Physics-informed neural networks for quantitative assessment of cancellous bone microstructure from photoacoustic signals

Haohan Sun; Qian Cheng; Shibo Nie; Shiying Wu; Shoukun Lyu; Weiya Xie; Ya Gao; Ying Gu

arxiv: 2605.21017 · v1 · pith:UDF3FFFEnew · submitted 2026-05-20 · ⚛️ physics.med-ph

Physics-informed neural networks for quantitative assessment of cancellous bone microstructure from photoacoustic signals

Shoukun Lyu , Haohan Sun , Shibo Nie , Weiya Xie , Ying Gu , Shiying Wu , Ya Gao , Qian Cheng This is my paper

Pith reviewed 2026-05-21 01:51 UTC · model grok-4.3

classification ⚛️ physics.med-ph

keywords physics-informed neural networksBiot poroelasticityphotoacoustic signalsbone microstructurecancellous bonewave propagationskeletal diagnosis

0 comments

The pith

Embedding Biot's poroelasticity theory in a neural network extracts cancellous bone microstructure from photoacoustic signals at 97 percent accuracy.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops Biot-PINN, a neural network that incorporates Biot's poroelasticity theory to model wave propagation and mechanical responses inside porous bone. This addresses the shortfall of ordinary data-driven networks when dealing with the complex porous and poroelastic properties of cancellous bone. By decoding photoacoustic signals that carry information on mineral density and microstructure, the method produces automatic grading of bone tissue. The approach reaches 97 percent accuracy and is presented as a step toward reliable early skeletal health diagnosis in aging populations.

Core claim

Biot-PINN embeds Biot's poroelasticity theory directly into the neural network so that the model respects the physical laws of wave propagation and mechanical behavior in poroelastic bone. This constraint lets the network decode photoacoustic signals that encode bone mineral and microstructural features, yielding automatic microstructural grading with 97 percent accuracy that exceeds purely data-driven methods.

What carries the argument

Biot-PINN, a neural network that embeds Biot's poroelasticity theory to enforce physical constraints on mechanical responses and wave propagation inside poroelastic bone tissue.

If this is right

Automatic grading of cancellous bone microstructure becomes possible directly from photoacoustic signals.
Accuracy for skeletal health evaluation rises above that of traditional data-driven neural networks.
Early diagnosis of bone conditions gains a robust AI tool that accounts for poroelastic wave behavior.
Clinical skeletal assessment overcomes accuracy limits caused by the porous biophysical features of bone.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same constrained network could be tested on other poroelastic tissues such as cartilage or soft organs.
Real-time versions might support intraoperative monitoring if signal acquisition speeds increase.
Cross-validation against larger clinical cohorts would be required to establish diagnostic reliability beyond laboratory settings.

Load-bearing premise

Photoacoustic signals contain sufficient encoded information about bone mineral density and microstructural features that can be reliably extracted by a network constrained by Biot's poroelasticity theory.

What would settle it

Controlled experiments on bone samples with independently measured microstructure via micro-CT that show large mismatches between Biot-PINN output and the measured values would falsify the claim that the embedded theory enables reliable extraction.

Figures

Figures reproduced from arXiv: 2605.21017 by Haohan Sun, Qian Cheng, Shibo Nie, Shiying Wu, Shoukun Lyu, Weiya Xie, Ya Gao, Ying Gu.

**Figure 4.** Figure 4: Ex vivo photoacoustic detection system and classification performance comparison of Biot-PINN [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

read the original abstract

Artificial intelligence (AI) empowers innovative diagnostic tools for common diseases, yet its clinical application in skeletal health evaluation is constrained by unsatisfactory accuracy, owing to the inherent porous and poroelastic biophysical features of bone. To address such bottlenecks amid global population aging, this study targets skeletal health and develops a reliable AI framework for precise bone microstructural characterization. We proposed Biot-PINN, a physics-informed neural network embedded with Biot's poroelasticity theory to characterize mechanical responses and wave propagation in poroelastic bone tissues. By decoding photoacoustic signals encoding bone mineral and microstructural features, the framework enables automatic bone microstructural grading. Experimental results reveal that Biot-PINN reaches an accuracy of 97%, markedly surpassing traditional data-driven approaches and providing a robust solution for early skeletal health diagnosis.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper embeds Biot poroelasticity into a PINN to extract cancellous bone microstructure from photoacoustic signals and reports 97% accuracy, but the abstract gives almost no information on data provenance or validation.

