- Email: [email protected]
Authors’ response
READERS' FORUM
Letters to the editor* Effect of different incisor movements on the soft tissue profile
W
e appreciate Dr Kuhn et al for their study published in the March issue (Kuhn M, Markic G, Doulis I, G€ ollner P, Patcas R, H€anggi MP. Effect of different incisor movements on the soft tissue profile measured in reference to a rough-surfaced palatal implant. Am J Orthod Dentofacial Orthop 2016;149:349-57). The article provides significant insight into the changes in the soft tissue profile by the movement of incisors using a palatal implant as a reference and is a valuable addition to orthodontic literature. Although the study emphasized the need for stable reference points in the form of palatal implants for evaluation of incisor movements, there were a few concerns on following points. 1.
2.
3.
The total sample size mentioned in the study was 47 subjects, of whom 17 patients had Class I malocclusion, 28 had Class II malocclusion, and 2 had Class III malocclusion. Of the 28 patients having Class II malocclusion, 22 were female, and 2 were male. The total of the Class II sample size thus comes out to be 24 subjects, which could not be comprehended and also was not discussed. In the study, the minimum chronologic ages of 16 years for female subjects and 18 years for male subjects were accepted if the residual growth could be excluded by hand-wrist radiographs. Since it was a retrospective study, were the hand-wrist radiographs obtained as a routine diagnostic aid in patients above the age of 16 years in females and 18 years in males during the times when they were being treated? The distance of the x-ray source to the coronal plane was set at 200 cm. The recommended distance from the x-ray source to the midsagittal plane is 152.4 cm, or 5 feet.1,2 What were the reasons for using the increased distance from the x-ray source against the standard norms and for using a custom-made x-ray device? Furthermore, were any changes made in the exposure parameters to compensate for the increased x-ray source to the coronal plane distance?
* The viewpoints expressed are solely those of the author(s) and do not reflect those of the editor(s), publisher(s), or Association.
We would be really grateful if the authors can clarify these points. Also, since it was a retrospective study, it would help us better comprehend if we can know the approximate past time frame when these patients were treated. Deepak Kumar Gupta Sanjeev Verma Devinder Preet Singh Kanish Aggarwal Chandigarh, India Am J Orthod Dentofacial Orthop 2016;150:397 0889-5406/$36.00 Ó 2016 by the American Association of Orthodontists. All rights reserved.
http://dx.doi.org/10.1016/j.ajodo.2016.06.019
REFERENCES 1. Jacobson A. Radiographic cephalometry from basics to video imaging. Carol Stream, Ill: Quintessence; 1995. p. 39–52. 2. Kumar V, Ludlow JB, Mol A, Cevidanes L. Comparison of conventional and cone beam CT synthesized cephalograms. Dentomaxillofac Radiol 2007;36:263–9.
Authors’ response
W
e appreciate your careful reading of our study and are thankful for your questions. Here are our responses. 1.
2.
3.
This part was added during the revision process, and unfortunately a typing error has been overlooked. The total of 28 is correct, but there should have been 6 male and 22 female subjects. Yes, at the University of Zurich, hand-wrist radiographs are taken routinely for diagnostic and educational purposes in teenagers. This x-ray device was set up more than 30 years ago, and the distance has been left unchanged for longitudinal purposes. The main reason for having a longer distance from the x-ray source to the midsagittal plane was to have less magnification. Mirjam Kuhn Goran Markic Raphael Patcas Zurich, Switzerland Ioannis Doulis Athens, Greece 397
398
Readers' forum
Peter G€ollner Bern, Switzerland Michael P. H€anggi Basel, Switzerland Am J Orthod Dentofacial Orthop 2016;150:397-398 0889-5406/$36.00 Ó 2016 by the American Association of Orthodontists. All rights reserved.
http://dx.doi.org/10.1016/j.ajodo.2016.06.018
Common 3-dimensional coordinate system for assessment of directional changes
W
e congratulate Ruellas et al for their innovative concept of a common coordinate system for cone-beam computed tomography orientation,1 which has direct implications on cross-sectional and longitudinal studies. However, one core point of this article's methodology demands further discussion. This article concludes that 3D distances are not affected by head orientation, and the amount of directional change in each plane of 3D space is strongly influenced by head orientation. This proves the fact that scalars are invariant under coordinate transformation, but vectors are not. In this case, the 3D distances are Euclidean distances between 2 landmarks, which is a scalar (no directional property), and the x-, y- and z-axes components of 3D distances are vectors (with directional properties).2 The results of this study showed insignificant changes in 3D distances between before and after orientations of mandibular width (Dist RCo-LCo) (B.or A.or 5 0.01 mm) and mandibular length (Dist RCo-Pog) (B.or A.or 5 0.25 mm). Similarly, between before and after orientations, maxillary changes (T2-T1) and mandibular changes (T2-T1) were 0.07 and 0.03 mm, respectively. It is pertinent to mention here that the Euclidean distances in 3 dimensions are defined by the following equation. 3D Euclidean distanceðDPQ Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (1) 2 2 2 5 ðx1 x2 Þ 1 ðy1 y2 Þ 1 ðz1 z2 Þ
where Pðx1 ; y1 ; z1 Þ and Qðx2 ; y2 ; z2 Þ are the coordinates of 2 landmarks. The x (x2 x1), y (y2 y1), and z (z2 z1) components of 3D distance between any 2 fixed landmarks will change due to translational and rotational coordinate system transformation. However, the 3D Euclidean distances resulting from equation 1 are invariant.
