Abstract
Purpose
To compare stress distribution in polyacetyl based flexible RPD (FRPD) with cast metal RPD (CRPD) by using three-dimensional finite element analysis (FEA) and patient satisfaction by using OHIP-14 questionnaire in participants with Kennedy's class I partially edentulous mandibular arch rehabilitated with CRPD and FRPD.
Material and methods
For FEA, 3D models of Kennedy's class I partially edentulous mandibular arch, CRPD in chrome-cobolt alloy, and polyacetyl based FRPD were geometrically modelled and subjected to a vertical load of 100 N bilaterally. The in vivo comparison of satisfaction was assessed by enrolling 22 participants with Kennedy's class I partially edentulous mandibular arch. After randomization, 11 participants were rehabilitated by CRPD (group C), and 11 participants by polyacetyl based FRPD (group F). OHIP-14 questionnaire in Hindi language was filled at 1 week and 1 year after denture insertion.
Results
Von Mises stress distribution in CRPD was maximum in mesial rest seat of the primary abutment (100 MPa) and minimum for edentulous ridge (7 MPa on bone and 6 MPa on mucosa). Von Mises stress distribution for polyaccetyl based FRPD was maximum in ridge (25 MPa) and minimum in periodontal ligament of the second premolar (3 MPa). Patient satisfaction in group F was significantly more than in group C at end of 1 year (P = .0158).
Conclusion
FRPD is useful in periodontally compromised abutment teeth and CRPD in resorbed ridge conditions. Patient satisfaction is more with polyacetyl based flexible RPD when compared with cast metal RPD at the end of 1 year.
Keywords: Flexible RPD, Cast metal RPD, FEA, Patient satisfaction
1. Introduction
The rising proportion of the partially edentulous population, restricted applicability of fixed dental prosthesis (FDP) in distal extension and long edentulous spans, and economic constraints associated with implants suggests that the need for removable partial denture (RPD) prostheses is high in prevailing times. This trend is likely to continue in future as well. However, in order to consider this treatment successful, the quality of RPD should be biomechanically favourable and the RPD prosthesis should provide optimal patient satisfaction.1, 2, 3, 4, 5
Cast RPD have been a popular choice in the treatment of partially edentulous conditions for several decades. The limitation of cast RPD is the unaesthetic display of the metal clasp arm and contraindication in conditions of severe soft and hard tissue undercuts.3 To overcome the shortcomings of cast RPD, polyacetyl based resin dentures have gained popularity.4,6, 7, 8, 9, 10, 11, 12, 13 However, due to the inherent flexibility of material and lack of use of occlusal rests and indirect retainers in the design of the prosthesis, polyacetyl resin based RPD lack rigidity. The aesthetic appearance, conservation of remaining oral structures due to minimal or no tooth preparation, and rapidity of fabrication procedure make polyacetyl based resin RPD a promising option in rehabilitation of partially edentulous scenarios.
The primary biomechanical requirement of a partial denture is to transmit uniform forces to the teeth and to the underlying soft and hard tissues.4 Numerous methods have been used to study biomechanical behaviour of prosthesis including photoelasticity measurements, strain gauge-based measurements, optic measurements, and computational measurements such as finite element analysis (FEA).14, 15, 16, 17, 18, 19, 20, 21 FEA investigates the biomechanical behaviour of objects by accurate presentation of complex geometries, often encountered intra orally. Since it is a numerical method of analyzing stresses in any given geometry, it does not adversely affect the physical properties of the analyzed materials and it is an easily repeatable method.16
The end point of prosthodontic rehabilitation is patient satisfaction.22, 23, 24, 25, 26 Clinical outcomes as appraised by a clinician differ from the variables characterising patients’ perception. Patient satisfaction is dependent on physical well being, psychosocial experience, social functions, and treatment cost effectiveness after the use of prosthesis. Oral health impact profile (OHIP) questionnaire and its abbreviated OHIP-14 version is a popular instrument that has been used to measure oral health related quality of life in elderly individuals using RPD.22,23
Although stress distribution and patient satisfaction with cast RPD have been widely reported, literature comparing the stress distribution and patient satisfaction in cast RPD with polyacetyl based resin RPD in Kennedy Class I situation is lacking. Therefore, this study assessed and compared the stress distribution by using 3-dimensional FEA and in vivo patient satisfaction by using OHIP-14 in cast RPD and polyacetyl based resin RPD for Kennedy Class I situation. The 2 hypothesis tested were that there is no difference in biomechanical stress distribution to abutment and residual ridge with polyacetyl resin based flexible RPD and cast RPD in Kennedy Class I situation; and, there is no difference in patient satisfaction between cast RPD and polyacetyl resin based RPD after 1 year of use in Kennedy Class I situation.