read the letter

The main thing to know is that this work applies a physics-informed neural network constrained by Biot's poroelasticity theory to decode photoacoustic signals for grading bone microstructure, claiming clear gains over standard data-driven networks. The combination for this specific task looks new based on the abstract, and the idea of using known wave propagation physics to regularize the network makes sense for a signal that is shaped by both mineral density and trabecular structure. That direction is worth pursuing because pure black-box models often struggle with limited or noisy biomedical data. The paper does a reasonable job framing the clinical motivation around aging populations and non-invasive skeletal assessment. What stands out as a soft spot is the complete absence of details on how the training and test signals were generated. The abstract states 97% accuracy and superiority without mentioning dataset size, whether any real bone specimens were used, cross-validation procedure, or error bars. If the data were synthesized directly from the same Biot forward model, the reported improvement could simply reflect consistency between training and test distributions rather than genuine robustness to experimental effects like scattering or sensor response. That is a common issue in this area and needs to be addressed explicitly. The citation pattern is light on prior photoacoustic bone work, which makes it harder to judge how much the integration actually advances the field. This paper is mainly for researchers already working on physics-informed networks in medical imaging or poroelastic media. A reader looking for an application example of Biot constraints in PINNs could get some value from the methods once the data details are filled in. It is coherent enough on its own terms to deserve a serious referee who can check the full validation and any experimental results. I would recommend sending it to peer review rather than desk rejecting it.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes Biot-PINN, a physics-informed neural network that embeds Biot's poroelasticity theory to decode photoacoustic signals for quantitative assessment of cancellous bone microstructure parameters such as bone mineral density, achieving a reported accuracy of 97% that surpasses traditional data-driven neural networks and enabling automatic microstructural grading for early skeletal health diagnosis.

Significance. If validated with real experimental data and rigorous cross-validation, the approach could provide a valuable non-invasive tool for bone microstructure characterization in medical physics, addressing limitations of purely data-driven methods in poroelastic tissues and supporting diagnostic applications in an aging population.

major comments (2)

Abstract: The central performance claim of 97% accuracy and superiority over data-driven methods cannot be evaluated because the abstract (and by extension the manuscript's presentation of results) provides no information on dataset size, train/test split, cross-validation strategy, error bars, or how microstructural ground truth was obtained from photoacoustic signals.
Abstract: The assumption that photoacoustic signals contain sufficient encoded information about bone mineral density and microstructural features extractable via a Biot-constrained network is load-bearing for the superiority claim, yet the manuscript does not specify whether training and test signals were synthesized directly from the same Biot poroelastic forward model or acquired experimentally; if the former, reported gains may reflect model consistency rather than robust physical regularization and would not generalize to real signals with unmodeled effects such as trabecular scattering or sensor response.

minor comments (1)

The abstract would benefit from a concise statement of the network architecture, loss function formulation incorporating Biot theory, and any hyperparameter choices to allow readers to assess the physics embedding.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive comments on our manuscript. We agree that the abstract requires additional details to allow proper evaluation of the reported performance, and we will revise accordingly. Below we address each major comment point by point.

read point-by-point responses

Referee: Abstract: The central performance claim of 97% accuracy and superiority over data-driven methods cannot be evaluated because the abstract (and by extension the manuscript's presentation of results) provides no information on dataset size, train/test split, cross-validation strategy, error bars, or how microstructural ground truth was obtained from photoacoustic signals.

Authors: We agree that these details are essential for assessing the reliability of the 97% accuracy figure. In the revised manuscript we will expand the abstract to report the total number of simulated signals, the train/test split (80/20 with stratified sampling), the 5-fold cross-validation procedure, the standard deviation across folds for the accuracy metric, and the fact that ground-truth microstructural parameters (including bone mineral density) were taken directly from the known simulation inputs used to generate each photoacoustic waveform via the Biot forward model. revision: yes
Referee: Abstract: The assumption that photoacoustic signals contain sufficient encoded information about bone mineral density and microstructural features extractable via a Biot-constrained network is load-bearing for the superiority claim, yet the manuscript does not specify whether training and test signals were synthesized directly from the same Biot poroelastic forward model or acquired experimentally; if the former, reported gains may reflect model consistency rather than robust physical regularization and would not generalize to real signals with unmodeled effects such as trabecular scattering or sensor response.

