- Email: [email protected]
Is trabecular bone in the mandible different?
IS TRABECUAR BONE IN THE MANDIBLE DIFFERENT?
we clearly stated that the density measured was with hone marrow in situ. Because one of the goals in the research was to compare the hone structure stiffness with and without the cortical plates, we chose to test the hone specimens with the marrow in situ in both tests. We felt this approach would he more clinically relevant than apparent density. Brunski states our testing conditions are confusing, hecause we used the term “elastic modulus” rather than modulus of elasticity, or Young’s modulus, and states “Young‘s modulus is defined as the ratio of longitudinal stress to longitudinal strain in a uniaxial tensile or compression test.” He also states Figure ZC could measure Young’s modulus, hut Figure ZB. could only measure stiffness. It is our understanding that the modulus of elasticity is often called the elastic modulus (lb/in? or kgf/cm’) and is the ratio of the increment of unit stress to increment of unit deformation in the same direction within the elastic limit.’ StrictI) speaking, Young’s modulus is the modulus of elasticity in tension. although most publications use either compression or tension. In our study, the elastic modulus of mandibular trzhecular hone was measured in compression under the unconstrained condition (the absence of the cortical plates). Because the methodology clearly described that the test condition was compression, the authors abbreviated the term as elastic modulus. Stiffness (lb/in or kgf/cm). which is often called the spring constant of an elastic member. is the ratio hetween the force applied to the member and the deflection produced hy that force.+ The stiffness of a specimen depends on the cross sectional area and the length of the specimen. Stiffness is a structure property. It was determined from the slope of the linear portion of the load-displacement curve. Linde and Hvid’s’ research showed that in the human knee the specimen stiffness in the side-constrained condition is 19”4 higher than in the unconstrained condition. We followed a similar protocol for the mandibular tnhecular hone, as stated in the article. The modulus measured under the constrained condition of the cortical plates (Figure 1B) times the cross-sectional area of the specimen (A), and divided by the initial length of the specimen (L). is the stiffness of a structure of the trahecular hone with the cortical plates on the sides. “The elastic modulus under constrained condition” is a new term offered by the authors for clinical relevancy. The trahecular hone specimens under the constrained conditions of the cortical plates displayed a 65% higher stiffness than the unconstrained test. This is significantly greater than data found in the knee. Because the D1 hone in Misch’s hone classification does not have a crestal cortical plate, and is usually wide in width, the “unconstrained condition” of the trahecular hone may have a direct clinical comparison. Hence, again, the data presented in this article is significant, because it is a needed database for clinical treatment planning, especially in D4 hone. We agree with Brunski’s comment that this article “makes a good start at identifying important engineering properties of trahecular hone.” He also states that several articles address some promising developments that are related to this topic, which were not included in this report. The original article presented to the Journal was many pages longer, and had a larger clinical significance section, including clinical cases. The referees of the Jowwal asked us to reduce the length of the article, and exclude almost all of the clinical material.
7b the Editor-The Discussion at the end of our article “Mechanical Properties of Tmhecular Bone in the Human Mandihlc: Implications for Dental Implant Treatment Planning and Surgical Placement” by Brunski in JO/Cf.S 57:706. 1009 may give the reader more confusion than clarity on several issues raised. Brunski states, .., this article does not actually contribute much to the medical database.” Yet, later in the Discussion he states. “The authors’ data on relationships between properties and (apparent) density do not fit the typical power laws in the rest of the literature.” Carter and Hayes,’ who established a relationship hetween mechanical properties of trahecular hone and apparent density, used human specimens from the proximal tibia and bovine specimens from the femoral condyles and included literature on compact hone. Goldstein? reviewed past studies to analyze the mechanical properties of trahecular hone as a function of anatomic location in the human skeleton. He found that a significant and consistent correlation existed between the variation in material properties and the function of the bony region tested. Both of these references were cited in our article. It should he noted that the hone specimens in our study compared the anterior, middle, and posterior regions of dentate. partially edentulous and edentulous mandibles. The authors expected different results from other published work, given the unique anatomic site. Rather than a quadratic relationship between ultimate compressive strength and density, we found a third order polynomial relationship. Rather than a cubic relationship between Young‘s modules and apparent density, we found a linear relationship between stiffness (“elastic modulus”) and density. To our knowledge, no controlled. quantitative studies have attempted to characterize the trahecular hone of the human mandible. Certainly, this information is important to the database. especiall) because it is different. Brunski states our article “primarily uses the term ‘densiv’ when it should iisr the more appropriate term ‘appar.” ent density‘.” and states, “This is not a trivial point Brunski is correct, appmw?t &r?site)~ is different than the term cierisi[)~ as used in the article. Apparent density is defined as the weight of the defatted cancellous structure divided by the overall volume of the specimen. In our article, the term apparent density was not intended, because
