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A model of temperature transients in dental implants
Biomaterials 22 (2001) 2795}2797
A model of temperature transients in dental implants Kevan Wong , Alan Boyde *, P.G.T. Howell Department of Anatomy and Developmental Biology, University College London, Gower Street, London WC1E 6BT, UK Department of Prosthetic Dentistry, Eastman Dental Institute, Gray+s Inn Road, London WC1X 8LD, UK Received 15 January 2000; accepted 9 January 2001
Abstract Dental implants provide a continuous interface between the oral environment and the deep core structures of the jaws. Implants and trans-mucosal superstructures are primarily metal and heat conduction occurs readily. A hypothetical heat conduction model is investigated to determine the ranges of temperature gradients that might occur in implants. This model showed that a 603C heat source will cause a heat front of*473C to advance'3 mm down an implant within one second. Oral temperature transients may be a factor in implant pathology. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Dental implants; Oral temperature; Heat conduction; Bone pathology
1. Introduction Dental implants can have diverse morphologies, but the most studied is that of a solid screw of pure titanium or titanium alloy passing the external cortical plate of the mandible or maxilla into the inner trabecular bone, and ideally seated into an opposing cortical endosteal surface to achieve bi-cortical "xation. Implants are commonly 3.3}6 mm in diameter and 7}20 mm in length. After osseointegration, the partial contact area between screw thread and bone varies from 25% to 72% [1]. After bony ingrowth, the screw threads and any machined recesses on the implant body provide a mechanism for retention and a &sink' via which excess heat may be dissipated into adjacent bone and soft tissues. The implant is connected to a prosthetic superstructure in the oral cavity by a titanium abutment connection. Dental implant reconstructions are predominantly metal and a continuous thermal conduction pathway is provided between the deep core of the jaw bone, through the "brous soft tissue layers of periosteum, connective tissue and mucosa to the oral thermal environment.
* Corresponding author. Tel.:#44-171-419-3316; fax:#44-171-3911302. E-mail addresses: [email protected] (A. Boyde), [email protected] (P.G.T. Howell).
The temperature of ingested food can range from iced beverages to scalding hot soups, and surface temperatures of the intra-oral structures lie between 03C}673C [2]. The extent of heat transfer from foods and drinks to the mucosa, tongue and exposed teeth or prosthetic substitutes will depend upon the type and the temperature of the ingested material and the duration of contact. Here, we simulate temperature e!ects within dental implants by computer modelling.
2. Method The transfer of heat along a metal rod or bar is treated in thermodynamics as thermal conduction [3]. The thermal conductivity, k, is de"ned as the rate at which heat is transferred through a material resulting in a temperature change of ¹ across surface area A. Then k"QA/¹, where Q is the quantity of heat transferred (Watts), A is the area (m) and ¹ is the change in temperature (K). A more useful measure of the potential for a material to transfer heat as a transient phenomenon is its thermal di!usivity, . This is de"ned by "k/(c ),
0142-9612/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 9 6 1 2 ( 0 1 ) 0 0 0 2 3 - 0
2796
K. Wong et al. / Biomaterials 22 (2001) 2795}2797
where k is the thermal conductivity (W m\ K\), is the density of the material (kg m\) and c is the speci"c heat (kJ kg\ K\). Values for the di!usivity, , for gold, titanium, bone, and dentine are given in Table 1. The model discussed here considers the implant to be a semi-in"nite solid, cylindrical in shape, which is initially at a uniform temperature of 373C. Heat is applied as a constant source at one end surface for periods of up to 5 s. It is assumed that no heat is lost to the surroundings by induction, convection, or radiation. Under these conditions, we may apply the equations derived from thermodynamics [3].
maintain its biological activity over a wide temperature range, the protein becomes denatured above 503C and is irreversibly damaged [5]. The denaturation temperature
x ¹ "¹ #¹ 1!erf V O ' 2(a
,
where ¹ is the temperature after a time at a distance V O x from the implant surface and the temperature ¹ is applied to a material of thermal di!usivity whose initial temperature was ¹ . The value of the function erf( ) may ' be calculated for the values of x, and its value derived from published tables [4]. A computer program was written in PASCAL to vary the applied ¹ over values from 503C to 703C. The thermal change in the implants after 0.2, 0.5, 1, 2 and 5 s was calculated.