2. Material and methods
This study was implemented in two parts after obtaining the ethical clearance from the Institute Ethics Committee (Ref. No. IECPG – 590/December 08, 2016). The first part investigated and compared the stress distribution on abutment teeth and residual ridge with cast RPD and polyacetyl based resin RPD by using FEA in Kennedy Class I situation. The second part of the study compared the patient satisfaction by using OHIP-14 questionnaire between cast RPD and polyacetyl resin based flexible RPD in Kennedy Class I situation after 1 year of use.
2.1. 3D finite element analysis
3D model of a partially edentulous mandible with Kennedy's class I situation representing missing molars bilaterally, cast RPD geometry, and polyacetyl based flexible RPD geometry was generated. Mechanical properties of the materials were applied for creation of the mesh.15,17,18,21 Load application and stress analysis were done for both the prosthesis designed.
Computer tomography (NewTom, QR, Inc. Verona, Italy) DICOM data and models of a 24 year old female participant with Kennedy's class I partially edentulous condition were used to construct the 3 dimensional FEA model by using 3D modelling software (CREO 3.0, Parametric Technology Corporation, USA) as is seen in Fig. 1. All the 3D modelled tissues, including the natural teeth, alveolar bone, periodontal ligament, and mucosa were assumed to be isotropic, elastic, and homogeneous.15,17,18
Fig. 1.
Simulated 3D Kennedy class I mandibular model.
Geometric models of both the RPD designs in three dimensions were constructed on the partially edentulous mandible. The first model was of cast RPD design, planned to restore the first and second molar bilaterally (Supplementary Fig. 1). The cast RPD was designed with lingual bar major connector. The shape of lingual bar was half pear in cross section. The lingual bar was designed to be 5 mm in height and 2 mm in thickness. The distance between the gingival margins and the superior border of the bar was 3 mm. The reciprocal parallel interface (RPI) design was incorporated in the cast RPD design by using a Y shaped retentive clasp on the primary abutment. The distal arm of the Y shaped retentive clasp was positioned below the height of contour and the mesial arm above the height of contour. Bilaterally, on the second premolar primary abutment, occlusal rest was incorporated on the mesial half and a proximal plate was designed on the distal surface. Occlusal rests were also incorporated bilaterally on the mesial half of the first premolars, which were selected as secondary abutment, to act as indirect retainers.
The polyacetyl based resin RPD model was designed to restore the first and second molar bilaterally (Supplementary Fig. 2). Physiological principle of broad stress distribution was implemented in designing the RPD such that the major connector of the RPD joined the components of the right and the left sides of the prosthesis. The major connector was adapted over the lingual slopes of the alveolar ridge, the alveolar mucosa, marginal gingival, and extended till the height of contour of the remaining natural anterior teeth engaging the gingival embrasures of the teeth with interdental projections superiorly. The inferior extent of the major connector was till the junction of the floor of the mouth and alveolar ridge. The retentive arm was incorporated on the primary abutment (mandibular second premolar).
The 3D models were exported to finite element software (ANSYS 14.0, Ansys, Inc., USA) for mesh generation, definition of material properties, boundary, and loading conditions. All involved structures were meshed using tetrahedral elements which were interconnected at nodes as is seen in Fig. 2a, Fig. 2ba and b. Meshing was done with mechanical properties determined by values obtained from previously published reports as seen in Table 1.16,21,22 The mesh size used was 1 mm. For the cast RPD the total number of tetrahedral elements were 348,632 and total number of nodes were 423,562. For the flexible RPD the total number of tetrahedral elements were 828,640 and total number of nodes were 546,871. The models were subjected to vertical (axial) loads of 100 N bilaterally on the first molar region to simulate the field variables in different elements by using the software (ANSYS 14.0, Ansys Inc., USA). At different regions, stress levels were calculated by von Mises criteria (see Fig. 3a, Fig. 3b, Fig. 3c, Fig. 4a, Fig. 4b).