Letters to the Editor anz considered for publication (subject to editing and abridgment), provided they ate submitted in one of two ways. If typewritten, they must be submitted in duplicate, signed by all authors, double-spaced, and should not exceed 40 typewritten I&s of man&pt text (excluding references). You may also E-mail your Letters to the Jiditor to [email protected]. The same length limits +pl$ ‘Ikttus should not duplicate similar material bebig sUbmitted or.published elsewhere. Jxttexs to a recentJou@Z arJlcl5, thust be received within 6 weeks of the aiticle’s publication. Re&i$t of ietters is not acknowledged and there is no guarantee that your letter will be published. We cannot provide prepubkadon proofs. Submitting the letter constitutes your permision fix its publication in any curnst or subsequent is& or Mition of the JournuJ ia any form or media, now known or heAfter developed.
247
248
LETTERS
In conclusion, we thank Professor Brunski for his comments and discussion of our research, and look forward to sharing our experiences with him and the reading audience in the future. CARL
E.
MIKH,
DDS,
MDS
Birmingham, MI ZHIMIN Qu, MS MARTHA W. BIIXX, PhD Birmingham, AL
References 1. Carter DR. Haynes WC: Bone compressive strength: The influence of density and strain rate. Science 194:1174.1977 2. Goldstein SA: The mechanical properties of trabccular bone: Dependence on anatomic location and function. J Biomech 20:1055. 1987 3. Baumeister T. Avallone EA. Baumcistcr III T: Mark’s Standard Handbook for Mechanical Engineers (cd 8). New York. m. McGraw-Hill,
1987
4. Linde F. Hvid I: The effect of constraint on the mechanical behavior
of tnbecular
bone
specimens.
J Biomech
22:485.
1989
In Rep&--I agree with the authors that some of the issues being discussed “. may give the reader more conhlsion than clarity.” That may be true in part because a hlii understanding of what is being discussed involves knowiedge of some of the finer points of mechanical testingwhich are probably not at the fingertips of most readers of this journal. Nevertheless, these details may help readers to realize that some of this article’s conclusions need a bit of caution and interpretation. On density versus apparent density, the authors‘ ciarification helps, although page 703 of the published article interchangeably uses the terms density and apparent density, which remains confusing to the reader for the reasons I stated earlier. In their letter, the authors state that “the term apparent density was not intended” (even though they used that term), and that they meant to use the term “density” throughout. Indeed, the article uses “density” most of the time. The only problem with using density alone is that essentially all other biomechanicai investigations on trdbecutar bone are couched in terms of apparent density. (Part of the reason for this has to do with modeling trabecuiar bone as a porous form of dense bone.) Hence, it remains difficult to compare the authors’ results with literature results, especially when it comes to the power law relationships between modulus or compressive strength and density, as discussed again shortly. On the topic of “elastic modulus,” the authors‘ remarks still do not fully justify for me the comparison of constrained and unconstrained “elastic moduii” in Figure 3. In my mind, what these data are showing is something that is already obvious-that a structural property of bone (as measured from Figure 2B) ought to differ from an intrinsic property of bone, namely the Young’s modulus (as measured via the test in Figure 2C). The two tests do not measure the same thing, and that is a key reason as to why there is a difference between the data in Figure 3. Figure 2C measures Young’s modulus (an intrinsic mechanical property of the material), while Figure 2B essentially describes an indentation test of a slab of bone, in which case the slope of a load-penetration
TO
THE
EDITOR
curve will not immediately yield a value for Young’s elastic modulus. On the authors’ reported power law relationships between elastic modulus and density. and between ultimate compressive strength and density, I still think these data remain difficult to interpret for 2 reasons. First, evidently the authors are establishing their relationships in terms of density and not the more commonly used apparent density. Hence it is difficult to compare their data against everyone else’s data. which are typically reported in terms of apparent density. If the mandibular bone properties are unique, it will be harder to figure this out, given their mode of reporting it. Second. although a linear relationship between modulus and density is possible. second order and third order laws also occur; typical data shows the third order law, but the authors are correct that this is not the only possibility. The book by Gibson and Ashby’ notes how the internal cellular structure of the trabecular bone can affect the relationship. I brought up this question because the authors might be able to rationalize their first order law by