3. Results Fig. 1 shows computed temperature gradients in an implant after applying a heat stimulus of 503C, 603C or 703C for 5 s. We calculate that 473C will be reached within 1 s at distances of 1.29, 3.45 and 4.54 mm down the implant after applied temperature pulses of 503C, 603C, and 703C, respectively.
4. Discussion Several factors suggest that temperature rises of around 103C might be harmful. For example, alkaline phosphatase is an enzyme that is detected in the membrane of osteoblasts and is often accepted as a useful primary marker of osteoblastic activity. Although it can
Fig. 1. Shows computed thermal changes in an implant after applying a heat stimulus of 503C, 603C or 703C after 0.2, 0.5, 1, 2 and 5 s.
Table 1 Physical properties of dental materials. Thermal conductivity, speci"c heat, density and thermal di!usivity Materials
Thermal conductivity k (W m\ K\)
Speci"c heat c (kJ kg\ K\)
Density r (kg m\)
Thermal di!usivity (m s\)
Gold [6] Titanium [6] Cancellous bone [7] Dentine [8] Enamel [8]
319 22.4 0.30 0.63 0.92
0.129 0.523 1.44 1.17 0.75
19300 4540 1920 2100 2900
0.128 9.434;10\ 0.109;10\ 0.256;10\ 0.423;10\
K. Wong et al. / Biomaterials 22 (2001) 2795}2797
of procollagen and collagen type I has been given as 423C in neutral bu!ers [6]. The present calculations suggest that 473C may occur regularly down the surface of an implant structure embedded in bone from unexceptional oral temperatures. This prediction is supported clinically by reports of discomfort and pain associated with eating hot food by patients in whom the mandibular nerve bundle has been placed into close contact with an implant. The results of this study provide an explanation for these observed symptoms, that is, signi"cant heat conduction does occur in dental implants in vivo. The results also support the notion that oral temperatures may be an additional stress factor in crestal bone pathology. The crestal bone, by being closest to the oral source of heat, will naturally be the most thermocycled element of alveolar bone. Short implant length is a signi"cant factor predisposing to implant failure. Current opinion is that such failures are due to the reduced #exural and structural strength of the shorter implant and physiological overload on the implant}bone interface supporting the occlusal loads in mastication. However, the present model
2797
predicts that short implants will be more a!ected by oral temperature transients.
References [1] Wilson TG, Schenk R, Buser D, Cochran D. Implants placed in immediate extraction sites: a report of histologic and histometric analyses of human biopsies. Int J Oral Maxillofac Implants 1998;13:333}41. [2] Palmer DS, Barco MT, Billy EJ. Temperature extremes produced orally by hot and cold liquids. J Prosthet Dent 1992;67:325}7. [3] Rogers GFC, Mayhew YR. Engineering thermodynamics, work and heat transfer, 4th ed. London: Longman, 1992. p. 501}32. [4] Wolfe H. Heat transfer. New York: Harper and Row, 1983. p. 95}161. [5] Lundskog J. Heat and bone tissue. An experimental investigation of the thermal properties of bone and threshold levels for thermal injury. Scand J Plast Reconstr Surg 1972;9:1}80. [6] Weast R. CRC handbook of chemistry and physics, 67th ed. Boca Raton: CRC Press, 1986. [7] Clattenburg R, Cohen J, Conner S, Cook N. Thermal properties of cancellous bone. J Biomed Mater Res 1975;9:169}82. [8] Braden M. Heat conduction in normal teeth. Arch oral Biol 1964;9:479}86.
