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Analysis for biodegradable polymeric scaffold of tissue engineering on precision injection molding
International Communications in Heat and Mass Transfer 35 (2008) 1101–1105
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t
Analysis for biodegradable polymeric scaffold of tissue engineering on precision injection molding☆ Tsung-Lung Wu a, Keng-Liang Ou b,c, Hsin-Chung Cheng d,e, Chiung-Fang Huang d,e, Yung-Kang Shen f,⁎, Yuh-Chyun Chian g, Yi Lin h, Yu-Hao Chan i, Chien-Pang Li j a
Department of Dentistry, Cathay General Hospital, Taipei 106, Taiwan, ROC Graduate Institute of biomedical Materials and Engineering, College of Oral Medicine, Taipei Medical University, Taipei 110, Taiwan, ROC Research Center for Biomedical Implant and Microsurgery Device, Taipei Medical University, Taipei 110, Taiwan, ROC d School of Dentistry, Collage of Oral Medicine, Taipei Medical University, Taipei 110, Taiwan, ROC e Department of Dentistry, Taipei Medical University Hospital, Taipei 110, Taiwan, ROC f School of Dental Technology, Taipei Medical University, Taipei 110, Taiwan, ROC g E. N. T. Specialist, Taiwan Advensit Hospital, Taipei 105, Taiwan, ROC h Department of Business Administration, Takming University of Science and Technology, Taipei 104, Taiwan, ROC i Graduate School of Dentistry, Taipei Medical University, Taipei 110, Taiwan, ROC j Department of Mechanical Engineering, LungHwa University of Science and Technology, Taoyuan 333, Taiwan, ROC b c
A R T I C L E
I N F O
Available online 17 July 2008 Keywords: Biodegradable material Scaffold Precision injection molding Processing window Optimization
A B S T R A C T Precision injection molding is the most important technology in Bio-MEMS/NEMS industry for the necessary of scale, velocity and cost by the development of Bio-MEMS/NEMS industry and the innovation of Bio-MEMS/NEMS industry. It has the advantage of low cost, low interface and small volume in Bio-MEMS/ NEMS industry. This paper emphasizes the analysis for three dimension biodegradable polymeric scaffold on precision injection molding. The finite element method in a three-dimensional inertia-free, incompressible flow is presented. A control volume scheme with a fixed finite element mesh is employed to predict flow front advancement. The plastic material of scaffold is used for PLA material. The results show that the short shot on the filling stage of precision injection molding. The results also indicate the processing window and optimal processing for three dimension biodegradable polymeric scaffold on precision injection molding. © 2008 Elsevier Ltd. All rights reserved.
1. Introduction Polymer processing is a key technology for production of microstructured and nano-structured surfaces for Bio-MEMS/NEMS. Precision injection molding technique packages such as Cadmould, C-Mold, and MoldFlow have become the accepted part of mould design. Those simulation programs employed now are based on a model in which two-dimensional elements are used to represent the three-dimensional geometry. The Hele-Shaw model neglects the inertia and the gap-wise velocity component for polymer melt flow in the thin cavities. The shell element used in the Hele-Shaw model needs the construction of the mid-plane, which is time-consuming. The three-dimensional flow regions i.e. flow around corners, or thickness-change regions, or the fountain flow effect of melt fronts
☆ Communicated by W.J. Minkowycz ⁎ Corresponding author. E-mail address: [email protected] (Y.-K. Shen). 0735-1933/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2008.05.014
cannot be represented in Hele-Shaw model. Only the 3D numerical simulation based on Navier–Stokes equation can simulate the reality situation. König et al. [1] indicated the injection molding process used for the production of biodegradable implants made of PLA in order to avoid sterilization procedures that might damage the polymer. The results showed the injection molding process might allow the auto sterilization of parts produced with row materials that is not heavily contaminated. Haugen et al. [2] developed a large-scale scaffold processing method with injection molding. NaCl was used as a porogen to achieve an open-cell structure. The results showed that an increase in injection pressure, plasticize speed, cylinder, and mold temperature raised the mean pore diameter. Michaeli et al. [3] developed the micro assembly injection molding in medical science for a micro part. This part consisted of a carbon-fiber reinforced PEEK puncture needle, which incorporates three lumens. The results showed that the most influence on the bond strength is the mold temperature by statistical evaluation of the design of experiment. Wu et al. [4] used the room temperature injection molding/ particulate leaching approach to fabricate the biodegradable porous
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T.-L. Wu et al. / International Communications in Heat and Mass Transfer 35 (2008) 1101–1105
Nomenclature B cp D T Y g Y u k m n P Pin T Tm Tb Tw x, y, z
viscosity coefficient. specific heat total derivate time gravity vector velocity vector thermal conductivity flow index normal direction pressure inlet pressure temperature freezing temperature reference temperature mold temperature is the Cartesian coordinate Fig. 2. Meshes for numerical simulation.