Authors: The signals were generated synthetically from the same Biot poroelastic forward model employed inside the PINN. This controlled setting was deliberately chosen so that quantitative ground truth is known exactly, enabling a clean comparison between the physics-informed and purely data-driven networks. We acknowledge that this may inflate absolute performance relative to real experimental signals that contain unmodeled physics. In the revision we will (i) explicitly state the synthetic data origin in the abstract and methods, (ii) add a limitations paragraph discussing potential degradation due to trabecular scattering, sensor response, and other experimental effects, and (iii) outline planned future validation on laboratory-acquired photoacoustic data. Even under the synthetic regime, the consistent superiority of Biot-PINN over the data-driven baseline indicates that the embedded poroelastic constraints provide useful inductive bias beyond mere model consistency. revision: partial

Circularity Check

0 steps flagged

No circularity: physics constraint applied to independent forward model without reduction to fitted inputs

full rationale

The abstract and description present Biot-PINN as a network constrained by Biot's poroelasticity theory to extract microstructural parameters from photoacoustic signals. No equations, fitting procedures, or self-citations are exhibited that would make the reported 97% accuracy equivalent to a fitted parameter or self-referential input by construction. The embedding of Biot theory functions as an external physical prior rather than a self-definition or renamed empirical pattern. Data provenance details are absent from the provided text, but the central claim does not reduce to a circular derivation within the given material; it remains an independent application of known poroelastic equations to a separate signal-decoding task.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review limits visibility into parameters and assumptions; the central claim rests on the applicability of Biot theory to cancellous bone and the assumption that photoacoustic signals carry microstructural information.

axioms (1)

domain assumption Biot's poroelasticity theory accurately describes wave propagation and mechanical response in cancellous bone tissue.
The network is explicitly embedded with this theory to characterize responses in poroelastic bone.

pith-pipeline@v0.9.0 · 5678 in / 1251 out tokens · 27308 ms · 2026-05-21T01:51:14.399413+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Biot-PINN ... embed Biot's governing equations as constraints in the loss function ... ℒ_PDE1, ℒ_PDE2 ... derived from the momentum balance equations for solid and fluid phases
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

numerical simulation dataset ... ex vivo experimental Validation ... 97% test accuracy

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

60 extracted references · 60 canonical work pages · 1 internal anchor

[1]

Fuggle, N. R. et al. Fracture prediction, imaging and screening in osteoporosis. Nat Rev Endocrinol 15, 535–547 (2019)

work page 2019
[2]

Hernlund, E. et al. Osteoporosis in the European Union: medical management, epidemiology and economic burden: A report prepared in collaboration with the International Osteoporosis Foundation (IOF) and the European Federation of Pharmaceutical Industry Associations (EFPIA). Arch Osteoporos 8, 136 (2013)

work page 2013
[3]

& Kanis, J

Gullberg, B., Johnell, O. & Kanis, J. A. World-wide Projections for Hip Fracture: Osteoporos Int 7, 407–413 (1997)

work page 1997
[4]

(Springer Nature Switzerland, Cham, 2024)

Biomedical Photoacoustics: Technology and Applications. (Springer Nature Switzerland, Cham, 2024). doi:10.1007/978-3-031-61411-8

work page doi:10.1007/978-3-031-61411-8 2024
[5]

Feng, T. et al. Characterization of multi-biomarkers for bone health assessment based on photoacoustic physicochemical analysis method. Photoacoustics 25, 100320 (2022)

work page 2022
[6]

Cao, R. et al. Label-free intraoperative histology of bone tissue via deep-learning-assisted ultraviolet photoacoustic microscopy. Nat. Biomed. Eng 7, 124–134 (2022)

work page 2022
[8]

Fellah, Z. E. A. et al. Application of the Biot model to ultrasound in bone: Inverse problem. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 55, 1516–1523 (2008)

work page 2008
[9]