Fig. 2a.
3D Meshed model of polyacetyl based resin flexible RPD.
Fig. 2b.
3D Meshed model of cast partial denture.
Table 1.
| Material | Elastic modulus (MPa) | Poisson's Ratio |
|---|---|---|
| Enamel | 41,400 | 0.35 |
| Dentin | 18,600 | 0.35 |
| Periodontal ligament | 0.0689 | 0.45 |
| Cortical bone | 11,760 | 0.25 |
| Cancellous bone | 1470 | 0.30 |
| Mucosa | 1 | 0.37 |
| Co–Cr alloys | 70,000 | 0.30 |
| Acrylic resin base | 1960 | 0.30 |
| Acrylic teeth | 2940 | 0.30 |
| Polyacetal resin | 2900 | 0.35 |
MPa, Mega Pascals.
Fig. 3a.
Von Mises stress on distal proximal plate for cast partial denture.
Fig. 3b.
Von Mises stress on the periodontal ligament of terminal abutment in cast partial denture.
Fig. 3c.
Von Mises stress in edentulous region in cast partial denture.
Fig. 4a.
Von Mises stress on distal surface of terminal abutment in polyacetyl based resin flexible RPD.
Fig. 4b.
Von Mises stress on the periodontal ligament of terminal abutment in polyacetyl based resin flexible RPD.
2.2. Patient satisfaction
This part of the study was a prospective, concurrent, parallel arm, randomized control trial. The study involved participants who had reported to the department of Prosthodontics in a tertiary care centre of a metropolitan city in India, from December 2016 to October 2017, and fulfilled the inclusion and exclusion criteria. Since previous clinical study results were not available during the establishment of the study design, biometric sample size calculation could not be done. Participants with mandibular Kennedy's class I partially edentulous intraoral situation, within the age range of 30–70 years, completely dentate opposing arch, well healed residual alveolar ridge with firm mucosa and no inflammation, healthy periodontal status of remaining natural teeth, good oral hygiene, first time denture wearers, and willing to participate were included in the study. Participants with underlying systemic medical conditions and previous denture wearers were excluded from the study. A total of 22 partially edentulous individuals, with Kennedy's Class I partially edentate status in mandibular arch, was included in the study. Complete history, including clinical and radiographic examinations was recorded for each participant. The entire treatment procedure, its benefits, and complications were explained to obtain informed consent before the procedure was started. Participants were randomly assigned to either experimental group (group F) or control group (group C) with a 1:1 allocation as per a computer-generated randomization table (block randomization). Within each group, 5 males and 6 females participants were enrolled. Random allocation sequence was implemented by sequentially numbered opaque sealed envelopes. Treatment plan for group F participants was rehabilitation by using polyacetyl based resin flexible RPD (Supplementary Fig. 3). Treatment plan for group C participants was rehabilitation by using cast RPD (Supplementary Fig. 4). All participants were treated by a single operator (N.K.).
Primary outcome measure was to evaluate patient satisfaction for both the groups using self administered Hindi version of OHIP-14 at baseline (1 week after denture delivery) and at 1 year follow up. OHIP-14 is an abridged version of OHIP-49 with satisfactory reliability and precision.25 Hindi version OHIP-14 evaluates seven different domains as listed in the table with two questions in each domain. For each question, participants were asked about the frequency of problems. Patients response were rated using a Likert scale with high scores indicating poor oral health and minimum score of zero indicating no problems. There were no changes to trial outcome after trial commencement.
Data for OHIP-14 was listed in a table and further analyzed with a statistical software program (Stata 14.0; StataCorp LLC). Quantitative variables were summarized as mean and standard deviation. Qualitative variables were described as frequency. Approximate normality was tested by using the Shapiro-Wilk test for quantitative data. Unpaired t-test was used to compare weight, height, and age between group F and group C. Fisher Exact test was used to compare gender distribution between group F and group C. Mann Whitney test was used to compare the domain scores between group F and group C at each time of observation. Wilcoxon signed rank test was used to compare the change in score of each domain within group F and group C at each time interval (α = .05).