Greek symbols ▿ Laplace operation vector η viscosity ρ density : γ shear rate η0 reference viscosity τ⁎ reference stress
Continuity Equation: Dρ @ρ ¼ þ j ðρt uÞ ¼ 0 Dt @t
ð1Þ
Momentum equation: Y
ρ scaffolds. The results showed this approach was conducted at room temperature under low pressure, and avoided the thermal degradation of polymers. The research papers are almost few for the biodegradable polymeric scaffold by numerical simulation on today. In this study, 3D numerical simulation (control volume finite element method) uses to simulate biodegradable polymeric scaffold of nose-shaped for an example. The analysis discusses the short shot of filling stage, processing window and optimal processing properties on precision injection molding. 2. Mathematical model The mass, momentum and energy conversation governing equations for the non-isothermal, generalized Newtonian fluid are given by:
Y
Y
Du @u Y Y Y Du Y ¼ jp þ ηj2 u þ ρg; ¼ þ u ju: Dt Dt @t
ð2Þ
Energy equation: ρCp
: 2 DT @T Y DT ¼ k j2 T þ η γ ; ¼ þ u jT Dt Dt @t
ð3Þ
The viscosity model of fluid: : η γ; T; P ¼
1þ
η0 ðT; P Þ : 1−m
ð4Þ
η0 ðT;P Þ γ τ4
T η0 ðT; P Þ ¼ Bexp b expðpÞ T
ð5Þ
Then : Y Y γ ¼ ju ju
ð6Þ
Boundary and initial conditions: Y
u ¼ 0 ; T ¼ Tw ; @Y u @T ¼ ¼0 @z @z p¼0
@p ¼0 @n
ð7Þ
on mold wall
ð8Þ
on center line
ð9Þ
on melt front
p ¼ pin ðx; y; z; t Þ ; T ¼ Tm
ð10Þ
on inlet:
Table 1 Processing parameters
Fig. 1. The model for nose-shaped scaffold.
Level
LEVEL1
LEVEL2
LEVEL3
Parameter A-Mold Temp. B-Melt Temp. C-Injection Press. D-Packing time
20(°C) 210(°C) 16(MPa) 1(s)
30(°C) 220(°C) 20(MPa) 1.5(s)
40(°C) 230(°C) 24(MPa) 2(s)
T.-L. Wu et al. / International Communications in Heat and Mass Transfer 35 (2008) 1101–1105
Fig. 6. 100% filling stage.
Fig. 3. 15% filling stage.
Fig. 7. Temperature distribution. Fig. 4. 45% filling stage.
Fig. 5. 95% filling stage.
Fig. 8. Pressure distribution.
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1104
T.-L. Wu et al. / International Communications in Heat and Mass Transfer 35 (2008) 1101–1105
Fig. 9. Shear stress distribution. Fig. 11. Processing window.
