# Osteolytic vs. Osteoblastic Metastatic Lesion: Computational Modeling of the Mechanical Behavior in the Human Vertebra after Screws Fixation Procedure

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Imaging and FE Geometric Reconstruction of the Screws-Vertebra Model

#### 2.2. Simulated Metastasis Description

#### 2.3. Constitutive Modeling

#### 2.4. Loading and Boundary Conditions

#### 2.5. Failure Criteria

#### 2.6. Numerical Procedure

#### 2.7. Parametric Analysis

## 3. Results

#### 3.1. Fracture Load

#### 3.1.1. Size, Position, and Shape Effects

#### 3.1.2. Comparison between Osteoblastic and Osteolytic Metastases

#### 3.2. Fracture Patterns

## 4. Discussion

#### Limitations and Perspectives

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Gasbarrini, A.; Boriani, S.; Capanna, R.; Casadei, R.; Di Martino, A.; Spinelli, M.S.; Papapietro, N.; Piccioli, A. The Italian Orthopaedic Society Bone Metastasis Study Group Management of patients with metastasis to the vertebrae: Recommendations from the Italian Orthopaedic Society (SIOT) Bone Metastasis Study Group. Expert Rev. Anticancer. Ther.
**2014**, 14, 143–150. [Google Scholar] [CrossRef] [PubMed] - Salvatore, G.; Berton, A.; Giambini, H.; Ciuffreda, M.; Florio, P.; Longo, U.G.; Denaro, V.; Thoreson, A.; An, K.N. Biomechanical effects of metastasis in the osteoporotic lumbar spine: A Finite Element Analysis. BMC Musculoskelet. Disord.
**2018**, 19, 38. [Google Scholar] [CrossRef] [PubMed] - Denaro, V.; Di Martino, A.; Papalia, R.; Denaro, L. Patients with Cervical Metastasis and Neoplastic Pachymeningitis are Less Likely to Improve Neurologically After Surgery. Clin. Orthop. Relat. Res.
**2011**, 469, 708–714. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Confavreux, C.B.; Follet, H.; Mitton, D.; Pialat, J.B.; Clezardin, P. Fracture Risk Evaluation of Bone Metastases: A Burning Issue. Cancers
**2021**, 13, 5711. [Google Scholar] [CrossRef] [PubMed] - Whyne, C.M.; Ferguson, D.; Clement, A.; Rangrez, M.; Hardisty, M. Biomechanical Properties of Metastatically Involved Osteolytic Bone. Curr. Osteoporos. Rep.
**2020**, 18, 705–715. [Google Scholar] [CrossRef] [PubMed] - Bouxsein, M.L. Determinants of skeletal fragility. Best Pract. Res. Clin. Rheumatol.
**2005**, 19, 897–911. [Google Scholar] [CrossRef] - Campbell, G.M.; Pena, J.A.; Giravent, S.; Thomsen, F.; Damm, T.; Gluer, C.C.; Borggrefe, J. Assessment of Bone Fragility in Patients With Multiple Myeloma Using QCT-Based Finite Element Modeling. J. Bone Miner. Res.
**2017**, 32, 151–156. [Google Scholar] [CrossRef] - Anitha, D.; Baum, T.; Kirschke, J.; Subburaj, K. Risk of vertebral compression fractures in multiple myeloma patients A finite-element study. Medicine
**2017**, 96, e5825. [Google Scholar] [CrossRef] - Costa, M.C.; Eltes, P.; Lazary, A.; Varga, P.P.; Viceconti, M.; Dall’Ara, E. Biomechanical assessment of vertebrae with lytic metastases with subject-specific finite element models. J. Mech. Behav. Biomed. Mater.
**2019**, 98, 268–290. [Google Scholar] [CrossRef] - Stadelmann, M.A.; Schenk, D.E.; Maquer, G.; Lenherr, C.; Buck, F.M.; Bosshardt, D.D.; Hoppe, S.; Theumann, N.; Alkalay, R.N.; Zysset, P.K. Conventional finite element models estimate the strength of metastatic human vertebrae despite alterations of the bone’s tissue and structure. Bone
**2020**, 141, 115598. [Google Scholar] [CrossRef] - Whyne, C.M.; Hu, S.S.; Lotz, J.C. Parametric finite element analysis of vertebral bodies affected by tumors. J. Biomech.
**2001**, 34, 1317–1324. [Google Scholar] [CrossRef] - Tschirhart, C.E.; Nagpurkar, A.; Whyne, C.M. Effects of tumor location, shape and surface serration on burst fracture riskin the metastatic spine. J. Biomech.