3. Results
3.1. 3D finite element analysis
The stress distribution was represented using different colour coding as is seen in Fig. 3b, Fig. 3c, Fig. 3aa, b, and 3c as well as Fig. 4b, Fig. 4c, Fig. 4aa, b, and 4c The descending order of stress distribution was represented by the colour sequence as follows: red, orange, yellow, light green, dark green, light blue, and dark blue. This colour coding was used to analyse the stress pattern on all the models (see Fig. 4a, Fig. 4b, Fig. 4c).
Fig. 4c.
Von Mises stress in edentulous region in polyacetyl based resin flexible RPD.
In the 3D model for cast RPD, as seen in Fig. 3b, Fig. 3c, Fig. 3aa, b, and 3c and Table 2, maximum stress was observed at the primary abutment (second premolar). On the primary abutment (second premolar), maximum stress was concentrated on the buccal aspect of cervical one-third, the mesial occlusal rest, the distal proximal plate, and the periodontal ligament. The mucosa and the supporting bone in the edentulous region (mandibular first molar) showed less stress than the primary abutment. The von Mises stress distribution was in the following descending order: the region of mesial rest seat of the primary (second premolar) abutment (100 MPa), the contact area of Y shaped clasp with the cervical portion of the primary abutment (second premolar) (90 MPa), the distal proximal plate (80 MPa), the periodontal ligament of the primary abutment (second premolar) (50 MPa), the edentulous area corresponding to the first and second molar (7 MPa).
Table 2.
von Mises stress values at different regions for cast partial denture.
| Region | Von Mises stress values (MPa) |
|---|---|
| Y shaped clasp | 90 |
| Distal proximal plate | 80 |
| Mesial rest | 100 |
| Periodontal ligament of the abtment tooth | 50 |
| Mucosa | 6 |
| Bone | 7 |
MPa, Mega Pascals.
In the 3D model for polyacetyl resin based flexible RPD, the areas with maximum stress values were the edentulous ridge, the mucosa covering the ridge and the periodontal ligament of the terminal, primary abutment tooth. The von Mises stress distribution was in the following descending order: the ridge mucosa and the supporting bone both (25 MPa), the distal surface of the primary abutment (second premolar) (11 MPa), the periodontal ligament of the second premolar (3 MPa). The stresses in the edentulous region were concentrated in the first molar region, with higher stress in the mucosa than the supporting bone as seen in Fig. 4b, Fig. 4c, Fig. 4aa, 4b, 4c and Table 3.
Table 3.
von Mises stress values at different regions for polyacetyl based resin flexible RPD.
| Region | Von Mises stress values in Mpa |
|---|---|
| Distal of 2nd premolar | 11 |
| pdl of the abtment tooth | 3 |
| Mucosa | 25 |
| Bone | 25 |
3.2. Patient satisfaction
The mean age of the group F was 42.92 ± 8.15 years and group C was 42.50 ± 7.49 years. There was no statistically significant difference with respect to age between group F and group C (P = .901, CI = −6.54,7.38). The percentage distribution of males and females was the same in both groups (45.45% males and 54.54% females) with no statistically significant difference between the gender in the two groups (P = 1). There was no statistically significant difference with respect to gender between group F and group C (P = 1). The mean height of group F was 162.38 ± 5.59 cm and for group C was 163.18 ± 7.25 cm. There was no statistically significant difference with respect to height between group F and group C (P = .774; CI = −6.55,4.95). The mean weight of group F was 64.17 ± 8.75 kg and for group C was 63.67 ± 8.88 kg. There was no statistically significant difference with respect to weight between group F and group C (P = .895; CI = −7.34 to 8.34).
At 1 week after denture insertion, the OHIP-14 score for group F (33.27 ± 6.37) was less than OHIP-14 score for group C (37.81 ± 8.80) and the difference was not statistically significant (P = .167, CI = −2.29 to 11.38). At 1 year, the OHIP-14 score for group F (13.63 ± 2.37) was less than OHIP-14 score for group C (16.90 ± 3.36) and the difference was statistically significant (P = .015, CI = 0.68 to 5.86). The change in OHIP-14 scores within group F and group C was statistically significant (P < .001, CI for group C = 16.14 to 25.67, and CI for group F = −15.94, 23.33). Comparison of scores at baseline and 1 year after denture insertion within each domain and comparison of scores between the group F and group C for each domain has been shown in Table 4. There was no loss of follow up or harm caused by either of the treatment modality.
Table 4.