Then this research uses the control volume finite element method (CVFEM) to solve the former equations [5]. 3. Results and discussions Fig. 1 shows the 3D model for scaffold of nose-shaped and Fig. 2 shows the meshes of model for numerical simulation on precision injection molding. The length, width and height of nosed cavity are 70 mm ⁎ 45.68 mm ⁎ 25 mm. Its thickness is about 25 mm. The calculation mesh numbers are 10200 and the mesh type is four-node tetrahedral element. The material of biodegradable polymeric scaffold is used the PLA (Natureworks PLA 7000D). The CPU type of the computer is Pentium 4.2 GB, the memory is 1.2 GB, and the hard disc is 100 GB. The simulated time of each case wastes 30 minutes. Table 1 shows the different processing parameters and values for precision injection molding. Because the processing parameters and values are too much, this paper uses the Taguchi method to find the optimal processing for biodegradable polymeric scaffold on precision injection molding. There are four processing parameters and each processing parameters has three values. This paper uses L9 table for the optimal processing. The goal of optimal processing is the minimum deflection for scaffold. Figs. 3–6 shows that the 15%, 45%, 95%, and 100% filling stage of precision injection molding. The real filling time is equal to 6.468 second. The temperature distribution is show on Fig. 7. The results show the temperature distribution is very uniform on full region of nose. So the warpage phenomenon can not happen. The pressure distribution of nose-shaped scaffold is shown on Fig. 8. The
Fig. 10. Velocity distribution.
results show the maximum injection pressure is 7.162 MPa. The pressure distribution is very uniform. Fig. 9 shows the shear stress distribution for nose-shaped scaffold. The results show that the shear stress distribution is very uniform. The Fig. 10 shows the velocity distribution for nose-shared scaffold. The maximum velocity is 136.2 cm/s. Fig. 11 shows the processing window for nose-shaped scaffold by precision injection molding. The results show the melt temperature is larger than 230 °C, the biodegradable polymeric scaffold induces the degradation situation. The melt temperature is smaller than 190 °C, the biodegradable polymeric scaffold induces the short shot situation. The results also indicate the injection pressure is lower than 12.5 MPa, the biodegradable polymeric scaffold induces short shot and it is larger than 50 MPa, the biodegradable polymeric scaffold induces the flash situation. Based on the Fig. 12, the minimum deflection appears at L4. The optimal factor levels represent a melt temperature of 210 °C, a mold temperature of 30 °C, an injection pressure of 20 MPa, and a packing time of 2 second. 4. Conclusions This research indicates the flow situation, processing window, and optimal processing of scaffold of nose-shaped on precision injection molding. The 3D numerical simulation can simulate very well for flow situation on precision injection molding of biodegradable polymeric
Fig. 12. L9 results for deflection.
T.-L. Wu et al. / International Communications in Heat and Mass Transfer 35 (2008) 1101–1105
scaffold. There are few research papers to indicate the scaffold of tissue engineering by numerical simulation. This research can provide the reference data for the processing window of biodegradable polymeric scaffold. The related data likes as injection pressure, melt temperature, mold temperature, and packing time can help the researchers to do the similar study on scaffold of tissue engineering. References [1] C. König, K. Ruffieux, E. Wintermantel, J. Blaser, Autosterilization of biodegradable implants by injection molding process, J. Biomed. Mater. Res. 38 (1997) 115–119.
1105
[2] H. Haugen, J. Will, W. Fuchs, E. Wintermantel, A novel processing method for injection-molded polyether-urethane scaffold. Part 1: processing, J. Biomed. Mater. Res. 77B (2006) 65–72. [3] W. Michaeli, D. Opsermann, T. Kamps, Advances in micro assembly injection molding for use in medical system, Int. J. Adv. Manuf. Technol. 33 (2007) 206–211. [4] L.B. Wu, D.Y. Jing, J.D. Ding, A “room-temperature” injection molding/particulate leaching approach for fabrication of biodegradable three-dimensional porous scaffolds, Biomaterials 27 (2006) 185–191. [5] Y.K. Shen, W.Y. Wu, S.Y. Yang, H.M. Jian, C.-C.A. Chen, Study on numerical simulation and experiment of lightguide plate in injection molding, J. Reinforced Plastics Composites 23 (2004) 1187–1206.
