1 Probabilistic modeling of the tensile properties of P3HB/nBG electrospun scaffolds for bone tissue engineering applications 1 In terms of mechanical performance, electrospun P3HB/nano-bioactive glass (nBG) scaffolds for bone tissue engineering show a non-monotonic, and even somewhat contradictive, dependence on nBG content, including an optimum tensile strength achieved at a representative loading of nBG and monotonic decrease in elastic modulus. To provide a predictive and reliable framework for design, we developed physics-informed, semi-empirical models for tensile strength and elastic modulus. The modified rule of mixtures, with an exponential efficiency factor, accurately predicted the peak edge-level tensile strength at 7.5 wt.% nBG (R² = 0.989), and attributed the decline in tensile strength at higher loading to the agglomeration of nanoparticles. To explain the unexpected decline in modulus, we proposed an exponential decay model, which attributed the softening effect to the disruption of hydrogen bonding within the P3HB matrix by nBG nanoparticles on the surface (R² = 0.956). Additionally, we applied Monte Carlo simulations to propagate experimental uncertainty and obtain a "success probability", whereby we defined "success" to be a tensile strength of > 1.8 MPa and an elastic modulus 80> Mpa (the scaffold properties should ultimately specify it for bone regeneration). This probabilistic framework showed that scaffolds that contained 7.5 to 10 wt.% nBG had the highest success probability (> 0.8) and therefore a strong, risk informed avenue for scaffold optimization. 1 5 Masoumeh Khamehchi Department of Basic Science, Hamedan University of Technology, Hamedan, 65169-1-3733 Iran mkhamehchi@gmail.com Jorge Trujillo-Mendoza School of Life Sciences, University of Nottingham, Nottingham NG7 2RD UK jorge.trujillomendoza@nottingham.ac.uk Tensile strength Tensile modulus Modeling Monte Carlo simulation Nano-bioactive glass [1] F.K. Ahmadi, K. Mikeladze, Developments in strontium-doped calcium phosphate composite scaffolds for dental applications and bone tissue engineering, Journal of Composites and Compounds 7(23) (2025).##[2] E. Naghashzargar, S. Farè, V. Catto, S. Bertoldi, D. Semnani, S. Karbasi, M.C. Tanzi, Nano/micro hybrid scaffold of PCL or P3HB nanofibers combined with silk fibroin for tendon and ligament tissue engineering, Journal of applied biomaterials and functional materials 13(2) (2015) 156–168.##[3] S. Huang, L. Zhou, M.-C. Li, Q. Wu, Y. Kojima, D. Zhou, Preparation and properties of electrospun poly (vinyl pyrrolidone)/cellulose nanocrystal/silver nanoparticle composite fibers, Materials 9(7) (2016) 523.##[4] Q.P. Pham, U. Sharma, A.G. Mikos, Electrospinning of polymeric nanofibers for tissue engineering applications: a review, Tissue engineering 12(5) (2006) 1197–1211.##[5] Q. Yao, J.G. Cosme, T. Xu, J.M. Miszuk, P.H. Picciani, H. Fong, H. Sun, Three dimensional electrospun PCL/PLA blend nanofibrous scaffolds with significantly improved stem cells osteogenic differentiation and cranial bone formation, Biomaterials 115 (2017) 115–127.##[6] K. Kaur, K. Singh, V. Anand, G. Bhatia, R. Kaur, M. Kaur, L. Nim, D.S. Arora, Scaffolds of hydroxyl apatite nanoparticles disseminated in 1, 6-diisocyanatohexane-extended poly (1, 4-butylene succinate)/poly (methyl methacrylate) for bone tissue engineering, Materials Science and Engineering: C 71 (2017) 780–790.##[7] N.B. Hoveizavi, F. Alihosseini, S. Lehner, P. Meier, S. Gaan, Colorimetric pH-responsive nanofibrous hydrogels for in vitro monitoring of wound infection, Journal of Materials Chemistry B 13(37) (2025) 11621-11639.##[8] A. El-Ghannam, Bone reconstruction: from bioceramics to tissue engineering, Expert review of medical devices 2(1) (2005) 87–101.##[9] M. Turk, A.M. Deliormanlı, Electrically conductive borate-based bioactive glass scaffolds for bone tissue engineering applications, Journal of biomaterials applications 32(1) (2017) 28–39.##[10] W. Nie, C. Peng, X. Zhou, L. Chen, W. Wang, Y. Zhang, P.X. Ma, C. He, Three-dimensional porous scaffold by self-assembly of reduced graphene oxide and nano-hydroxyapatite composites for bone tissue engineering, Carbon 116 (2017) 325–337.##[11] K. Yang, Q. Han, B. Chen, Y. Zheng, K. Zhang, Q. Li, J. Wang, Antimicrobial hydrogels: promising materials for medical application, International journal of nanomedicine (2018) 2217–2263.##[12] A. Hasan, G. Waibhaw, V. Saxena, L.M. Pandey, Nano-biocomposite scaffolds of chitosan, carboxymethyl cellulose and silver nanoparticle modified cellulose nanowhiskers for bone tissue engineering applications, International journal of biological macromolecules 111 (2018) 923–934.##[13] A.N. Hayati, S. Hosseinalipour, H. Rezaie, M. Shokrgozar, Characterization of poly (3-hydroxybutyrate)/nano-hydroxyapatite composite scaffolds fabricated without the use of organic solvents for bone tissue engineering applications, Materials science and engineering: C 32(3) (2012) 416–422.##[14] H. Hajiali, S. Karbasi, M. Hosseinalipour, H.R. Rezaie, Preparation of a novel biodegradable nanocomposite scaffold based on poly (3-hydroxybutyrate)/bioglass nanoparticles for bone tissue engineering, Journal of Materials Science: Materials in Medicine 21(7) (2010) 2125–2132.##[15] D.P. Bhattarai, L.E. Aguilar, C.H. Park, C.S. Kim, A review on properties of natural and synthetic based electrospun fibrous materials for bone tissue engineering, Membranes 8(3) (2018) 62.##[16] R. Iron, M. Mehdikhani, E. Naghashzargar, S. Karbasi, D. Semnani, Effects of nano-bioactive glass on structural, mechanical and bioactivity properties of Poly (3-hydroxybutyrate) electrospun scaffold for bone tissue engineering applications, Materials Technology 34(9) (2019) 540–548.##[17] M. Khamehchi, A. Chkhenkeli, Influence of Ionic Size on the concentration of Ag+ and Zn2+ in Simulated Body Fluid: Modeling and Monte Carlo Simulation with Dental Applications, Journal of Composites and Compounds 6(21) (2024).##[18] N.B. Hoveizavi, M.H. Al-Musawi, Probabilistic modeling of mechanical properties in thymol-loaded gelatin films for nano wound dressing applications, Journal of Composites and Compounds 6(20) (2024).##[19] R.F. Landel, L.E. Nielsen, Mechanical properties of polymers and composites, CRC press1993.##[20] A.H. Tehrani, A. Zadhoush, S. Karbasi, S.N. Khorasani, Experimental investigation of the governing parameters in the electrospinning of poly (3‐hydroxybutyrate) scaffolds: Structural characteristics of the pores, Journal of Applied Polymer Science 118(5) (2010) 2682–2689.