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Load Distribution in Dorsally-Angulated Distal Radius Deformity Using Finite Element Analysis

Open AccessPublished:August 13, 2022DOI:https://doi.org/10.1016/j.jhsa.2022.02.022

      Purpose

      The load axis of the carpals is located on the volar side of the normal distal radius. A volar lunate facet fracture (VLFF) is exposed to volar-shearing stress, which can cause volar displacement of the carpus. A previous biomechanical study reported that the load at the scaphoid fossa was located more dorsally and the pressure at the lunate fossa decreased in a dorsally-angulated model. However, the distal radius load distribution for various volar tilts remains unclear. We speculate that if the volar tilt decreases, the load distribution moves dorsally and decreases the stress on the VLFF. Therefore, we analyzed a dorsally-angulated distal radius model to evaluate changes in the load distribution using finite element analysis.

      Methods

      A 3-dimensional finite element wrist model was developed using computed tomography images. The ligaments were modeled as tension-only spring elements. We considered the intact wrist model for a volar tilt of 15° and created 5 additional models for volar tilts of 10°, 5°, 0°, −5°, and −10°.

      Results

      As the dorsal angulation increased, the stress distribution moved from volar to dorsal and from the lunate fossa toward the scaphoid fossa. The maximum stress on the volar lunate facet was reduced as volar tilt decreased. The maximum stress was higher on the lunate fossa for volar tilts from 15° to 5°. In contrast, the maximum stress was higher on the scaphoid fossa for volar tilts of ≤0°.

      Conclusions

      Load transmission moved from volar to dorsal and from the lunate fossa to the scaphoid fossa when the volar tilt decreased. Therefore, a decrease in the volar tilt would reduce the load on the VLFF.

      Clinical relevance

      This study provides surgeons accurate knowledge regarding load distribution of the distal radius for various volar tilts that could be helpful in treating patients with VLFFs.