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t
Analysis for biodegradable polymeric scaffold of tissue engineering on precision injection molding☆ Tsung-Lung Wu a, Keng-Liang Ou b,c, Hsin-Chung Cheng d,e, Chiung-Fang Huang d,e, Yung-Kang Shen f,⁎, Yuh-Chyun Chian g, Yi Lin h, Yu-Hao Chan i, Chien-Pang Li j a
Department of Dentistry, Cathay General Hospital, Taipei 106, Taiwan, ROC Graduate Institute of biomedical Materials and Engineering, College of Oral Medicine, Taipei Medical University, Taipei 110, Taiwan, ROC Research Center for Biomedical Implant and Microsurgery Device, Taipei Medical University, Taipei 110, Taiwan, ROC d School of Dentistry, Collage of Oral Medicine, Taipei Medical University, Taipei 110, Taiwan, ROC e Department of Dentistry, Taipei Medical University Hospital, Taipei 110, Taiwan, ROC f School of Dental Technology, Taipei Medical University, Taipei 110, Taiwan, ROC g E. N. T. Specialist, Taiwan Advensit Hospital, Taipei 105, Taiwan, ROC h Department of Business Administration, Takming University of Science and Technology, Taipei 104, Taiwan, ROC i Graduate School of Dentistry, Taipei Medical University, Taipei 110, Taiwan, ROC j Department of Mechanical Engineering, LungHwa University of Science and Technology, Taoyuan 333, Taiwan, ROC b c
A R T I C L E
I N F O
Available online 17 July 2008 Keywords: Biodegradable material Scaffold Precision injection molding Processing window Optimization
A B S T R A C T Precision injection molding is the most important technology in Bio-MEMS/NEMS industry for the necessary of scale, velocity and cost by the development of Bio-MEMS/NEMS industry and the innovation of Bio-MEMS/NEMS industry. It has the advantage of low cost, low interface and small volume in Bio-MEMS/ NEMS industry. This paper emphasizes the analysis for three dimension biodegradable polymeric scaffold on precision injection molding. The finite element method in a three-dimensional inertia-free, incompressible flow is presented. A control volume scheme with a fixed finite element mesh is employed to predict flow front advancement. The plastic material of scaffold is used for PLA material. The results show that the short shot on the filling stage of precision injection molding. The results also indicate the processing window and optimal processing for three dimension biodegradable polymeric scaffold on precision injection molding. © 2008 Elsevier Ltd. All rights reserved.
1. Introduction Polymer processing is a key technology for production of microstructured and nano-structured surfaces for Bio-MEMS/NEMS. Precision injection molding technique packages such as Cadmould, C-Mold, and MoldFlow have become the accepted part of mould design. Those simulation programs employed now are based on a model in which two-dimensional elements are used to represent the three-dimensional geometry. The Hele-Shaw model neglects the inertia and the gap-wise velocity component for polymer melt flow in the thin cavities. The shell element used in the Hele-Shaw model needs the construction of the mid-plane, which is time-consuming. The three-dimensional flow regions i.e. flow around corners, or thickness-change regions, or the fountain flow effect of melt fronts
☆ Communicated by W.J. Minkowycz ⁎ Corresponding author. E-mail address: [email protected] (Y.-K. Shen). 0735-1933/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2008.05.014
cannot be represented in Hele-Shaw model. Only the 3D numerical simulation based on Navier–Stokes equation can simulate the reality situation. König et al. [1] indicated the injection molding process used for the production of biodegradable implants made of PLA in order to avoid sterilization procedures that might damage the polymer. The results showed the injection molding process might allow the auto sterilization of parts produced with row materials that is not heavily contaminated. Haugen et al. [2] developed a large-scale scaffold processing method with injection molding. NaCl was used as a porogen to achieve an open-cell structure. The results showed that an increase in injection pressure, plasticize speed, cylinder, and mold temperature raised the mean pore diameter. Michaeli et al. [3] developed the micro assembly injection molding in medical science for a micro part. This part consisted of a carbon-fiber reinforced PEEK puncture needle, which incorporates three lumens. The results showed that the most influence on the bond strength is the mold temperature by statistical evaluation of the design of experiment. Wu et al. [4] used the room temperature injection molding/ particulate leaching approach to fabricate the biodegradable porous
1102
T.-L. Wu et al. / International Communications in Heat and Mass Transfer 35 (2008) 1101–1105
Nomenclature B cp D T Y g Y u k m n P Pin T Tm Tb Tw x, y, z
viscosity coefficient. specific heat total derivate time gravity vector velocity vector thermal conductivity flow index normal direction pressure inlet pressure temperature freezing temperature reference temperature mold temperature is the Cartesian coordinate Fig. 2. Meshes for numerical simulation.