looking at the cellular structure of the trabecuiar bone and comparing it with the idealized models in Gibson and Ashby. As for the authors’ claimed third order polynomial relationship between ultimate compressive strength and density, this is a somewhat unusual finding in light of the 9 studies referenced in Gibson and Ashby’s review that ail fit a second order relationship. Grdnted, the authors’ current data are from bone in the mandible, and maybe mandibular trabecutar bone is very different from trabecular bone elsewhere in the body. However, as noted with modulus, there have been attempts to predict power law relationships for trabecular bone on the basis of specific assumed geometries of the foam-like internal network structure of trdbecuiar bone (as reviewed in Gibson and Ashby’). For example, trabecular bone with a pronounced “stress-orientation”’ shows a second order relationship between strength and apparent density in the transverse direction, but a first order relationship in the longitudinal direction. Notably, no theoretical model predicts a third order relationship between compressive strength and density, although there is a model predicting a 3/2 power relationship. Maybe the authors are right in suggesting that mandibular trabecular bone might be ver) different from trabecuiar bone elsewhere in the body, but this remains to be seen. Although I applaud the authors’ attempt to measure the properties of bone in the human mandible, after ail is said and done here I remain unclear on another key issue of clinical relevance: Exactly how can the data in this article be readily used in treatment planning? Among other problems. I am still unsure about how these properties of bone in an edentulous mandible will relate to the properties of bone that develop after the healing that follows implantation surgery. JOHN
PhD Troy, NY
BRUNSKI,
Reference 1. Gibson
LJ. Ashby
MF:
Stnlcture and Properties. 316-331
Cancellous Tarrytown,
bone, it2 Cellular Solids: NY, Pegamon. 1988. pp
we clearly stated that the density measured was with hone marrow in situ. Because one of the goals in the research was to compare the hone structure stiffness with and without the cortical plates, we chose to test the hone specimens with the marrow in situ in both tests. We felt this approach would he more clinically relevant than apparent density. Brunski states our testing conditions are confusing, hecause we used the term “elastic modulus” rather than modulus of elasticity, or Young’s modulus, and states “Young‘s modulus is defined as the ratio of longitudinal stress to longitudinal strain in a uniaxial tensile or compression test.” He also states Figure ZC could measure Young’s modulus, hut Figure ZB. could only measure stiffness. It is our understanding that the modulus of elasticity is often called the elastic modulus (lb/in? or kgf/cm’) and is the ratio of the increment of unit stress to increment of unit deformation in the same direction within the elastic limit.’ StrictI) speaking, Young’s modulus is the modulus of elasticity in tension. although most publications use either compression or tension. In our study, the elastic modulus of mandibular trzhecular hone was measured in compression under the unconstrained condition (the absence of the cortical plates). Because the methodology clearly described that the test condition was compression, the authors abbreviated the term as elastic modulus. Stiffness (lb/in or kgf/cm). which is often called the spring constant of an elastic member. is the ratio hetween the force applied to the member and the deflection produced hy that force.+ The stiffness of a specimen depends on the cross sectional area and the length of the specimen. Stiffness is a structure property. It was determined from the slope of the linear portion of the load-displacement curve. Linde and Hvid’s’ research showed that in the human knee the specimen stiffness in the side-constrained condition is 19”4 higher than in the unconstrained condition. We followed a similar protocol for the mandibular tnhecular hone, as stated in the article. The modulus measured under the constrained condition of the cortical plates (Figure 1B) times the cross-sectional area of the specimen (A), and divided by the initial length of the specimen (L). is the stiffness of a structure of the trahecular hone with the cortical plates on the sides. “The elastic modulus under constrained condition” is a new term offered by the authors for clinical relevancy. The trahecular hone specimens under the constrained conditions of the cortical plates displayed a 65% higher stiffness than the unconstrained test. This is significantly greater than data found in the knee. Because the D1 hone in Misch’s hone classification does not have a crestal cortical plate, and is usually wide in width, the “unconstrained condition” of the trahecular hone may have a direct clinical comparison. Hence, again, the data presented in this article is significant, because it is a needed database for clinical treatment planning, especially in D4 hone. We agree with Brunski’s comment that this article “makes a good start at identifying important engineering properties of trahecular hone.” He also states that several articles address some promising developments that are related to this topic, which were not included in this report. The original article presented to the Journal was many pages longer, and had a larger clinical significance section, including clinical cases. The referees of the Jowwal asked us to reduce the length of the article, and exclude almost all of the clinical material.