**2004**, 37, 653–660. [Google Scholar] [CrossRef] [PubMed] - Galbusera, F.; Qian, Z.; Casaroli, G.; Bassani, T.; Costa, F.; Schlager, B.; Wilke, H.J. The role of the size and location of the tumors and of the vertebral anatomy in determining the structural stability of the metastatically involved spine: A finite element study. Transl. Oncol.
**2018**, 11, 639–646. [Google Scholar] [CrossRef] [PubMed] - Costa, M.C.; Bresani Campello, L.B.; Ryan, M.; Rochester, J.; Viceconti, M.; Dall’Ara, E. Effect of size and location of simulated lytic lesions on the structural properties of human vertebral bodies, a micro-finite element study. Bone Rep.
**2020**, 12, 100257. [Google Scholar] [CrossRef] [PubMed] - Alkalay, R.N. Effect of the metastatic defect on the structural response and failure process of human vertebrae: An experimental study. Clin. Biomech.
**2015**, 30, 121–128. [Google Scholar] [CrossRef] - Alkalay, R.N.; Harrigan, T.P. Mechanical assessment of the effects of metastatic lytic defect on the structural response of human thoracolumbar spine. J. Orthop. Res.
**2016**, 34, 1808–1819. [Google Scholar] [CrossRef] [Green Version] - Palanca, M.; Brodano Barbanti, G.; Cristofolini, L. The size of simulated lytic metastases affects the strain distribution on the anterior surface of the vertebra. J. Biomech. Eng.
**2018**, 140, 111005. [Google Scholar] [CrossRef] - Moussazadeh, N.; Rubin, D.G.; McLaughlin, L.; Lis, E.; Bilsky, M.H.; Laufer, I. Short-segment percutaneous pedicle screw fixation with cement augmentation for tumor-induced spinal instability. Spine J.
**2015**, 15, 1609–1617. [Google Scholar] [CrossRef] - Kim, P.; Kim, S.W. Bone cement-augmented percutaneous screw fixation for malignant spinal metastases: Is it feasible? J. Korean Neurosurg. Soc.
**2017**, 60, 189–194. [Google Scholar] [CrossRef] - Di Martino, A.; Vincenzi, B.; Denaro, L.; Barnaba, S.A.; Papalia, R.; Santini, D.; Tonini, G.; Denaro, V. Internal bracing’ surgery in the management of solid tumor metastases of the thoracic and lumbar spine. Oncol. Rep.
**2009**, 21, 431–435. [Google Scholar] [CrossRef] - Veersteg, A.L.; Verlaan, J.J.; de Baat, P.; Jiya, T.U.; Stadhouder, A.; Diekerhof, C.H.; van Solinge, G.B.; Oner, F.C. Complications After Percutaneous Pedicle Screw Fixation for the Treatment of Unstable Spinal Metastases. Ann. Surg. Oncol.
**2016**, 23, 2043–2049. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Di Martino, A.; Caldaria, A.; De Vivo, V.; Denaro, V. Metastatic epidural spinal cord compression. Expert Rev. Anticancer. Ther.
**2016**, 16, 1189–1198. [Google Scholar] [CrossRef] [PubMed] - Dea, N.; Versteeg, A.; Fisher, C.; Kelly, A.; Hartig, D.; Boyd, M.; Paquette, S.; Kwon, B.K.; Dvorak, M.; Street, J. Adverse events in emergency oncological spine surgery: A prospective analysis. J. Neurosurg. Spine
**2014**, 21, 698–703. [Google Scholar] [CrossRef] [PubMed] - Wagner, A.; Haag, E.; Joerger, A.K.; Jost, P.; Combs, S.E.; Wostrack, M.; Gempt, J.; Meyer, B. Comprehensive surgical treatment strategy for spinal metastases. Sci. Rep.
**2021**, 11, 7988. [Google Scholar] [CrossRef] - Molinari, L.; Falcinelli, C.; Gizzi, A.; Di Martino, A. Effect of pedicle screw angles on the fracture risk of the human vertebra: A patient-specific computational model. J. Mech. Behav. Biomed. Mater.
**2021**, 116, 104359. [Google Scholar] [CrossRef] - Molinari, L.; Falcinelli, C.; Gizzi, A.; Di Martino, A. Biomechanical modeling of metal screw loadings on the human vertebra. Acta. Mech. Sin.
**2021**, 37, 307–320. [Google Scholar] [CrossRef] - Falcinelli, C.; Di Martino, A.; Gizzi, A.; Vairo, G.; Denaro, V. Mechanical behavior of metastatic femurs through patient-specific computational models accounting for bone-metastasis interaction. J. Mech. Behav. Biomed. Mater.