Greek symbols ▿ Laplace operation vector η viscosity ρ density : γ shear rate η0 reference viscosity τ⁎ reference stress
Continuity Equation: Dρ @ρ ¼ þ j ðρt uÞ ¼ 0 Dt @t
ð1Þ
Momentum equation: Y
ρ scaffolds. The results showed this approach was conducted at room temperature under low pressure, and avoided the thermal degradation of polymers. The research papers are almost few for the biodegradable polymeric scaffold by numerical simulation on today. In this study, 3D numerical simulation (control volume finite element method) uses to simulate biodegradable polymeric scaffold of nose-shaped for an example. The analysis discusses the short shot of filling stage, processing window and optimal processing properties on precision injection molding. 2. Mathematical model The mass, momentum and energy conversation governing equations for the non-isothermal, generalized Newtonian fluid are given by:
Y
Y
Du @u Y Y Y Du Y ¼ jp þ ηj2 u þ ρg; ¼ þ u ju: Dt Dt @t
ð2Þ
Energy equation: ρCp
: 2 DT @T Y DT ¼ k j2 T þ η γ ; ¼ þ u jT Dt Dt @t
ð3Þ
The viscosity model of fluid: : η γ; T; P ¼
1þ
η0 ðT; P Þ : 1−m
ð4Þ
η0 ðT;P Þ γ τ4
T η0 ðT; P Þ ¼ Bexp b expðpÞ T
ð5Þ
Then : Y Y γ ¼ ju ju
ð6Þ
Boundary and initial conditions: Y
u ¼ 0 ; T ¼ Tw ; @Y u @T ¼ ¼0 @z @z p¼0
@p ¼0 @n
ð7Þ
on mold wall
ð8Þ
on center line
ð9Þ
on melt front
p ¼ pin ðx; y; z; t Þ ; T ¼ Tm
ð10Þ
on inlet:
Table 1 Processing parameters
Fig. 1. The model for nose-shaped scaffold.
Level
LEVEL1
LEVEL2
LEVEL3
Parameter A-Mold Temp. B-Melt Temp. C-Injection Press. D-Packing time
20(°C) 210(°C) 16(MPa) 1(s)
30(°C) 220(°C) 20(MPa) 1.5(s)
40(°C) 230(°C) 24(MPa) 2(s)
T.-L. Wu et al. / International Communications in Heat and Mass Transfer 35 (2008) 1101–1105
Fig. 6. 100% filling stage.
Fig. 3. 15% filling stage.
Fig. 7. Temperature distribution. Fig. 4. 45% filling stage.
Fig. 5. 95% filling stage.
Fig. 8. Pressure distribution.
1103
1104
T.-L. Wu et al. / International Communications in Heat and Mass Transfer 35 (2008) 1101–1105
Fig. 9. Shear stress distribution. Fig. 11. Processing window.