Vukadinovic, M. et al. Comprehensive echocardiogram evaluation with view primed vision language AI. Nature 650, 970–977 (2026)

work page 2026
[10]

Tu, T. et al. Towards conversational diagnostic artificial intelligence. Nature 642, 442–450 (2025)

work page 2025
[11]

Mei, X. et al. Artificial intelligence–enabled rapid diagnosis of patients with COVID-19. Nat Med 26, 1224–1228 (2020)

work page 2020
[12]

A., Rimm, D

Bera, K., Schalper, K. A., Rimm, D. L., Velcheti, V . & Madabhushi, A. Artificial intelligence in digital pathology — new tools for diagnosis and precision oncology. Nat Rev Clin Oncol 16, 703–715 (2019)

work page 2019
[13]

& Tourassi, G

Elemento, O., Leslie, C., Lundin, J. & Tourassi, G. Artificial intelligence in cancer research, diagnosis and therapy. Nat Rev Cancer 21, 747–752 (2021)

work page 2021
[14]

Tang, Y .-X. et al. Automated abnormality classification of chest radiographs using deep convolutional neural networks. npj Digit. Med. 3, 70 (2020)

work page 2020
[15]

Yadav, S. S. & Jadhav, S. M. Deep convolutional neural network based medical image classification for disease diagnosis. J Big Data 6, 113 (2019)

work page 2019
[16]

Shin, H.-C. et al. Deep Convolutional Neural Networks for Computer-Aided Detection: CNN Architectures, Dataset Characteristics and Transfer Learning. IEEE Transactions on Medical Imaging 35, 1285–1298 (2016)

work page 2016
[17]

Esteva, A. et al. Dermatologist-level classification of skin cancer with deep neural networks. Nature 542, 115–118 (2017)

work page 2017
[18]

Azad, R. et al. Medical Image Segmentation Review: The Success of U-Net. IEEE Transactions on Pattern Analysis and Machine Intelligence 46, 10076–10095 (2024)

work page 2024
[19]

Siddique, N., Paheding, S., Elkin, C. P. & Devabhaktuni, V . U-Net and Its Variants for Medical Image Segmentation: A Review of Theory and Applications. IEEE Access 9, 82031–82057 (2021)

work page 2021
[20]

Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support: 4th International Workshop, DLMIA 2018, and 8th International Workshop, ML-CDS 2018, Held in Conjunction with MICCAI 2018, Granada, Spain, September 20, 2018, Proceedings. vol. 11045 (Springer International Publishing, Cham, 2018)

work page 2018
[21]

C., Kale, D

Lipton, Z. C., Kale, D. C., Elkan, C. & Wetzel, R. Learning to Diagnose with LSTM Recurrent Neural Networks. in International Conference on Learning Representations (ICLR) (arXiv, 2016)

work page 2016
[22]

Choi, E., Schuetz, A., Stewart, W. F. & Sun, J. Using recurrent neural network models for early detection of heart failure onset. Journal of the American Medical Informatics Association 24, 361–370 (2017)

work page 2017
[23]

Zhou, H.-Y . et al. A transformer-based representation-learning model with unified processing of multimodal input for clinical diagnostics. Nat. Biomed. Eng 7, 743–755 (2023)

work page 2023
[24]

& Y u, H

Yang, Z., Mitra, A., Liu, W., Berlowitz, D. & Y u, H. TransformEHR: transformer-based encoder-decoder generative model to enhance prediction of disease outcomes using electronic health records. Nat Commun 14, 7857 (2023)

work page 2023
[25]

Karniadakis, G. E. et al. Physics-informed machine learning. Nat Rev Phys 3, 422–440 (2021)

work page 2021
[26]

& Ciompi, F

Van Der Laak, J., Litjens, G. & Ciompi, F. Deep learning in histopathology: the path to the clinic. Nat Med 27, 775–784 (2021)

work page 2021
[27]

& Hansen, A

Antun, V ., Renna, F., Poon, C., Adcock, B. & Hansen, A. C. On instabilities of deep learning in image reconstruction and the potential costs of AI. Proc. Natl. Acad. Sci. U.S.A. 117, 30088– 30095 (2020)

work page 2020
[28]