      Key words

      Distal radius fracture associated with a volar lunate facet fragment (VLFF) can cause volar displacement of the carpus.
      • Harness N.G.
      • Jupiter J.B.
      • Orbay J.L.
      • Raskin K.B.
      • Fernandez D.L.
      Loss of fixation of the volar lunate facet fragment in fractures of the distal part of the radius.
      • Beck J.D.
      • Harness N.G.
      • Spencer H.T.
      Volar plate fixation failure for volar shearing distal radius fractures with small lunate facet fragments.
      • O'Shaughnessy M.A.
      • Shin A.Y.
      • Kakar S.
      Volar marginal rim fracture fixation with volar fragment-specific hook plate fixation.
      • Kachooei A.R.
      • Tarabochia M.
      • Jupiter J.B.
      Distal radius volar rim fracture fixation using DePuy-Synthes volar rim plate.
      Harness et al
      • Harness N.G.
      • Jupiter J.B.
      • Orbay J.L.
      • Raskin K.B.
      • Fernandez D.L.
      Loss of fixation of the volar lunate facet fragment in fractures of the distal part of the radius.
      reported that carpal displacement occurred in patients with a volar-shearing fracture who failed VLFF fixation. The volar lunate facet (VLF) has a narrow flat surface and projects anteriorly; therefore, achieving secure fixation is challenging.
      • Beck J.D.
      • Harness N.G.
      • Spencer H.T.
      Volar plate fixation failure for volar shearing distal radius fractures with small lunate facet fragments.
      ,
      • Andermahr J.
      • Lozano-Calderon S.
      • Trafton T.
      • Crisco J.J.
      • Ring D.
      The volar extension of the lunate facet of the distal radius: a quantitative anatomic study.
      Recent reports show that using specifically designed plates or surgical methods can support the volar rim fragment.
      • O'Shaughnessy M.A.
      • Shin A.Y.
      • Kakar S.
      Volar marginal rim fracture fixation with volar fragment-specific hook plate fixation.
      ,
      • Kachooei A.R.
      • Tarabochia M.
      • Jupiter J.B.
      Distal radius volar rim fracture fixation using DePuy-Synthes volar rim plate.
      However, to our knowledge a widely accepted approach to stabilizing this fracture type has not been established. Furthermore, salvage surgery for failed VLFF, such as repeat reduction, arthrodesis, and intra-articular osteotomy, also is challenging.
      • Harness N.G.
      • Jupiter J.B.
      • Orbay J.L.
      • Raskin K.B.
      • Fernandez D.L.
      Loss of fixation of the volar lunate facet fragment in fractures of the distal part of the radius.
      ,
      • Ruch D.S.
      • Wray III, W.H.
      • Papadonikolakis A.
      • Richard M.J.
      • Leversedge F.J.
      • Goldner R.D.
      Corrective osteotomy for isolated malunion of the palmar lunate facet in distal radius fractures.
      The articular surface of the distal radius is inclined volarly, and the load axis is located on the volar side.
      • Daniele L.
      • McLean A.
      • Cocks N.
      • Kalamaras M.
      • Bindra R.
      • Ezekiel Tan S.L.
      Anatomic variation in volar tilt of the scaphoid and lunate facet of the distal radius.
      • Majima M.
      • Horii E.
      • Matsuki H.
      • Hirata H.
      • Genda E.
      Load transmission through the wrist in the extended position.
      • Márquez-Florez K.
      • Vergara-Amador E.
      • de Las Casas E.B.
      • Garzón-Alvarado D.A.
      Theoretical distribution of load in the radius and ulna carpal joint.
      Therefore, once a VLFF occurs, the fragment is exposed to volar-shearing stress. In this regard, Orbay et al
      • Orbay J.L.
      • Rubio F.
      • Vernon L.L.
      Prevent collapse and salvage failures of the volar rim of the distal radius.
      reported a salvage procedure for failed VLFF fixation based on a volar opening wedge osteotomy to decrease volar tilt. Short et al
      • Short W.H.
      • Palmer A.K.
      • Werner F.W.
      • Murphy D.J.
      A biomechanical study of distal radial fractures.
      reported a biomechanical study of the distal radius articular surface using pressure-sensitive film. For 20° dorsal angulation from the original position, the load on the scaphoid fossa and ulnocarpal joint moved more dorsally, and the pressure at the lunate fossa decreased.
      • Short W.H.
      • Palmer A.K.
      • Werner F.W.
      • Murphy D.J.
      A biomechanical study of distal radial fractures.
      However, load distribution in the distal radius for various volar tilts remains unclear. We speculate that if the volar tilt decreases, then the load distribution moves toward the dorsal side. In this case, stress in the VLFF would decrease, and volar displacement of the carpus could be avoidable.
      We hypothesized that reducing volar tilt can decrease the load on the volar rim. We analyzed a dorsally-angulated distal radius model using finite element analysis.