**2019**, 93, 9–22. [Google Scholar] [CrossRef] - Falcinelli, C.; Di Martino, A.; Gizzi, A.; Vairo, G.; Denaro, V. Fracture risk assessment in metastatic femurs: A patient- specific CT-based finite-element approac. Meccanica
**2020**, 55, 861–881. [Google Scholar] [CrossRef] - Chappard, D.; Bouvard, B.; Basle, M.F.; Legrand, E.; Audran, M. Bone metastasis: Histological changes and pathophysiological mechanisms in osteolytic or osteosclerotic localizations. A review. Morphologie
**2011**, 95, 65–75. [Google Scholar] [CrossRef] [Green Version] - Ford, C.; Keaveny, T.; Hayes, W. The effect of impact direction on the structural capacity of the proximal femur during falls. J. Bone Miner. Res.
**1996**, 11, 377–383. [Google Scholar] [CrossRef] - Taddei, F.; Pancanti, A.; Viceconti, M. An improved method for the automatic mapping of computed tomography numbers onto finite element models. Med. Eng. Phys.
**2004**, 26, 61–69. [Google Scholar] [CrossRef] - Lee, D.C.; Hoffmann, P.F.; Kopperdahl, D.L.; Keaveny, T.M. Phantomless calibration of CT scans for measurement of BMD and bone strength—Inter-operator reanalysis precision. Bone
**2017**, 103, 325–333. [Google Scholar] [CrossRef] [PubMed] - Lee, Y.H.; Kim, J.J.; Jang, I.G. Patient-specific phantomless estimation of bone mineral density and its effects on finite element analysis results: A feasibility study. Comput. Math. Methods Med.
**2019**, 2019, 4102410. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Eggermont, F.; Verdonschot, N.; van der Linden, Y.; Tanck, E. Calibration with or without phantom for fracture risk prediction in cancer patients with femoral bone metastases using CT-based finite element models. PLoS ONE
**2019**, 14, e0220564. [Google Scholar] [CrossRef] [Green Version] - Morgan, E.F.; Bayraktar, H.H.; Keaveny, T.M. Trabecular bone modulus–density relationships depend on anatomic site. J. Biomech.
**2003**, 36, 897–904. [Google Scholar] [CrossRef] - Fields, A.J.; Lee, G.L.; Keaveny, T.M. Mechanisms of initial endplate failure in the human vertebral body. J. Biomech.
**2010**, 43, 3126–3131. [Google Scholar] [CrossRef] [Green Version] - Eggermont, F.; Derikx, L.C.; Verdonschot, N.; van der Geest, I.C.M.; de Jong, M.A.A.; Snyers, A.; van der Linden, Y.M.; Tanck, E. Can patient-specific finite element models better predict fractures in metastatic bone disease than experienced clinicians? Bone Joint Res.
**2018**, 7, 430–439. [Google Scholar] [CrossRef] - Bailey, S.; Hackney, D.; Vashishth, D.; Alkalay, R.N. The effects of metastatic lesion on the structural determinants of bone: Current clinical and experimental approaches. Bone
**2020**, 138, 115159. [Google Scholar] [CrossRef] - Ulano, A.; Bredella, M.A.; Burke, P.; Chebib, I.; Simeone, F.J.; Huang, A.J.; Torriani, M.; Chang, C.Y. Distinguishing Untreated Osteoblastic Metastases From Enostoses Using CT Attenuation Measurements. AJR Am. J. Roentgenol.
**2016**, 207, 362–368. [Google Scholar] [CrossRef] - Hipp, J.A.; Rosenberg, A.E.; Hayes, W.C. Mechanical properties of trabecular bone within and adjacent to osseous metastases. JBMR
**1992**, 7, 1165–1171. [Google Scholar] [CrossRef] - Keyak, J.H.; Lee, I.Y.; Skinner, H.B. Correlations between orthogonal mechanical properties and density of trabecular bone: Use of different densitometric measures. J. Biomed. Mater. Res.
**1994**, 28, 1329–1336. [Google Scholar] [CrossRef] [PubMed] - Keller, T.S. Predicting the compressive mechanical behavior of bone. J. Biomech.
**1994**, 27, 1159–1168. [Google Scholar] [CrossRef] - Bayraktar, H.H.; Morgan, E.F.; Niebur, G.L.; Morris, G.E.; Wong, E.K.; Keaveny, T.M. Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. J. Biomech.
**2004**, 37, 27–35. [Google Scholar] [CrossRef] - Algra, P.R.; Heimans, J.J.; Valk, J.; Nauta, J.J.; Lachniet, M.; Van Kooten, B. Do metastases in vertebrae begin in the body or the pedicles? Imaging study in 45 patients. AJR Am. J. Roentgenol.