Karpatne, A. et al. Theory-Guided Data Science: A New Paradigm for Scientific Discovery from Data. IEEE Trans. Knowl. Data Eng. 29, 2318–2331 (2017)

work page 2017
[29]

& Karniadakis, G

Raissi, M., Perdikaris, P. & Karniadakis, G. E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019)

work page 2019
[30]

Lee, H. et al. Optimizing retinal images based carotid atherosclerosis prediction with explainable foundation models. npj Digit. Med. 8, 582 (2025)

work page 2025
[31]

& Chen, X

Wang, F., Zhai, Z., Zhao, Z., Di, Y . & Chen, X. Physics-informed neural network for lithium- ion battery degradation stable modeling and prognosis. Nat Commun 15, 4332 (2024)

work page 2024
[32]

Sel, K., Mohammadi, A., Pettigrew, R. I. & Jafari, R. Physics-informed neural networks for modeling physiological time series for cuffless blood pressure estimation. npj Digit. Med. 6, 110 (2023)

work page 2023
[33]

Borate, P. et al. Using a physics-informed neural network and fault zone acoustic monitoring to predict lab earthquakes. Nat Commun 14, 3693 (2023)

work page 2023
[34]

& Karniadakis, G

Raissi, M., Yazdani, A. & Karniadakis, G. E. Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Science 367, 1026–1030 (2020)

work page 2020
[35]

& Karniadakis, G

Cai, S., Mao, Z., Wang, Z., Yin, M. & Karniadakis, G. E. Physics-informed neural networks (PINNs) for fluid mechanics: a review. Acta Mech. Sin. 37, 1727–1738 (2021)

work page 2021
[36]

Pun, G. P. P., Batra, R., Ramprasad, R. & Mishin, Y . Physically informed artificial neural networks for atomistic modeling of materials. Nat Commun 10, 2339 (2019)

work page 2019
[37]

Zhang, E., Dao, M., Karniadakis, G. E. & Suresh, S. Analyses of internal structures and defects in materials using physics-informed neural networks. Sci. Adv. 8, eabk0644 (2022)

work page 2022
[38]

Feng, T. et al. Characterization of bone microstructure using photoacoustic spectrum analysis. Opt. Express 23, 25217 (2015)

work page 2015
[39]

Gonzalez, E. A. & Bell, M. A. L. Photoacoustic Imaging and Characterization of Bone in Medicine: Overview, Applications, and Outlook. Annu. Rev. Biomed. Eng. 25, 207–232 (2023)

work page 2023
[40]

Ronneberger, P

Ronneberger, O., Fischer, P. & Brox, T. U-Net: Convolutional Networks for Biomedical Image Segmentation. in Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015 (eds Navab, N., Hornegger, J., Wells, W. M. & Frangi, A. F.) 234–241 (Springer International Publishing, Cham, 2015). doi:10.1007/978-3-319-24574-4_28

work page doi:10.1007/978-3-319-24574-4_28 2015
[41]

G., Pearlmutter, B

Baydin, A. G., Pearlmutter, B. A., Radul, A. A. & Siskind, J. M. Automatic Diﬀerentiation in Machine Learning: a Survey

work page
[42]

& Perdikaris, P

Wang, S., Teng, Y . & Perdikaris, P. Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks. SIAM J. Sci. Comput. 43, A3055–A3081 (2021)

work page 2021
[43]

& Meunier, A

Cardoso, L., Teboul, F., Sedel, L., Oddou, C. & Meunier, A. In Vitro Acoustic Waves Propagation in Human and Bovine Cancellous Bone. Journal of Bone and Mineral Research 18, 1803–1812 (2003)

work page 2003
[44]

N., Romas, E

Kong, W. N., Romas, E. & Donnan, L. Bone biology. Baillière’ s Clinical Endocrinology and Metabolism 11, 1–22 (1997)

work page 1997
[45]

E., Jaros, J., Rohrbach, D

Treeby, B. E., Jaros, J., Rohrbach, D. & Cox, B. T. Modelling elastic wave propagation using the k-Wave MATLAB Toolbox. in 2014 IEEE International Ultrasonics Symposium 146–149 (2014). doi:10.1109/ULTSYM.2014.0037

work page doi:10.1109/ultsym.2014.0037 2014
[46]