      Materials and Methods

      Finite element model of the distal radius and carpal

      This study was approved by our institutional review board (Iwate Medical University; No. MH2021-063). A 3-dimensional finite element method wrist model was developed using computed tomography images (Fig. 1). The distal end of the radius and ulna to the proximal one-third of the metacarpals from a skeletally mature man was scanned with the wrist in a neutral position. The wrist had a type 1 lunate without a medial (hamate) facet.
      • Viegas S.F.
      • Wagner K.
      • Patterson R.
      • Peterson P.
      Medial (hamate) facet of the lunate.
      The scanned model was differentiated into cortical and cancellous bone. Image analysis software (Simpleware Scan IP Version Q-2020.6; Synopsys, Inc) was used, and the model was divided into 4-node tetrahedral elements. All meshed parts of the model were imported from the initial software to the secondary software, (Patran 2020; MSC Software, Inc), as pre–post processors. The model used isotropic and linear elastic material properties. Thus, Young’s moduli of 18,000 MPa and 100 MPa were assigned to the cortical and cancellous bones, respectively.
      • Gislason M.K.
      • Stansfield B.
      • Nash D.H.
      Finite element model creation and stability considerations of complex biological articulation.
      The Poisson ratio was set to 0.2 for cortical bone and 0.25 for cancellous bone.
      • Gislason M.K.
      • Stansfield B.
      • Nash D.H.
      Finite element model creation and stability considerations of complex biological articulation.
      The ligaments were modeled as linear mechanical links, where the position of the insertion points was estimated based on previous studies (Fig. 2).
      • Nagao S.
      • Patterson R.M.
      • Buford Jr., W.L.
      • Andersen C.R.
      • Shah M.A.
      • Viegas S.F.
      Three-dimensional description of ligamentous attachments around the lunate.
      • Bajuri M.N.
      • Abdul Kadir M.R.
      • Murali M.R.
      • Kamarul T.
      Biomechanical analysis of the wrist arthroplasty in rheumatoid arthritis: a finite element analysis.
      • Alonso Rasgado T.
      • Zhang Q.
      • Jimenez Cruz D.
      • et al.
      Analysis of tenodesis techniques for treatment of scapholunate instability using the finite element method.
      The stiffness of the ligaments was defined as 10–350 N/mm, as in previous studies (Table 1).
      • Bajuri M.N.
      • Abdul Kadir M.R.
      • Murali M.R.
      • Kamarul T.
      Biomechanical analysis of the wrist arthroplasty in rheumatoid arthritis: a finite element analysis.
      ,
      • Alonso Rasgado T.
      • Zhang Q.
      • Jimenez Cruz D.
      • et al.
      Analysis of tenodesis techniques for treatment of scapholunate instability using the finite element method.
      Multiple parallel links were used to better model the distribution of ligaments.
      • Gislason M.K.
      • Stansfield B.
      • Nash D.H.
      Finite element model creation and stability considerations of complex biological articulation.
      ,
      • Gislason M.K.
      • Nash D.H.
      • Nicol A.
      • et al.
      A three dimensional finite element model of maximal grip loading in the human wrist.
      The wrist model had a total of 59,470 nodal points and 276,100 elements.
      Figure thumbnail gr1
      Figure 1Three-dimensional finite element model of the wrist developed using computed tomography images.
      Figure thumbnail gr2
      Figure 2Ligaments were modeled as linear mechanical links where the position of the insertion points was estimated based on previous studies.
      Table 1Ligaments Included in the Model and Stiffness Parameters
      LigamentStiffness (N/mm)
      Dorsal radiocarpal27
      Dorsal intercarpal128
      Long radiolunate75
      Short radiolunate75
      Volar radioscapholunate (scaphoid)50
      Volar radioscapholunate (lunate)75
      Radioscaphocapitate50
      Volar radioulnar50
      Dorsal radioulnar50
      Radial collateral carpal10
      Ulnar collateral100
      Ulnolunate40
      Ulnotriquetral40
      Volar lunotriquetral350
      Dorsal lunotriquetral350
      Dorsal scapholunate interosseous230
      Palmar carpometacarpal100
      Pisohamate100

      Angulated distal radius modeling

      The intact wrist model for a volar tilt of 15° was developed. The volar tilt was measured at the point of bisecting scaphoid fossa as described by Daniele et al.
      • Daniele L.
      • McLean A.
      • Cocks N.
      • Kalamaras M.
      • Bindra R.
      • Ezekiel Tan S.L.
      Anatomic variation in volar tilt of the scaphoid and lunate facet of the distal radius.
      In their report, the normal anatomic volar tilt at this point was 13° (±5.1). Moreover, the volar cortical angle was reported as the angle formed by a straight line drawn along the volar surface of the distal radius and a line drawn parallel to the volar cortex.
      • Gandhi R.A.
      • Hesketh P.J.
      • Bannister E.R.
      • Sebro R.
      • Mehta S.
      Age- related variations in volar cortical angle of the distal radius.
      The normal volar cortical angle of a man was reported from 30.4° to 34.1°.
      • Gandhi R.A.
      • Hesketh P.J.
      • Bannister E.R.
      • Sebro R.
      • Mehta S.
      Age- related variations in volar cortical angle of the distal radius.
      In the model, the volar cortical angle was 31°. Five additional models were developed, based on the intact wrist model, to simulate the dorsally-angulated distal radius. The dorsal angulation was modified in increments of 5° with volar tilt angles of 10°, 5°, 0°, −5°, and −10°. In these models, the volar cortical angles were 26°, 21°, 16°, 11°, and 6°. These models all were developed in a 3-dimensional finite element method model, and each ligament was attached similarly to the intact model. Thus, 6 different volar tilt models were created for the analysis.