Then this research uses the control volume finite element method (CVFEM) to solve the former equations [5]. 3. Results and discussions Fig. 1 shows the 3D model for scaffold of nose-shaped and Fig. 2 shows the meshes of model for numerical simulation on precision injection molding. The length, width and height of nosed cavity are 70 mm ⁎ 45.68 mm ⁎ 25 mm. Its thickness is about 25 mm. The calculation mesh numbers are 10200 and the mesh type is four-node tetrahedral element. The material of biodegradable polymeric scaffold is used the PLA (Natureworks PLA 7000D). The CPU type of the computer is Pentium 4.2 GB, the memory is 1.2 GB, and the hard disc is 100 GB. The simulated time of each case wastes 30 minutes. Table 1 shows the different processing parameters and values for precision injection molding. Because the processing parameters and values are too much, this paper uses the Taguchi method to find the optimal processing for biodegradable polymeric scaffold on precision injection molding. There are four processing parameters and each processing parameters has three values. This paper uses L9 table for the optimal processing. The goal of optimal processing is the minimum deflection for scaffold. Figs. 3–6 shows that the 15%, 45%, 95%, and 100% filling stage of precision injection molding. The real filling time is equal to 6.468 second. The temperature distribution is show on Fig. 7. The results show the temperature distribution is very uniform on full region of nose. So the warpage phenomenon can not happen. The pressure distribution of nose-shaped scaffold is shown on Fig. 8. The
Fig. 10. Velocity distribution.
results show the maximum injection pressure is 7.162 MPa. The pressure distribution is very uniform. Fig. 9 shows the shear stress distribution for nose-shaped scaffold. The results show that the shear stress distribution is very uniform. The Fig. 10 shows the velocity distribution for nose-shared scaffold. The maximum velocity is 136.2 cm/s. Fig. 11 shows the processing window for nose-shaped scaffold by precision injection molding. The results show the melt temperature is larger than 230 °C, the biodegradable polymeric scaffold induces the degradation situation. The melt temperature is smaller than 190 °C, the biodegradable polymeric scaffold induces the short shot situation. The results also indicate the injection pressure is lower than 12.5 MPa, the biodegradable polymeric scaffold induces short shot and it is larger than 50 MPa, the biodegradable polymeric scaffold induces the flash situation. Based on the Fig. 12, the minimum deflection appears at L4. The optimal factor levels represent a melt temperature of 210 °C, a mold temperature of 30 °C, an injection pressure of 20 MPa, and a packing time of 2 second. 4. Conclusions This research indicates the flow situation, processing window, and optimal processing of scaffold of nose-shaped on precision injection molding. The 3D numerical simulation can simulate very well for flow situation on precision injection molding of biodegradable polymeric
Fig. 12. L9 results for deflection.
T.-L. Wu et al. / International Communications in Heat and Mass Transfer 35 (2008) 1101–1105
scaffold. There are few research papers to indicate the scaffold of tissue engineering by numerical simulation. This research can provide the reference data for the processing window of biodegradable polymeric scaffold. The related data likes as injection pressure, melt temperature, mold temperature, and packing time can help the researchers to do the similar study on scaffold of tissue engineering. References [1] C. König, K. Ruffieux, E. Wintermantel, J. Blaser, Autosterilization of biodegradable implants by injection molding process, J. Biomed. Mater. Res. 38 (1997) 115–119.
1105
[2] H. Haugen, J. Will, W. Fuchs, E. Wintermantel, A novel processing method for injection-molded polyether-urethane scaffold. Part 1: processing, J. Biomed. Mater. Res. 77B (2006) 65–72. [3] W. Michaeli, D. Opsermann, T. Kamps, Advances in micro assembly injection molding for use in medical system, Int. J. Adv. Manuf. Technol. 33 (2007) 206–211. [4] L.B. Wu, D.Y. Jing, J.D. Ding, A “room-temperature” injection molding/particulate leaching approach for fabrication of biodegradable three-dimensional porous scaffolds, Biomaterials 27 (2006) 185–191. [5] Y.K. Shen, W.Y. Wu, S.Y. Yang, H.M. Jian, C.-C.A. Chen, Study on numerical simulation and experiment of lightguide plate in injection molding, J. Reinforced Plastics Composites 23 (2004) 1187–1206.