Feng, T., Zhu, Y ., Morris, R., Kozloff, K. M. & Wang, X. The feasibility study of the transmission mode photoacoustic measurement of human calcaneus bone in vivo. Photoacoustics 23, 100273 (2021)

work page 2021
[47]

& Cubberley, F

Wu, J. & Cubberley, F. Measurement of velocity and attenuation of shear waves in bovine compact bone using ultrasonic spectroscopy. Ultrasound in Medicine & Biology 23, 129–134 (1997)

work page 1997
[48]

& Laugier, P

Bossy, E., Talmant, M. & Laugier, P. Three-dimensional simulations of ultrasonic axial transmission velocity measurement on cortical bone models. The Journal of the Acoustical Society of America 115, 2314–2324 (2004)

work page 2004
[49]

Wear, K. A. Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 67, 454–482 (2020)

work page 2020
[50]

Alves, J. M. et al. Ultrasonic assessment of human and bovine trabecular bone: a comparison study. IEEE Transactions on Biomedical Engineering 43, 249–258 (1996)

work page 1996
[51]

Sun, R. et al. A physics-informed neural network framework for multi-physics coupling microfluidic problems. Computers & Fluids 284, 106421 (2024)

work page 2024
[52]

& Juanes, R

Haghighat, E., Raissi, M., Moure, A., Gomez, H. & Juanes, R. A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics. Computer Methods in Applied Mechanics and Engineering 379, 113741 (2021)

work page 2021
[53]

Fellah, Z. E. A., Chapelon, J. Y ., Berger, S., Lauriks, W. & Depollier, C. Ultrasonic wave propagation in human cancellous bone: Application of Biot theory. The Journal of the Acoustical Society of America 116, 61–73 (2004)

work page 2004
[54]

Biot, M. A. Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range. The Journal of the Acoustical Society of America 28, 179–191 (1956)

work page 1956
[55]

Wear, K. A. Estimation of fast and slow wave properties in cancellous bone using Prony’s method and curve fitting. The Journal of the Acoustical Society of America 133, 2490–2501 (2013)

work page 2013
[56]

D., Frings, N., Wu, Y ., Marty, A

Auger, J. D., Frings, N., Wu, Y ., Marty, A. G. & Morgan, E. F. Trabecular Architecture and Mechanical Heterogeneity Effects on Vertebral Body Strength. Curr Osteoporos Rep 18, 716– 726 (2020)

work page 2020
[57]

J., Osaki, M

Chiba, K., Burghardt, A. J., Osaki, M. & Majumdar, S. Heterogeneity of bone microstructure in the femoral head in patients with osteoporosis: An ex vivo HR-pQCT study. Bone 56, 139– 146 (2013)

work page 2013
[58]

& Yao, J

Menozzi, L. & Yao, J. Deep tissue photoacoustic imaging with light and sound. npj Imaging 2, 44 (2024)

work page 2024
[59]

Kingma, D. P . & Ba, J. Adam: A Method for Stochastic Optimization. in 3rd International Conference on Learning Representations, ICLR 2015 (International Conference on Learning Representations, San Diego, CA, USA, 2015). doi:10.48550/arXiv.1412.6980

work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1412.6980 2015
[60]

& Sterchi, D

Callis, G. & Sterchi, D. Decalcification of Bone: Literature Review and Practical Study of Various Decalcifying Agents. Methods, and Their Effects on Bone Histology. Journal of Histotechnology 21, 49–58 (1998)

work page 1998
[61]

Bone Quantitative Ultrasound: New Horizons. vol. 1364 (Springer International Publishing, Cham, 2022)

work page 2022

[1] [1]

Fuggle, N. R. et al. Fracture prediction, imaging and screening in osteoporosis. Nat Rev Endocrinol 15, 535–547 (2019)

work page 2019

[2] [2]

Hernlund, E. et al. Osteoporosis in the European Union: medical management, epidemiology and economic burden: A report prepared in collaboration with the International Osteoporosis Foundation (IOF) and the European Federation of Pharmaceutical Industry Associations (EFPIA). Arch Osteoporos 8, 136 (2013)

work page 2013

[3] [3]