**1992**, 158, 1275–1279. [Google Scholar] [CrossRef] [PubMed] - Whealan, K.M.; Kwak, S.D.; Tedrow, J.R.; Inoue, K.; Snyder, B.D. Noninvasive Imaging Predicts Failure Load of the Spine with Simulated Osteolytic Defects. JBJS
**2000**, 82, 1240–1251. [Google Scholar] [CrossRef] [PubMed] - Palanca, M.; De Donno, G.; Dall’Ara, E. A novel approach to evaluate the effects of artificial bone focal lesion on the threedimensional strain distributions within the vertebral body. PLoS ONE
**2021**, 16, e0251873. [Google Scholar] [CrossRef] [PubMed] - Tschirhart, C.E.; Finkelstein, J.A.; Whyne, C.M. Biomechanics of vertebral level, geometry, and transcortical tumors in the metastatic spine. J. Biomech.
**2007**, 40, 46–54. [Google Scholar] [CrossRef] - Palanca, M.; Barbanti-Brodano, G.; Marras, D.; Marciante, M.; Serra, M.; Gasbarrini, A.; Dall’Ara, E.; Cristofolini, L. Type, size, and position of metastatic lesions explain the deformation of the vertebrae under complex loading conditions. Bone
**2021**, 151, 116028. [Google Scholar] [CrossRef] - Hipp, J.; Katz, G.; Hayes, W. Local Demineralization as a Model for Bone Strength Reductions in Lytic Transcortical Metastatic Lesions. Invest. Radiol.
**1991**, 26, 934–938. [Google Scholar] [CrossRef] - Malandrino, A.; Kamm, R.D.; Moeendarbary, E. In Vitro Modeling of Mechanics in Cancer Metastasis. ACS Biomater. Sci. Eng.
**2018**, 4, 294–301. [Google Scholar] [CrossRef] [Green Version] - Whyne, C.M.; Hu, S.S.; Workman, K.L.; Lotz, J.C. Biphasic material properties of lytic bone metastases. Ann. Biomed. Eng.
**2000**, 28, 1154–1158. [Google Scholar] [CrossRef] [PubMed] - Tanck, E.; van Aken, J.B.; van der Linden, Y.M.; Bart Schreuder, H.W.; Binkowski, M.; Huizenga, H.; Verdonschot, N. Pathological fracture prediction in patients with metastatic lesions can be improved with quantitative computed tomography based computer models. Bone
**2009**, 45, 777–783. [Google Scholar] [CrossRef] [PubMed] - Goodheart, J.R.; Cleary, R.J.; Damron, T.A.; Mann, K.A. Simulating activities of daily living with finite element analysis improves fracture prediction for patients with metastatic femoral lesions. J. Orthop. Res.
**2015**, 33, 1226–1234. [Google Scholar] [CrossRef] [PubMed] - Derikx, L.C.; Verdonschot, N.; Tanck, E. Towards clinical application of biomechanical tools for the prediction of fracture risk i nmetastatic bone disease. J. Biomech.
**2015**, 48, 761–766. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sciumè, G.; Shelton, S.; Gray, W.G.; Miller, C.T.; Hussain, F.; Ferrari, M.; Decuzzi, P.; Schrefler, B.A. A multiphase model for three-dimensional tumor growth. New. J. Phys.
**2013**, 15, 015005. [Google Scholar] [CrossRef] [PubMed] - Sciumè, G.; Gray, W.G.; Ferrari, M.; Decuzzi, P.; Schrefler, B.A. On computational modeling in tumor growth. Arch. Comput. Methods Eng.
**2013**, 20, 327–352. [Google Scholar] [CrossRef] - Sciumè, G.; Santagiuliana, R.; Ferrari, M.; Decuzzi, P.; Schrefler, B.A. A tumor growth model with deformable ECM. Phys. Biol.
**2014**, 11, 065004. [Google Scholar] [CrossRef] [Green Version] - Katsamba, I.; Evangelidis, P.; Voutouri, C.; Tsamis, A.; Vavourakis, V.; Stylianopoulos, T. Biomechanical modelling of spinal tumour anisotropic growth. Proc. R. Soc. A
**2020**, 476, 20190364. [Google Scholar] [CrossRef] - Gu, Y.; Dong, J.; Jiang, X.; Wang, Y. Minimally invasive pedicle screws fixation and percutaneous vertebroplasty for the surgical treatment of thoracic metastatic tumors with neurologic compression. Spine
**2016**, 41, B14–B22. [Google Scholar] [CrossRef] - Hsieh, Y.Y.; Kuo, Y.J.; Chen, C.H.; Wu, L.C.; Chiang, C.J.; Lin, C.L. Biomechanical assessment of vertebroplasty combined with cement-augmented screw fixation for lumbar burst fractures: A finite element analysis. Appl. Sci.
**2020**, 10, 2133. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**CT-based FE modeling procedure. Starting from CT scan (