7b the Editor-The Discussion at the end of our article “Mechanical Properties of Tmhecular Bone in the Human Mandihlc: Implications for Dental Implant Treatment Planning and Surgical Placement” by Brunski in JO/Cf.S 57:706. 1009 may give the reader more confusion than clarity on several issues raised. Brunski states, .., this article does not actually contribute much to the medical database.” Yet, later in the Discussion he states. “The authors’ data on relationships between properties and (apparent) density do not fit the typical power laws in the rest of the literature.” Carter and Hayes,’ who established a relationship hetween mechanical properties of trahecular hone and apparent density, used human specimens from the proximal tibia and bovine specimens from the femoral condyles and included literature on compact hone. Goldstein? reviewed past studies to analyze the mechanical properties of trahecular hone as a function of anatomic location in the human skeleton. He found that a significant and consistent correlation existed between the variation in material properties and the function of the bony region tested. Both of these references were cited in our article. It should he noted that the hone specimens in our study compared the anterior, middle, and posterior regions of dentate. partially edentulous and edentulous mandibles. The authors expected different results from other published work, given the unique anatomic site. Rather than a quadratic relationship between ultimate compressive strength and density, we found a third order polynomial relationship. Rather than a cubic relationship between Young‘s modules and apparent density, we found a linear relationship between stiffness (“elastic modulus”) and density. To our knowledge, no controlled. quantitative studies have attempted to characterize the trahecular hone of the human mandible. Certainly, this information is important to the database. especiall) because it is different. Brunski states our article “primarily uses the term ‘densiv’ when it should iisr the more appropriate term ‘appar.” ent density‘.” and states, “This is not a trivial point Brunski is correct, appmw?t &r?site)~ is different than the term cierisi[)~ as used in the article. Apparent density is defined as the weight of the defatted cancellous structure divided by the overall volume of the specimen. In our article, the term apparent density was not intended, because
Letters to the Editor anz considered for publication (subject to editing and abridgment), provided they ate submitted in one of two ways. If typewritten, they must be submitted in duplicate, signed by all authors, double-spaced, and should not exceed 40 typewritten I&s of man&pt text (excluding references). You may also E-mail your Letters to the Jiditor to [email protected]. The same length limits +pl$ ‘Ikttus should not duplicate similar material bebig sUbmitted or.published elsewhere. Jxttexs to a recentJou@Z arJlcl5, thust be received within 6 weeks of the aiticle’s publication. Re&i$t of ietters is not acknowledged and there is no guarantee that your letter will be published. We cannot provide prepubkadon proofs. Submitting the letter constitutes your permision fix its publication in any curnst or subsequent is& or Mition of the JournuJ ia any form or media, now known or heAfter developed.
247
248
LETTERS
In conclusion, we thank Professor Brunski for his comments and discussion of our research, and look forward to sharing our experiences with him and the reading audience in the future. CARL
E.
MIKH,
DDS,
MDS
Birmingham, MI ZHIMIN Qu, MS MARTHA W. BIIXX, PhD Birmingham, AL
References 1. Carter DR. Haynes WC: Bone compressive strength: The influence of density and strain rate. Science 194:1174.1977 2. Goldstein SA: The mechanical properties of trabccular bone: Dependence on anatomic location and function. J Biomech 20:1055. 1987 3. Baumeister T. Avallone EA. Baumcistcr III T: Mark’s Standard Handbook for Mechanical Engineers (cd 8). New York. m. McGraw-Hill,
1987
4. Linde F. Hvid I: The effect of constraint on the mechanical behavior
of tnbecular
bone
specimens.