      Boundary conditions and analysis

      The loading on the finite element model was applied to each metacarpal along its longitudinal axis with a resultant force of 647.6 N. The load was determined based on a previous biomechanical study.
      • Gislason M.K.
      • Nash D.H.
      • Nicol A.
      • et al.
      A three dimensional finite element model of maximal grip loading in the human wrist.
      The magnitudes of forces for the thumb, index, middle, ring, and little fingers were 255.6, 120.3, 106.4, 88.0, and 77.3 N, respectively.
      • Gislason M.K.
      • Nash D.H.
      • Nicol A.
      • et al.
      A three dimensional finite element model of maximal grip loading in the human wrist.
      The loading condition simulates half of the maximum gripping force for a healthy individual.
      • Gislason M.K.
      • Nash D.H.
      • Nicol A.
      • et al.
      A three dimensional finite element model of maximal grip loading in the human wrist.
      The proximal parts of the radius and ulna were fixed. In addition, articular contact was established between the scaphoid and the scaphoid fossa of the radius and between the lunate and the lunate fossa of the radius. The contact was frictionless, and a friction coefficient of 0.02 was assigned.
      • Gislason M.K.
      • Stansfield B.
      • Nash D.H.
      Finite element model creation and stability considerations of complex biological articulation.
      For other articulations, the distal carpal bones were tightly bound to each other, and the motion between them was considered negligible.
      • Kijima Y.
      • Viegas S.F.
      Wrist anatomy and biomechanics.
      Similarly, these settings were applied to all developed models. Under these conditions, we evaluated the stress distribution with von Mises stress using the stress contour map in Marc 2020 (MSC Software, Inc) as a solver. The results were compared for all 6 models to evaluate the effect of dorsal angulation on the loading at the radiocarpal joint and the VLF.

      Results

      In the intact wrist model, the maximum stress on the volar aspect of the lunate fossa and scaphoid fossa was 90 and 88 MPa, respectively (Fig. 3). As dorsal angulation increased, the stress distribution moved from volar to dorsal and from the lunate fossa toward the scaphoid fossa (Fig. 4). The maximum stress on the VLF gradually reduced with an increase in dorsal angulation (Figs. 5, 6). The maximum stress was higher on the lunate fossa for a volar tilt of 15° to 5°. In contrast, the maximum stress on the scaphoid fossa was higher for a volar tilt of ≤0°.
      Figure thumbnail gr3
      Figure 3Magnitude of the reaction force acting on the scaphoid fossa and lunate fossa in the intact wrist and dorsally-angulated models. The maximum stress was higher on the lunate fossa for a volar tilt of 15°–5°. In contrast, the maximum stress was higher on the scaphoid fossa for a volar tilt of ≤0°. VT, volar tilt.
      Figure thumbnail gr4
      Figure 4Von Mises stress plots at the distal end of the radius in the intact wrist and dorsally-angulated models. The intact wrist for a volar tilt of 15°. As the dorsal angulation increased, the stress distribution moved gradually from the volar to the dorsal and from the lunate fossa towards the scaphoid fossa. VT, volar tilt.
      Figure thumbnail gr5
      Figure 5Von Mises stress plots at the VLF. VT, volar tilt.
      Figure thumbnail gr6
      Figure 6Magnitude of the reaction force acting on the VLF. The maximum stress on the VLF gradually reduced with a dorsal angulation increase. VT, volar tilt.