September 2016 Vol 150 Issue 3
3D Euclidean distance 5 DPQ 5 D0PQ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2ffi x 01 x 02 þ y01 y02 þ z 01 z 02 5
(2)
where P 0 ðx10 ; y10 ; z10 Þ and Q0 ðx20 ; y20 ; z20 Þ are the oriented coordinates of P and Q landmarks, respectively. Therefore, the 3D distances resulting from equation 2 should be exactly the same for any type of coordinate transformation. Although the differences in 3D distance reported here might be statistically and clinically insignificant, logically, there should be no differences unless there is an error in landmark plotting or a limitation associated with measurement accuracy of the software. The authors have already taken care of the precision of landmark plotting by prelabeling the landmarks before head orientation; therefore, any further measurement differences could be due to imprecision of the software. The authors may like to provide some insight regarding the 3D measurement (scalar) differences due to coordinate transformations. There could be other reasons for which the authors can shed some light. Rajiv Balachandran Om P. Kharbanda Abhishek Gupta New Delhi, Delhi, India Am J Orthod Dentofacial Orthop 2016;150:398 0889-5406/$36.00 Ó 2016 by the American Association of Orthodontists. All rights reserved.
http://dx.doi.org/10.1016/j.ajodo.2016.06.021 REFERENCES 1. Ruellas AC, Tonello C, Gomes LR, Yatabe MS, Macron L, Lopinto J, et al. Common 3-dimensional coordinate system for assessment of directional changes. Am J Orthod Dentofacial Orthop 2016; 149:645–56. 2. Arfken GB, Weber HJ, Harris FE. Mathematical methods for physicists: a comprehensive guide. 7th ed. Oxford, United Kingdom: Elsevier; 2013.
Authors’ response
T
hank you very much for your interesting comments on our article.1 We agree that the concept of a common coordinate system for cone-beam computed tomography orientation has direct implications for clinicians’ assessments of the amount of directional changes in both cross-sectional and longitudinal studies. Our article was written for clinician readers, and so we described the implications of head orientation on components of directions in 3D distances rather than describing the mathematical formulas and scalar vs vectorial variations in transformations of the coordinate system.
American Journal of Orthodontics and Dentofacial Orthopedics
Letters to the editor* Effect of different incisor movements on the soft tissue profile
W
e appreciate Dr Kuhn et al for their study published in the March issue (Kuhn M, Markic G, Doulis I, G€ ollner P, Patcas R, H€anggi MP. Effect of different incisor movements on the soft tissue profile measured in reference to a rough-surfaced palatal implant. Am J Orthod Dentofacial Orthop 2016;149:349-57). The article provides significant insight into the changes in the soft tissue profile by the movement of incisors using a palatal implant as a reference and is a valuable addition to orthodontic literature. Although the study emphasized the need for stable reference points in the form of palatal implants for evaluation of incisor movements, there were a few concerns on following points. 1.
2.
3.
The total sample size mentioned in the study was 47 subjects, of whom 17 patients had Class I malocclusion, 28 had Class II malocclusion, and 2 had Class III malocclusion. Of the 28 patients having Class II malocclusion, 22 were female, and 2 were male. The total of the Class II sample size thus comes out to be 24 subjects, which could not be comprehended and also was not discussed. In the study, the minimum chronologic ages of 16 years for female subjects and 18 years for male subjects were accepted if the residual growth could be excluded by hand-wrist radiographs. Since it was a retrospective study, were the hand-wrist radiographs obtained as a routine diagnostic aid in patients above the age of 16 years in females and 18 years in males during the times when they were being treated? The distance of the x-ray source to the coronal plane was set at 200 cm. The recommended distance from the x-ray source to the midsagittal plane is 152.4 cm, or 5 feet.1,2 What were the reasons for using the increased distance from the x-ray source against the standard norms and for using a custom-made x-ray device? Furthermore, were any changes made in the exposure parameters to compensate for the increased x-ray source to the coronal plane distance?
* The viewpoints expressed are solely those of the author(s) and do not reflect those of the editor(s), publisher(s), or Association.
We would be really grateful if the authors can clarify these points. Also, since it was a retrospective study, it would help us better comprehend if we can know the approximate past time frame when these patients were treated. Deepak Kumar Gupta Sanjeev Verma Devinder Preet Singh Kanish Aggarwal Chandigarh, India Am J Orthod Dentofacial Orthop 2016;150:397 0889-5406/$36.00 Ó 2016 by the American Association of Orthodontists. All rights reserved.
http://dx.doi.org/10.1016/j.ajodo.2016.06.019
REFERENCES 1. Jacobson A. Radiographic cephalometry from basics to video imaging. Carol Stream, Ill: Quintessence; 1995. p. 39–52. 2. Kumar V, Ludlow JB, Mol A, Cevidanes L. Comparison of conventional and cone beam CT synthesized cephalograms. Dentomaxillofac Radiol 2007;36:263–9.