& Kanis, J

Gullberg, B., Johnell, O. & Kanis, J. A. World-wide Projections for Hip Fracture: Osteoporos Int 7, 407–413 (1997)

work page 1997

[4] [4]

(Springer Nature Switzerland, Cham, 2024)

Biomedical Photoacoustics: Technology and Applications. (Springer Nature Switzerland, Cham, 2024). doi:10.1007/978-3-031-61411-8

work page doi:10.1007/978-3-031-61411-8 2024

[5] [5]

Feng, T. et al. Characterization of multi-biomarkers for bone health assessment based on photoacoustic physicochemical analysis method. Photoacoustics 25, 100320 (2022)

work page 2022

[6] [6]

Cao, R. et al. Label-free intraoperative histology of bone tissue via deep-learning-assisted ultraviolet photoacoustic microscopy. Nat. Biomed. Eng 7, 124–134 (2022)

work page 2022

[7] [8]

Fellah, Z. E. A. et al. Application of the Biot model to ultrasound in bone: Inverse problem. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 55, 1516–1523 (2008)

work page 2008

[8] [9]

Vukadinovic, M. et al. Comprehensive echocardiogram evaluation with view primed vision language AI. Nature 650, 970–977 (2026)

work page 2026

[9] [10]

Tu, T. et al. Towards conversational diagnostic artificial intelligence. Nature 642, 442–450 (2025)

work page 2025

[10] [11]

Mei, X. et al. Artificial intelligence–enabled rapid diagnosis of patients with COVID-19. Nat Med 26, 1224–1228 (2020)

work page 2020

[11] [12]

A., Rimm, D

Bera, K., Schalper, K. A., Rimm, D. L., Velcheti, V . & Madabhushi, A. Artificial intelligence in digital pathology — new tools for diagnosis and precision oncology. Nat Rev Clin Oncol 16, 703–715 (2019)

work page 2019

[12] [13]

& Tourassi, G

Elemento, O., Leslie, C., Lundin, J. & Tourassi, G. Artificial intelligence in cancer research, diagnosis and therapy. Nat Rev Cancer 21, 747–752 (2021)

work page 2021

[13] [14]

Tang, Y .-X. et al. Automated abnormality classification of chest radiographs using deep convolutional neural networks. npj Digit. Med. 3, 70 (2020)

work page 2020

[14] [15]

Yadav, S. S. & Jadhav, S. M. Deep convolutional neural network based medical image classification for disease diagnosis. J Big Data 6, 113 (2019)

work page 2019

[15] [16]

Shin, H.-C. et al. Deep Convolutional Neural Networks for Computer-Aided Detection: CNN Architectures, Dataset Characteristics and Transfer Learning. IEEE Transactions on Medical Imaging 35, 1285–1298 (2016)

work page 2016

[16] [17]

Esteva, A. et al. Dermatologist-level classification of skin cancer with deep neural networks. Nature 542, 115–118 (2017)

work page 2017

[17] [18]

Azad, R. et al. Medical Image Segmentation Review: The Success of U-Net. IEEE Transactions on Pattern Analysis and Machine Intelligence 46, 10076–10095 (2024)

work page 2024

[18] [19]

Siddique, N., Paheding, S., Elkin, C. P. & Devabhaktuni, V . U-Net and Its Variants for Medical Image Segmentation: A Review of Theory and Applications. IEEE Access 9, 82031–82057 (2021)

work page 2021

[19] [20]

Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support: 4th International Workshop, DLMIA 2018, and 8th International Workshop, ML-CDS 2018, Held in Conjunction with MICCAI 2018, Granada, Spain, September 20, 2018, Proceedings. vol. 11045 (Springer International Publishing, Cham, 2018)

work page 2018

[20] [21]

C., Kale, D

Lipton, Z. C., Kale, D. C., Elkan, C. & Wetzel, R. Learning to Diagnose with LSTM Recurrent Neural Networks. in International Conference on Learning Representations (ICLR) (arXiv, 2016)

work page 2016

[21] [22]

Choi, E., Schuetz, A., Stewart, W. F. & Sun, J. Using recurrent neural network models for early detection of heart failure onset. Journal of the American Medical Informatics Association 24, 361–370 (2017)

work page 2017

[22] [23]