A model of temperature transients in dental implants Kevan Wong , Alan Boyde *, P.G.T. Howell Department of Anatomy and Developmental Biology, University College London, Gower Street, London WC1E 6BT, UK Department of Prosthetic Dentistry, Eastman Dental Institute, Gray+s Inn Road, London WC1X 8LD, UK Received 15 January 2000; accepted 9 January 2001
Abstract Dental implants provide a continuous interface between the oral environment and the deep core structures of the jaws. Implants and trans-mucosal superstructures are primarily metal and heat conduction occurs readily. A hypothetical heat conduction model is investigated to determine the ranges of temperature gradients that might occur in implants. This model showed that a 603C heat source will cause a heat front of*473C to advance'3 mm down an implant within one second. Oral temperature transients may be a factor in implant pathology. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Dental implants; Oral temperature; Heat conduction; Bone pathology
1. Introduction Dental implants can have diverse morphologies, but the most studied is that of a solid screw of pure titanium or titanium alloy passing the external cortical plate of the mandible or maxilla into the inner trabecular bone, and ideally seated into an opposing cortical endosteal surface to achieve bi-cortical "xation. Implants are commonly 3.3}6 mm in diameter and 7}20 mm in length. After osseointegration, the partial contact area between screw thread and bone varies from 25% to 72% [1]. After bony ingrowth, the screw threads and any machined recesses on the implant body provide a mechanism for retention and a &sink' via which excess heat may be dissipated into adjacent bone and soft tissues. The implant is connected to a prosthetic superstructure in the oral cavity by a titanium abutment connection. Dental implant reconstructions are predominantly metal and a continuous thermal conduction pathway is provided between the deep core of the jaw bone, through the "brous soft tissue layers of periosteum, connective tissue and mucosa to the oral thermal environment.
* Corresponding author. Tel.:#44-171-419-3316; fax:#44-171-3911302. E-mail addresses: [email protected] (A. Boyde), [email protected] (P.G.T. Howell).
The temperature of ingested food can range from iced beverages to scalding hot soups, and surface temperatures of the intra-oral structures lie between 03C}673C [2]. The extent of heat transfer from foods and drinks to the mucosa, tongue and exposed teeth or prosthetic substitutes will depend upon the type and the temperature of the ingested material and the duration of contact. Here, we simulate temperature e!ects within dental implants by computer modelling.
2. Method The transfer of heat along a metal rod or bar is treated in thermodynamics as thermal conduction [3]. The thermal conductivity, k, is de"ned as the rate at which heat is transferred through a material resulting in a temperature change of ¹ across surface area A. Then k"QA/¹, where Q is the quantity of heat transferred (Watts), A is the area (m) and ¹ is the change in temperature (K). A more useful measure of the potential for a material to transfer heat as a transient phenomenon is its thermal di!usivity, . This is de"ned by "k/(c ),
0142-9612/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 9 6 1 2 ( 0 1 ) 0 0 0 2 3 - 0
2796
K. Wong et al. / Biomaterials 22 (2001) 2795}2797
where k is the thermal conductivity (W m\ K\), is the density of the material (kg m\) and c is the speci"c heat (kJ kg\ K\). Values for the di!usivity, , for gold, titanium, bone, and dentine are given in Table 1. The model discussed here considers the implant to be a semi-in"nite solid, cylindrical in shape, which is initially at a uniform temperature of 373C. Heat is applied as a constant source at one end surface for periods of up to 5 s. It is assumed that no heat is lost to the surroundings by induction, convection, or radiation. Under these conditions, we may apply the equations derived from thermodynamics [3].
maintain its biological activity over a wide temperature range, the protein becomes denatured above 503C and is irreversibly damaged [5]. The denaturation temperature
x ¹ "¹ #¹ 1!erf V O ' 2(a
,
where ¹ is the temperature after a time at a distance V O x from the implant surface and the temperature ¹ is applied to a material of thermal di!usivity whose initial temperature was ¹ . The value of the function erf( ) may ' be calculated for the values of x, and its value derived from published tables [4]. A computer program was written in PASCAL to vary the applied ¹ over values from 503C to 703C. The thermal change in the implants after 0.2, 0.5, 1, 2 and 5 s was calculated.