Descriptive data of scores within each domain, comparison of scores at baseline and 1 year after denture insertion within each domain, comparison of scores between the group F and group C for each domain.
| I | II | III | IV | V | VI | VII | VIII | |
|---|---|---|---|---|---|---|---|---|
| FL | 5.63 ± 2.46 | 1.63 ± 0.80 | 4.90 ± 1.97 | 1.09 ± 0.53 | P = .357 | P = .048 | P = .003 | P = .003 |
| PP | 5.90 ± 2.50 | 2.54 ± 0.93 | 4.81 ± 1.83 | 2.09 ± 0.53 | P = .158 | P = .429 | P = .007 | P = .008 |
| PD | 6.18 ± 1.72 | 2.72 ± 0.78 | 5.54 ± 1.29 | 2.18 ± 0.98 | P = .211 | P = .211 | P = .005 | P = .003 |
| PyD | 6.36 ± 1.74 | 2.90 ± 1.13 | 5.90 ± 1.57 | 2.54 ± 0.82 | P = .447 | P = .490 | P = .004 | P = .005 |
| PsyD | 5.09 ± 1.75 | 2.81 ± 0.98 | 4.63 ± 1.12 | 2.45 ± 0.68 | P = .741 | P = .373 | P = .007 | P = .005 |
| SD | 4.54 ± 1.29 | 2.09 ± 1.04 | 3.72 ± 1.10 | 1.63 ± 0.50 | P = .211 | P = .357 | P = .005 | P = .005 |
| H | 4.81 ± 1.66 | 2.18 ± 0.40 | 4.27 ± 1.19 | 1.63 ± 0.50 | P = .447 | P = .061 | P = .005 | P = .003 |
Group F: Polyacetyl based resin flexible RPD.
Group C: Cast partial denture.
I: Score at baseline in group C.
II: Score at 1 year in group C.
III: Score at baseline in group F.
IV: Score at 1 year in group F.
V: Comparison between group F and group C at baseline.
VI: Comparison between group F and group C at 1 year.
VII: Comparison within group C at the two time intervals.
VIII: Intragroup comparison for group F.
FL: Functional limitation.
PP: Physical pain.
PD: Physical disability.
PyD: Physical discomfort.
PsyD: Psychological disability.
SD: Social disability.
H: Handicap.
4. Discussion
The primary objective of prosthesis, including RPD, is preservation of the health of the remaining hard and soft tissues of the oral cavity and restoration of function, thereby improving patient satisfaction and quality of life. To accomplish the objective of preservation, numerous materials and designs of removable prosthesis have evolved over the years, such as polyacetyl resin based flexible RPD. Despite the popularity, literature is scanty on the distribution of stress when flexible polyacetyl resin based RPD is used.
Stress evaluation in biomaterials and oral tissues often use 2D and 3D FEA studies, as in vivo measurement of stress distribution is not feasible due to the limitation in designing an accurate model for complex oral structures.16, 17, 18,20 This study was designed to evaluate and compare the stress distribution pattern in polyacetyl resin based flexible RPD and in cast RPD in Kennedy class I situation using 3D finite element analysis. In order to evaluate and compare the change in quality of life as end point of treatment, the in vivo component of the study evaluated and compared the patient satisfaction by using OHIP-14 as a tool in patients with Kennedy's class I mandibular arch who were rehabilitated by using polyacetyl resin based flexible RPD and cast RPD after 1 year.
The numerical values of the von Mises stress produced in different supporting areas with both the dentures were evaluated by using 3D FEA on a model constructed from CT data from a participant as this ensures the modelling accuracy.12 All the materials used in this study were considered to be linearly elastic, homogenous, and isotropic, in order to decrease the complexity of analysis.14,15 Linear elastic equations were used to represent all the materials in FEA as the loading condition simulated was a static load of 100 N parallel to the long axis was applied on the first molar region of the prosthesis.
In the cast RPD model, maximum von Mises stress were noted on the primary abutment, suggesting that maximum amount of load was transferred to the terminal abutment, while the ridge and mucosa were spared. Lesser amount of stresses were evident in the edentulous region on the mucosa and the supporting bone. These results were consistent with the results of other FEM studies of the cast partial dentures.14,17 This implies that the edentulous ridge region provides less support than the terminal, primary abutment with a cast RPD.