**a**), the vertebra geometry is reconstructed through segmentation (

**b**). In addition, the CAD models of two pedicle screws are designed and virtually inserted in the vertebra (

**b**). Then, a simulated metastasis with a spherical shape is included in the model, and it is assumed that the metastatic lesion induces an alteration of Young’s modulus in the bone region close to the metastasis (

**c**). Appropriate boundary conditions are chosen to replicate realistic scenarios (

**d**). Finally, the screws–vertebra model is discretized using ten-nodes tetrahedral elements (

**e**).

**Figure 2.**Screw insertion trajectory. Starting from the neutral position (dashed line) corresponding to an angle of 0${}^{\circ}$ in craniocaudal and mediolateral directions, the screws are rotated +5${}^{\circ}$ in both directions (solid line) to obtain craniolateral trajectory.

**Figure 3.**The local effect induced by osteolytic and osteoblastic metastasis on bone material properties is shown. On the left, Young’s modulus E distribution without metastasis is reported. On the right, the effects of osteolytic and osteoblastic lesions are circled in red. In the case of an osteolytic lesion, a local weakening is produced, whereas an osteoblastic metastasis induces a local stiffening.

**Figure 4.**Boundary conditions applied on the vertebra and screws to mimic extension and left lateral bending loading cases. ${F}_{vert}$ and ${F}_{art}$ represent the compressive forces applied on the superior end plate and articular facets of the vertebra, respectively. The blue arrows indicate the loading direction applied on the screws. For the two loading cases, a uniform momentum was also applied along two different axes.

**Figure 5.**The different positions analyzed for the metastases are shown in transverse (

**a**), anterior (

**b**), and (

**c**) sagittal planes: lateral right P1 (magenta circle); anterior right P2 (yellow circle); and anterior P3 (green circle).

**Figure 6.**Coordinates of the lesion’s center (in mm) with respect to the center of the vertebral body for each position analyzed. The reference system is localized in the center of the vertebral body. From left to right: lateral right P1 (magenta circle); anterior right P2 (yellow circle); and anterior P3 (green circle).

**Figure 7.**Load-displacement curves obtained for osteoblastic, (

**a**,

**b**); and osteolytic, (

**c**,

**d**); metastases in bending, (

**a**,

**c**); and extension, (

**b**,

**d**); loading modes using the stress-based failure criterion varying the radius and position of metastasis.

**Figure 8.**Load-displacement curves obtained for osteoblastic, (

**a**,

**b**); and osteolytic, (

**c**,

**d**); metastases in bending, (

**a**,

**c**); and extension, (

**b**,

**d**); loading modes using the strain-based failure criterion varying the radius and position of metastasis.

**Figure 9.**On the left, load-displacement curves obtained for multiple osteolytic lesions with a radius of 10 mm in bending loading mode using the strain-based failure criterion are reported. On the right, the distribution of Young’s modulus in case of multiple osteolytic lesions (P1+P2+P3) is shown.