J Biomech
22:485.
1989
In Rep&--I agree with the authors that some of the issues being discussed “. may give the reader more conhlsion than clarity.” That may be true in part because a hlii understanding of what is being discussed involves knowiedge of some of the finer points of mechanical testingwhich are probably not at the fingertips of most readers of this journal. Nevertheless, these details may help readers to realize that some of this article’s conclusions need a bit of caution and interpretation. On density versus apparent density, the authors‘ ciarification helps, although page 703 of the published article interchangeably uses the terms density and apparent density, which remains confusing to the reader for the reasons I stated earlier. In their letter, the authors state that “the term apparent density was not intended” (even though they used that term), and that they meant to use the term “density” throughout. Indeed, the article uses “density” most of the time. The only problem with using density alone is that essentially all other biomechanicai investigations on trdbecutar bone are couched in terms of apparent density. (Part of the reason for this has to do with modeling trabecuiar bone as a porous form of dense bone.) Hence, it remains difficult to compare the authors’ results with literature results, especially when it comes to the power law relationships between modulus or compressive strength and density, as discussed again shortly. On the topic of “elastic modulus,” the authors‘ remarks still do not fully justify for me the comparison of constrained and unconstrained “elastic moduii” in Figure 3. In my mind, what these data are showing is something that is already obvious-that a structural property of bone (as measured from Figure 2B) ought to differ from an intrinsic property of bone, namely the Young’s modulus (as measured via the test in Figure 2C). The two tests do not measure the same thing, and that is a key reason as to why there is a difference between the data in Figure 3. Figure 2C measures Young’s modulus (an intrinsic mechanical property of the material), while Figure 2B essentially describes an indentation test of a slab of bone, in which case the slope of a load-penetration
TO
THE
EDITOR
curve will not immediately yield a value for Young’s elastic modulus. On the authors’ reported power law relationships between elastic modulus and density. and between ultimate compressive strength and density, I still think these data remain difficult to interpret for 2 reasons. First, evidently the authors are establishing their relationships in terms of density and not the more commonly used apparent density. Hence it is difficult to compare their data against everyone else’s data. which are typically reported in terms of apparent density. If the mandibular bone properties are unique, it will be harder to figure this out, given their mode of reporting it. Second. although a linear relationship between modulus and density is possible. second order and third order laws also occur; typical data shows the third order law, but the authors are correct that this is not the only possibility. The book by Gibson and Ashby’ notes how the internal cellular structure of the trabecular bone can affect the relationship. I brought up this question because the authors might be able to rationalize their first order law by looking at the cellular structure of the trabecuiar bone and comparing it with the idealized models in Gibson and Ashby. As for the authors’ claimed third order polynomial relationship between ultimate compressive strength and density, this is a somewhat unusual finding in light of the 9 studies referenced in Gibson and Ashby’s review that ail fit a second order relationship. Grdnted, the authors’ current data are from bone in the mandible, and maybe mandibular trabecutar bone is very different from trabecular bone elsewhere in the body. However, as noted with modulus, there have been attempts to predict power law relationships for trabecular bone on the basis of specific assumed geometries of the foam-like internal network structure of trdbecuiar bone (as reviewed in Gibson and Ashby’). For example, trabecular bone with a pronounced “stress-orientation”’ shows a second order relationship between strength and apparent density in the transverse direction, but a first order relationship in the longitudinal direction. Notably, no theoretical model predicts a third order relationship between compressive strength and density, although there is a model predicting a 3/2 power relationship. Maybe the authors are right in suggesting that mandibular trabecular bone might be ver) different from trabecuiar bone elsewhere in the body, but this remains to be seen. Although I applaud the authors’ attempt to measure the properties of bone in the human mandible, after ail is said and done here I remain unclear on another key issue of clinical relevance: Exactly how can the data in this article be readily used in treatment planning? Among other problems. I am still unsure about how these properties of bone in an edentulous mandible will relate to the properties of bone that develop after the healing that follows implantation surgery. JOHN
PhD Troy, NY
BRUNSKI,
Reference 1. Gibson
LJ. Ashby
MF:
Stnlcture and Properties. 316-331
Cancellous Tarrytown,
bone, it2 Cellular Solids: NY, Pegamon. 1988. pp