In the model for polyacetyl resin based flexible RPD, the von Mises Stress on the distal surface of the terminal abutment was less than the stress on the edentulous region, including the bone and the mucosa. The larger stress in the edentulous region with polyacetyl resin based flexible RPD can be attributed to the absence of occlusal rests and the low stiffness of the major connector.18 Lack of use of occlusal rests on terminal abutment teeth with polyacetyl resin based flexible RPD largely transmits occlusal forces to the residual alveolar ridge. This is suggestive that the edentulous region shields or protects the terminal primary abutment tooth when a polyacetyl resin based flexible RPD is used. This is also suggestive that the design of the flexible RPD should include the maximum support bearing area underneath the base, in order to distribute the occlusal load.
When compared to cast RPD, stress on the edentulous region is 5 times more with flexible polyacetyl resin based RPD. This can have clinical implications in the form of either local tenderness or excessive resorption of residual ridge. The stress on the abutment teeth supporting cast RPD is nearly 9 times that of stress on abutment teeth with resin polyacetyl based flexible RPD. The clinical implication of this can be deterioration in periodontal status of the tooth with time.
The outcome of the OHIP-14 patient satisfaction questionnaire does not support the ill effects of either polyacetyl resin based RPD or cast RPD. An overall decrease in scores was observed with both polyacetyl resin based RPD and cast RPD after 1 year of use when compared with scores at baseline. This trend was observed in individual domains as well. The possible reason for this is attributed to adaptation and learning curve associated with the use of prosthesis. The OHIP-14 scores with polyacetyl resin based flexible RPD was significantly lower than cast RPD at the baseline as well as at the end of 1 year, thus implying better patient satisfaction with polyacetyl resin based RPD at all stages of follow up. The lesser patient satisfaction with cast RPD as compared with flexible polyacetyl resin based RPD can be attributed to the multiple appointments, mouth preparation, bulk and weight of the denture, and the metal display associated with cast RPD.7,11 This can also be attributed to the inherent flexible nature of the material, lack of necessity of abutment teeth preparation, and an overall better performance perception by the patient with polyacetyl resin based RPD.6, 7, 8,11, 12, 13
The outcome of the FEA and OHIP-14 scores are suggestive of favourable features of polyacetyl resin based RPD when compared to cast RPD, including protection of the terminal, distal most abutment tooth, superior patient satisfaction, and lack of short term ill effects. When viewed along with other previously documented advantages such as rapidity of fabrication, omission of teeth preparation, and economic expenditure, polyacetyl resin based RPD can be considered superior to cast RPD. The clinical aspects of patient satisfaction and the status of residual ridge resorption associated with flexible resin based RPD will however need to be investigated further through a longer, well controlled trial.
The limitations of the study include unidirectional (vertical) application of force for the FEA. The mastication cycle has forces vectors in multiple directions that can affect the stress distribution patterns and this was not accounted for in the FEA. It was also assumed that the cortical and cancellous bones were isotropic, that the mucosa was linearly elastic. Clinically this may be subject to variability. The in vivo component of the study includes a small sample size and has a short observation period. It can be followed up by a long term study with larger sample size, followed over a longer duration.
5. Conclusion
Cast RPD are associated with larger force transmission to the abutment tooth than flexible resin based RPD. Flexible resin base RPD can thus be useful in periodontally compromised abutment teeth. Cast RPD exert lesser force on residual ridge and mucosa than polyacetyl resin based flexible RPD. Long term effects of greater force transmission to residual ridge by use of polyacetyl resin based flexible RPD need to be studied. Improvement in patient satisfaction with time is observed after use of polyacetyl resin based RPD and cast RPD, although the level of satisfaction is more with polyacetyl resin based RPD. Long term changes in patient satisfaction after use of the prosthesis needs to be studied for more conclusive results.
FUNDING
This research did not receive any special grant from funding agencies in the public, commercial, or not-for-profit sectors.
Acknowledgements
The authors acknowledge Prof. Pandey, Department of Biostatistics, AIIMS, New Delhi for the statistical compilation of results and LeLogix Design Solutions Pvt. Ltd, Greater Noida, Uttar Pradesh, India for technical assistance in FEA.
Footnotes
Supplementary data to this article can be found online at https://doi.org/10.1016/j.jobcr.2021.06.004.
Appendix A. Supplementary data
The following are the Supplementary data to this article:
figs1.
figs2.
figs3.
figs4.
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