which would be obtained by random, or ‘pure guesswork’. Examination of Fig. 2(aac) and Table 2 shows clearly that the densitometric method was of no value, with no obvious observer differences. In contrast, MCT and PM1 gave encouraging results, although there were differences between the two observers with better sensitivities and specificities obtained by the radiologist (observer 1). This presumably reflects training and experience, but suggests that practical use of MCT and PM1 in future studies might

be complicated by inter-observer variation. Furthermore, bearing in mind the problems in obtaining repeatable measurements to derive PMI, described above, the ROC analysis suggests that PM1 offers no advantages over the simpler measurement of MCT. When the ROC curves were subjected to statistical analysis by comparison of areas, most were not significantly different. This reflects the relatively small number of ‘abnormal’ individuals (five), i.e. with ‘low’ mandibular BMD. Thus caution should be exercised in extending the results from this study to larger numbers of patients. More extensive studies will be required to obtain more reliable data for assessment of validity. Overall, MCT and PM1 were significantly correlated with mandibular BMD. MCT is the simplest of the methods assessed and its measurement requires no specialized facilities. Obviously simple linear measurements from any radiograph must be considered in the light of radiographic magnification variation. In our study the same X-ray unit was used for all patients, but any research using MCT obtained from radiographs from different panoramic machines would need to modify the measurements appropriately to permit comparison. Measurements from panoramic radiographs must also be selected with reference to the potential error caused by positioning inaccuracies. Horizontal measurements vary markedly with relatively small antero-posterior positioning differences. However, vertical measurements are not similarly affected32 and it is likely that typical antero-posterior and head-tilting positioning inaccuracies would not significantly affect MCT.

CONCLUSIONS (1) Densitometric measurements of panoramic radiographs did not correlate with mandibular BMD values obtained by DXA. Densitometry showed poor sensitivity and specificity for determining mandibular BMD. (2) MCT and PM1 were significantly correlated with mandibular BMD and showed moderate sensitivity and specificity for diagnosis of mandibular BMD. (3) ROC analysis showed that both MCT and PM1 had significantly better diagnostic validity than densitometry for one observer (the radiologist). Studies with larger patient numbers would be necessary to allow more meaningful assessment of diagnostic validity of panoramic measurements in diagnosis of mandibular BMD. (4) All three radiographic measurements (densitometry, MCT and PMI) showed problems with repeatability and inter-observer variation which suggests that careful training and calibration of observers would be important if they were to be used as an indicator of mandibular BMD.

Horner and Devlin: Mandibular

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Participants completed a shortened version of Big Five Inventory (BFI) and a Healthy Eating Behavior and. Attitude scale. We found a significant and ... Their data showed that when the other four traits were controlled, the ..... The Big Five Invento

The relationships between two indices of mandibular ...
Mandibular body BMD was calculated by manual analysis of DXA scans. ... sample of 40 patients, giving data which showed ... (Rs) using SPSS PC+,20.

The relationships between two indices of mandibular ...
densitometry3,4 and morphometry.5±8. Many of these require specialised facilities or are time-consuming and necessitate radiography of the highest standards.

The relationships between two indices of mandibular ...
Objectives: To establish whether a relationship exists between the bone quality index (BQI), the mandibular cortical index (MCI) and bone mineral density (BMD) of the body of the mandible as measured by dual energy X-ray absorptiometry (DXA). Methods

Bone mineral density in mandibles of ovariectomized ...
May 26, 2006 - In this study, bone mineral density (BMD) analysis has been performed .... the trabecular threshold but exceeding the soft tissue threshold.

Comparisons of noninvasive bone mineral measurements
(QUS) of the calcaneus for speed of sound (SOS CALC) and broadband ultrasound attenuation (BUA CALC). In ... techniques providing the best results were: (1) spine, QCT TRAB BMD (annual loss, 1.2% ... The only established techniques for noninvasive ..

Comparisons of noninvasive bone mineral ... - Wiley Online Library
0.40. 0.37. 0.31. 0.41. 0.37. 0.34. 0.42. 0.29. 0.27. 0.28. 0.45. 0.52. 1. 0.24. 0.56. WS. 39.2. 23.3. 16.3. 17.2. 18.6. 18.1. 15.1. 23.9. 36.0. 16.2. 14.9. 22.2. 12.1. 2.4.

Volumetric Bone Mineral Density in Normal Subjects ...
D UAL ENERGY x-ray absorptiometry (DXA), with its high accuracy and ..... Alternative methods that have been employed to calculate bone volume use different ...

Comparisons of noninvasive bone mineral ... - Wiley Online Library
techniques: (1) quantitative computed tomography of the L1–L4 lumbar .... used in the data analysis). ... were applied to the bone image data to compute bone.

The Relationship Between the UNIVAC Computer and ... - IJEECS
Similarly, we show the diagram used by our heuristic in Figure 1. While futurists rarely assume the exact opposite, ... Intel 386s from the NSA's Internet-2 cluster to better understand our mobile telephones. We only characterized ... space of our se

The relationship within and between the extrinsic and intrinsic systems ...
Apr 1, 2007 - aDepartment of Biomedical Engineering, School of Computer and Information .... system. These resting state functional network patterns have been .... peaks in a previous study (Tian et al., in press), and the one for the.

Establishing the Nexus The Definitive Relationship Between Child ...
http://www.missingkids.com/en_US/publications/NC70.pdf [hereinafter ... However, in United States v. Leon,. 6. the Supreme Court. 3. U.S. CONST. amend. IV. 4.

RELATIONSHIP BETWEEN GIBBERELLINS, HEIGHT ...
and for giving me the opportunity to pursue my Masters degree under his ...... activity was discovered du ring fungicide screening programs in the 1 970s (Davis .... with paclobutrazol is increased interveinal distance (Sopher et al., 1999). In.

The Relationship Between the Sense of Self-Agency ...
that a sense of self-agency can be experienced even if some degree of temporal bias is perceived. Furthermore, they determined that highly schizotypal people ...