3. Results Fig. 1 shows computed temperature gradients in an implant after applying a heat stimulus of 503C, 603C or 703C for 5 s. We calculate that 473C will be reached within 1 s at distances of 1.29, 3.45 and 4.54 mm down the implant after applied temperature pulses of 503C, 603C, and 703C, respectively.
4. Discussion Several factors suggest that temperature rises of around 103C might be harmful. For example, alkaline phosphatase is an enzyme that is detected in the membrane of osteoblasts and is often accepted as a useful primary marker of osteoblastic activity. Although it can
Fig. 1. Shows computed thermal changes in an implant after applying a heat stimulus of 503C, 603C or 703C after 0.2, 0.5, 1, 2 and 5 s.
Table 1 Physical properties of dental materials. Thermal conductivity, speci"c heat, density and thermal di!usivity Materials
Thermal conductivity k (W m\ K\)
Speci"c heat c (kJ kg\ K\)
Density r (kg m\)
Thermal di!usivity (m s\)
Gold [6] Titanium [6] Cancellous bone [7] Dentine [8] Enamel [8]
319 22.4 0.30 0.63 0.92
0.129 0.523 1.44 1.17 0.75
19300 4540 1920 2100 2900
0.128 9.434;10\ 0.109;10\ 0.256;10\ 0.423;10\
K. Wong et al. / Biomaterials 22 (2001) 2795}2797
of procollagen and collagen type I has been given as 423C in neutral bu!ers [6]. The present calculations suggest that 473C may occur regularly down the surface of an implant structure embedded in bone from unexceptional oral temperatures. This prediction is supported clinically by reports of discomfort and pain associated with eating hot food by patients in whom the mandibular nerve bundle has been placed into close contact with an implant. The results of this study provide an explanation for these observed symptoms, that is, signi"cant heat conduction does occur in dental implants in vivo. The results also support the notion that oral temperatures may be an additional stress factor in crestal bone pathology. The crestal bone, by being closest to the oral source of heat, will naturally be the most thermocycled element of alveolar bone. Short implant length is a signi"cant factor predisposing to implant failure. Current opinion is that such failures are due to the reduced #exural and structural strength of the shorter implant and physiological overload on the implant}bone interface supporting the occlusal loads in mastication. However, the present model
2797
predicts that short implants will be more a!ected by oral temperature transients.
References [1] Wilson TG, Schenk R, Buser D, Cochran D. Implants placed in immediate extraction sites: a report of histologic and histometric analyses of human biopsies. Int J Oral Maxillofac Implants 1998;13:333}41. [2] Palmer DS, Barco MT, Billy EJ. Temperature extremes produced orally by hot and cold liquids. J Prosthet Dent 1992;67:325}7. [3] Rogers GFC, Mayhew YR. Engineering thermodynamics, work and heat transfer, 4th ed. London: Longman, 1992. p. 501}32. [4] Wolfe H. Heat transfer. New York: Harper and Row, 1983. p. 95}161. [5] Lundskog J. Heat and bone tissue. An experimental investigation of the thermal properties of bone and threshold levels for thermal injury. Scand J Plast Reconstr Surg 1972;9:1}80. [6] Weast R. CRC handbook of chemistry and physics, 67th ed. Boca Raton: CRC Press, 1986. [7] Clattenburg R, Cohen J, Conner S, Cook N. Thermal properties of cancellous bone. J Biomed Mater Res 1975;9:169}82. [8] Braden M. Heat conduction in normal teeth. Arch oral Biol 1964;9:479}86.