      Discussion

      The volar margin of the distal radius projects and forms the lunate facet.
      • Andermahr J.
      • Lozano-Calderon S.
      • Trafton T.
      • Crisco J.J.
      • Ring D.
      The volar extension of the lunate facet of the distal radius: a quantitative anatomic study.
      The VLF includes the insertion of the short radiolunate ligament, with a height and width of approximately 3 and 19 mm, respectively.
      • Andermahr J.
      • Lozano-Calderon S.
      • Trafton T.
      • Crisco J.J.
      • Ring D.
      The volar extension of the lunate facet of the distal radius: a quantitative anatomic study.
      ,
      • Nagao S.
      • Patterson R.M.
      • Buford Jr., W.L.
      • Andersen C.R.
      • Shah M.A.
      • Viegas S.F.
      Three-dimensional description of ligamentous attachments around the lunate.
      A previous study reported that the transmission of forces to the lunate fossa, scaphoid fossa, and triangular fibrocartilage was 29% to 47%, 43% to 55%, and 6% to 25%, respectively.
      • Majima M.
      • Horii E.
      • Matsuki H.
      • Hirata H.
      • Genda E.
      Load transmission through the wrist in the extended position.
      In the lunate fossa, the centroid of the pressure is located volarly in the neutral position.
      • Majima M.
      • Horii E.
      • Matsuki H.
      • Hirata H.
      • Genda E.
      Load transmission through the wrist in the extended position.
      Márquez-Florez et al
      • Márquez-Florez K.
      • Vergara-Amador E.
      • de Las Casas E.B.
      • Garzón-Alvarado D.A.
      Theoretical distribution of load in the radius and ulna carpal joint.
      estimated the load distribution of the radiocarpal joint using a rigid body spring model method. Our model for a volar tilt of 15° showed a similar load distribution to that in their report.
      • Márquez-Florez K.
      • Vergara-Amador E.
      • de Las Casas E.B.
      • Garzón-Alvarado D.A.
      Theoretical distribution of load in the radius and ulna carpal joint.
      This study revealed that the maximum stress on the VLF gradually reduced when the dorsal angulation increased. Therefore, we considered that a decrease in volar tilt would reduce the load on the VLFF and possibly prevent volar displacement of the carpus in the clinical setting. Moreover, a decrease in the volar tilt may be an option in the case of corrective osteotomy for failed primary surgery of volar rim fractures. Several studies have reported that loss of the volar tilt or radial length reduction did not correlate with functional outcomes.
      • Arora R.
      • Lutz M.
      • Deml C.
      • Krappinger D.
      • Haug L.
      • Gabl M.
      A prospective randomized trial comparing nonoperative treatment with volar locking plate fixation for displaced and unstable distal radial fractures in patients sixty-five years of age and older.
      • Finsen V.
      • Rod O.
      • Rød K.
      • Rajabi B.
      • Alm-Paulsen P.S.
      • Russwurm H.
      The relationship between displacement and clinical outcome after distal radius (Colles') fracture.
      • Yu X.
      • Yu Y.
      • Shao X.
      • Bai Y.
      • Zhou T.
      Volar locking plate versus external fixation with optional additional K-wire for treatment of AO type C2/C3 fractures: a retrospective comparative study.
      However, other reports have indicated that dorsal angulation of the radius is the primary cause of wrist disabilities.
      • Taleisnik J.
      • Watson H.K.
      Midcarpal instability caused by malunited fractures of the distal radius.
      ,
      • Padmore C.E.
      • Stoesser H.
      • Nishiwaki M.
      • et al.
      The effect of dorsally angulated distal radius deformities on carpal kinematics: an in vitro biomechanical study.
      Taleisnik and Watson
      • Taleisnik J.
      • Watson H.K.
      Midcarpal instability caused by malunited fractures of the distal radius.
      reported on patients who complained of midcarpal pain and instability in the presence of a distal radius malunion with an average dorsal angulation of 23°. They concluded that abnormal dorsal angulation leads to midcarpal instability. In addition, Padmore et al
      • Padmore C.E.
      • Stoesser H.
      • Nishiwaki M.
      • et al.
      The effect of dorsally angulated distal radius deformities on carpal kinematics: an in vitro biomechanical study.
      conducted a biomechanical study on dorsally-angulated distal radius deformities. In their report, the radiocarpal motion arc increased, but the midcarpal motion arc decreased when dorsal angulation increased.
      • Padmore C.E.
      • Stoesser H.
      • Nishiwaki M.
      • et al.
      The effect of dorsally angulated distal radius deformities on carpal kinematics: an in vitro biomechanical study.
      The study also indicated that the altered contribution of the radiocarpal and midcarpal joints might result in pain, stiffness, and arthritis development. Saito et al
      • Saito T.
      • Nakamura T.
      • Nagura T.
      • Nishiwaki M.
      • Sato K.
      • Toyama Y.
      The effects of dorsally angulated distal radius fractures on distal radioulnar joint stability: a biomechanical study.