Authors’ response
W
e appreciate your careful reading of our study and are thankful for your questions. Here are our responses. 1.
2.
3.
This part was added during the revision process, and unfortunately a typing error has been overlooked. The total of 28 is correct, but there should have been 6 male and 22 female subjects. Yes, at the University of Zurich, hand-wrist radiographs are taken routinely for diagnostic and educational purposes in teenagers. This x-ray device was set up more than 30 years ago, and the distance has been left unchanged for longitudinal purposes. The main reason for having a longer distance from the x-ray source to the midsagittal plane was to have less magnification. Mirjam Kuhn Goran Markic Raphael Patcas Zurich, Switzerland Ioannis Doulis Athens, Greece 397
398
Readers' forum
Peter G€ollner Bern, Switzerland Michael P. H€anggi Basel, Switzerland Am J Orthod Dentofacial Orthop 2016;150:397-398 0889-5406/$36.00 Ó 2016 by the American Association of Orthodontists. All rights reserved.
http://dx.doi.org/10.1016/j.ajodo.2016.06.018
Common 3-dimensional coordinate system for assessment of directional changes
W
e congratulate Ruellas et al for their innovative concept of a common coordinate system for cone-beam computed tomography orientation,1 which has direct implications on cross-sectional and longitudinal studies. However, one core point of this article's methodology demands further discussion. This article concludes that 3D distances are not affected by head orientation, and the amount of directional change in each plane of 3D space is strongly influenced by head orientation. This proves the fact that scalars are invariant under coordinate transformation, but vectors are not. In this case, the 3D distances are Euclidean distances between 2 landmarks, which is a scalar (no directional property), and the x-, y- and z-axes components of 3D distances are vectors (with directional properties).2 The results of this study showed insignificant changes in 3D distances between before and after orientations of mandibular width (Dist RCo-LCo) (B.or A.or 5 0.01 mm) and mandibular length (Dist RCo-Pog) (B.or A.or 5 0.25 mm). Similarly, between before and after orientations, maxillary changes (T2-T1) and mandibular changes (T2-T1) were 0.07 and 0.03 mm, respectively. It is pertinent to mention here that the Euclidean distances in 3 dimensions are defined by the following equation. 3D Euclidean distanceðDPQ Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (1) 2 2 2 5 ðx1 x2 Þ 1 ðy1 y2 Þ 1 ðz1 z2 Þ
where Pðx1 ; y1 ; z1 Þ and Qðx2 ; y2 ; z2 Þ are the coordinates of 2 landmarks. The x (x2 x1), y (y2 y1), and z (z2 z1) components of 3D distance between any 2 fixed landmarks will change due to translational and rotational coordinate system transformation. However, the 3D Euclidean distances resulting from equation 1 are invariant.
September 2016 Vol 150 Issue 3
3D Euclidean distance 5 DPQ 5 D0PQ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2ffi x 01 x 02 þ y01 y02 þ z 01 z 02 5
(2)
where P 0 ðx10 ; y10 ; z10 Þ and Q0 ðx20 ; y20 ; z20 Þ are the oriented coordinates of P and Q landmarks, respectively. Therefore, the 3D distances resulting from equation 2 should be exactly the same for any type of coordinate transformation. Although the differences in 3D distance reported here might be statistically and clinically insignificant, logically, there should be no differences unless there is an error in landmark plotting or a limitation associated with measurement accuracy of the software. The authors have already taken care of the precision of landmark plotting by prelabeling the landmarks before head orientation; therefore, any further measurement differences could be due to imprecision of the software. The authors may like to provide some insight regarding the 3D measurement (scalar) differences due to coordinate transformations. There could be other reasons for which the authors can shed some light. Rajiv Balachandran Om P. Kharbanda Abhishek Gupta New Delhi, Delhi, India Am J Orthod Dentofacial Orthop 2016;150:398 0889-5406/$36.00 Ó 2016 by the American Association of Orthodontists. All rights reserved.
http://dx.doi.org/10.1016/j.ajodo.2016.06.021 REFERENCES 1. Ruellas AC, Tonello C, Gomes LR, Yatabe MS, Macron L, Lopinto J, et al. Common 3-dimensional coordinate system for assessment of directional changes. Am J Orthod Dentofacial Orthop 2016; 149:645–56. 2. Arfken GB, Weber HJ, Harris FE. Mathematical methods for physicists: a comprehensive guide. 7th ed. Oxford, United Kingdom: Elsevier; 2013.
Authors’ response
T
hank you very much for your interesting comments on our article.1 We agree that the concept of a common coordinate system for cone-beam computed tomography orientation has direct implications for clinicians’ assessments of the amount of directional changes in both cross-sectional and longitudinal studies. Our article was written for clinician readers, and so we described the implications of head orientation on components of directions in 3D distances rather than describing the mathematical formulas and scalar vs vectorial variations in transformations of the coordinate system.
American Journal of Orthodontics and Dentofacial Orthopedics