**Figure 10.**For each position (P1 (

**a**); P2 (

**b**); P3 (

**c**)), the load-displacement curves obtained for osteoblastic and osteolytic metastases with radii of 5 and 10 mm in bending (

**d**–

**f**) and extension-loading (

**g**–

**i**) conditions using the stress-based failure criterion are shown.

**Figure 11.**For each position (P1 (

**a**); P2 (

**b**); P3 (

**c**)), the load-displacement curves obtained for osteoblastic and osteolytic metastases of 5 and 10 mm of radius in bending (

**d**–

**f**) and extension-loading (

**g**–

**i**) conditions using the strain-based failure criterion are shown.

**Figure 12.**Progression of fracture patterns in an extension-loading condition for osteolytic lesions of 5 mm (

**a**–

**c**) and 10 mm (

**d**–

**f**) located in P1 using the stress-based criterion. Failed elements are highlighted in red.

**Figure 13.**Progression of fracture patterns in an extension-loading condition for an osteoblastic lesion of 10 mm of radius located in P1 (

**a**–

**c**) and in P3 (

**d**–

**f**) using the stress-based criterion. Failed elements are highlighted in red.

**Figure 14.**Fracture evolution of an osteolytic (

**a**–

**c**) and osteoblastic (

**d**–

**f**) lesion of 10 mm of radius located in P2 in a bending loading condition using a stress-based criterion. Failed elements are highlighted in red color.

**Table 1.**The fracture load (FL) expressed in N is reported for each loading condition, failure criterion, type, size, and location of metastasis. EXT (extension) and LLB (left lateral bending) correspond to the loading cases analyzed. The symbols ${\sigma}_{max}$ and ${\u03f5}_{max}$ refer to maximum principal stress and strain criteria, respectively. P1 (lateral right), P2 (anterior right), and P3 (anterior) correspond to locations of metastases. ${R}_{1}$ and ${R}_{2}$ are the radii of metastasis (5 and 10 mm, respectively).

Metastasis | Radius | EXT | LLB | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathbf{\sigma}}_{\mathbf{max}}$ | ${\mathbf{\u03f5}}_{\mathbf{max}}$ | ${\mathbf{\sigma}}_{\mathbf{max}}$ | ${\mathbf{\u03f5}}_{\mathbf{max}}$ | ||||||||||

P1 | P2 | P3 | P1 | P2 | P3 | P1 | P2 | P3 | P1 | P2 | P3 | ||

FL | FL | FL | FL | FL | FL | FL | FL | FL | FL | FL | FL | ||

Osteoblastic | ${R}_{1}$ | 4467 | 4709 | 4751 | 10,388 | 9775 | 9602 | 3877 | 3269 | 3543 | 11,704 | 9773 | 10,368 |

${R}_{2}$ | 5570 | 4741 | 4809 | 9781 | 10,402 | 11,905 | 3343 | 3145 | 3148 | 10,907 | 8632 | 11,829 | |

Osteolytic | ${R}_{1}$ | 4456 | 4111 | 4788 | 10,138 | 10,811 | 8947 | 3763 | 3508 | 3581 | 10,466 | 9713 | 9678 |

${R}_{2}$ | 4045 | 4253 | 4659 | 9449 | 9402 | 9711 | 3565 | 3685 | 3446 | 9284 | 9645 | 8937 |

**Table 2.**The fracture load (FL) expressed in N is reported for the cases in which multiple osteolytic lesions are considered. Results are reported in left lateral bending loading condition and using the maximum principal strain criterion.

Metastasis | Radius | LLB | |||
---|---|---|---|---|---|

${\mathbf{\u03f5}}_{\mathbf{max}}$ | |||||

P1+P2 | P1+P3 | P2+P3 | P1+P2+P3 | ||

FL | FL | FL | FL | ||

Osteolytic | ${R}_{2}$ | 9359 | 9362 | 9373 | 9024 |

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**MDPI and ACS Style**

Bianchi, D.; Falcinelli, C.; Molinari, L.; Gizzi, A.; Di Martino, A.
Osteolytic vs. Osteoblastic Metastatic Lesion: Computational Modeling of the Mechanical Behavior in the Human Vertebra after Screws Fixation Procedure. *J. Clin. Med.* **2022**, *11*, 2850.
https://doi.org/10.3390/jcm11102850

**AMA Style**

Bianchi D, Falcinelli C, Molinari L, Gizzi A, Di Martino A.
Osteolytic vs. Osteoblastic Metastatic Lesion: Computational Modeling of the Mechanical Behavior in the Human Vertebra after Screws Fixation Procedure. *Journal of Clinical Medicine*. 2022; 11(10):2850.
https://doi.org/10.3390/jcm11102850

**Chicago/Turabian Style**

Bianchi, Daniele, Cristina Falcinelli, Leonardo Molinari, Alessio Gizzi, and Alberto Di Martino.
2022. "Osteolytic vs. Osteoblastic Metastatic Lesion: Computational Modeling of the Mechanical Behavior in the Human Vertebra after Screws Fixation Procedure" *Journal of Clinical Medicine* 11, no. 10: 2850.
https://doi.org/10.3390/jcm11102850