      conducted a biomechanical study of distal radioulnar joint stability using a dorsally-angulated distal radius fracture model for volar tilts of 10°, 0°, −10°, and −20°. They reported that the distal radioulnar joint stiffness decreased at volar tilts of −10° and −20°. Their findings suggested that dorsal angulation of the radius should be corrected to be less than −10° of the volar tilt.
      Stresses between the scaphoid fossa and lunate fossa were well balanced in models for volar tilts of 15° and 0°. Nevertheless, volar tilts of 10° and 5° showed higher maximum stress in the lunate fossa. These results imply that a slight decrease in volar tilt might increase the joint stress in the lunate fossa except for VLF. Surgeons must be aware of this when treating patients with comminuted distal radial fractures with VLFF. Although the load to the VLFF would reduce with a decrease in the volar tilt, other parts of the fragment might be subjected to higher forces. Based on our results, fixation in a volar tilt of 0° could be the recommended angle to treat a distal radial comminuted fracture with VLFF.
      Some possibilities could be considered regarding the increase in the maximum stress of the lunate fossa in the models for volar tilts of 10° and 5°. First, the lunate fossa is different from the scaphoid fossa in size and shape. In the sagittal plane, the concavity of the lunate fossa is wider than that of the scaphoid fossa.
      • Andermahr J.
      • Lozano-Calderon S.
      • Trafton T.
      • Crisco J.J.
      • Ring D.
      The volar extension of the lunate facet of the distal radius: a quantitative anatomic study.
      In the axial plane, the lunate fossa presents an oval shape spanning the dorsovolar direction, whereas the scaphoid fossa has a longer oval shape spanning the radioulnar direction. The volar tilt of the scaphoid fossa is approximately 4° greater than that of the lunate fossa.
      • Daniele L.
      • McLean A.
      • Cocks N.
      • Kalamaras M.
      • Bindra R.
      • Ezekiel Tan S.L.
      Anatomic variation in volar tilt of the scaphoid and lunate facet of the distal radius.
      These morphologic features might have contributed to our observations. A decreased volar tilt can generate nonphysiologic forces that could lead to radiocarpal arthritis. In addition, dorsally-angulated distal radius malunion was associated with a risk of flexor tendon rupture.
      • Wurtzel C.N.W.
      • Burns G.T.
      • Zhu A.F.
      • Ozer K.
      Effects of volar tilt, wrist extension, and plate position on contact between flexor pollicis longus tendon and volar plate.
      Recent commercial volar locking plates have a mediolateral extension; therefore, the contact between the tendon and plate occurs more readily in the dorsally-angulated distal radius than in anatomic tilt.
      • Wurtzel C.N.W.
      • Burns G.T.
      • Zhu A.F.
      • Ozer K.
      Effects of volar tilt, wrist extension, and plate position on contact between flexor pollicis longus tendon and volar plate.
      ,
      • Kikuchi Y.
      • Sato K.
      • Mimata Y.
      • Murakami K.
      • Takahashi G.
      • Doita M.
      Ulnar facet locking screw locations of volar locking plates placed without flexor pollicis longus tendon contact: a cadaver study.
      Although a decrease in volar tilt might contribute to preventing a volar dislocation of the carpus, it is uncertain how much dorsal angulation can be tolerated before producing other harmful effects. Further studies are required to validate the extent to which dorsal angulation is suitable for treating distal radius fractures with VLFFs.
      This study has several limitations. First, this model had simplifications, including assumptions of the bones as rigid bodies and ligaments as linear elastic materials. Second, we modeled the triangular fibrocartilage complex through various ligaments according to previous reports.
      • Bajuri M.N.
      • Abdul Kadir M.R.
      • Murali M.R.
      • Kamarul T.
      Biomechanical analysis of the wrist arthroplasty in rheumatoid arthritis: a finite element analysis.
      ,
      • Alonso Rasgado T.
      • Zhang Q.
      • Jimenez Cruz D.
      • et al.
      Analysis of tenodesis techniques for treatment of scapholunate instability using the finite element method.
      Although we did not replicate the fibrocartilage, the proposed intact wrist model showed similar pressure distribution to previous reports.
      • Majima M.
      • Horii E.
      • Matsuki H.
      • Hirata H.
      • Genda E.
      Load transmission through the wrist in the extended position.
      ,
      • Gislason M.K.
      • Stansfield B.
      • Nash D.H.
      Finite element model creation and stability considerations of complex biological articulation.
      Third, we used a normal bone model without a VLFF. The size and shape of these fragments might affect the results. Finally, the experiments focused on a single volunteer; therefore, individual differences in distal radius morphology could affect the results. However, future work could expand on these results by including additional participants to address this possibility.

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