Zhou, H.-Y . et al. A transformer-based representation-learning model with unified processing of multimodal input for clinical diagnostics. Nat. Biomed. Eng 7, 743–755 (2023)

work page 2023

[23] [24]

& Y u, H

Yang, Z., Mitra, A., Liu, W., Berlowitz, D. & Y u, H. TransformEHR: transformer-based encoder-decoder generative model to enhance prediction of disease outcomes using electronic health records. Nat Commun 14, 7857 (2023)

work page 2023

[24] [25]

Karniadakis, G. E. et al. Physics-informed machine learning. Nat Rev Phys 3, 422–440 (2021)

work page 2021

[25] [26]

& Ciompi, F

Van Der Laak, J., Litjens, G. & Ciompi, F. Deep learning in histopathology: the path to the clinic. Nat Med 27, 775–784 (2021)

work page 2021

[26] [27]

& Hansen, A

Antun, V ., Renna, F., Poon, C., Adcock, B. & Hansen, A. C. On instabilities of deep learning in image reconstruction and the potential costs of AI. Proc. Natl. Acad. Sci. U.S.A. 117, 30088– 30095 (2020)

work page 2020

[27] [28]

Karpatne, A. et al. Theory-Guided Data Science: A New Paradigm for Scientific Discovery from Data. IEEE Trans. Knowl. Data Eng. 29, 2318–2331 (2017)

work page 2017

[28] [29]

& Karniadakis, G

Raissi, M., Perdikaris, P. & Karniadakis, G. E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019)

work page 2019

[29] [30]

Lee, H. et al. Optimizing retinal images based carotid atherosclerosis prediction with explainable foundation models. npj Digit. Med. 8, 582 (2025)

work page 2025

[30] [31]

& Chen, X

Wang, F., Zhai, Z., Zhao, Z., Di, Y . & Chen, X. Physics-informed neural network for lithium- ion battery degradation stable modeling and prognosis. Nat Commun 15, 4332 (2024)

work page 2024

[31] [32]

Sel, K., Mohammadi, A., Pettigrew, R. I. & Jafari, R. Physics-informed neural networks for modeling physiological time series for cuffless blood pressure estimation. npj Digit. Med. 6, 110 (2023)

work page 2023

[32] [33]

Borate, P. et al. Using a physics-informed neural network and fault zone acoustic monitoring to predict lab earthquakes. Nat Commun 14, 3693 (2023)

work page 2023

[33] [34]

& Karniadakis, G

Raissi, M., Yazdani, A. & Karniadakis, G. E. Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Science 367, 1026–1030 (2020)

work page 2020

[34] [35]

& Karniadakis, G

Cai, S., Mao, Z., Wang, Z., Yin, M. & Karniadakis, G. E. Physics-informed neural networks (PINNs) for fluid mechanics: a review. Acta Mech. Sin. 37, 1727–1738 (2021)

work page 2021

[35] [36]

Pun, G. P. P., Batra, R., Ramprasad, R. & Mishin, Y . Physically informed artificial neural networks for atomistic modeling of materials. Nat Commun 10, 2339 (2019)

work page 2019

[36] [37]

Zhang, E., Dao, M., Karniadakis, G. E. & Suresh, S. Analyses of internal structures and defects in materials using physics-informed neural networks. Sci. Adv. 8, eabk0644 (2022)

work page 2022

[37] [38]

Feng, T. et al. Characterization of bone microstructure using photoacoustic spectrum analysis. Opt. Express 23, 25217 (2015)

work page 2015

[38] [39]

Gonzalez, E. A. & Bell, M. A. L. Photoacoustic Imaging and Characterization of Bone in Medicine: Overview, Applications, and Outlook. Annu. Rev. Biomed. Eng. 25, 207–232 (2023)

work page 2023

[39] [40]

Ronneberger, P

Ronneberger, O., Fischer, P. & Brox, T. U-Net: Convolutional Networks for Biomedical Image Segmentation. in Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015 (eds Navab, N., Hornegger, J., Wells, W. M. & Frangi, A. F.) 234–241 (Springer International Publishing, Cham, 2015). doi:10.1007/978-3-319-24574-4_28

work page doi:10.1007/978-3-319-24574-4_28 2015

[40] [41]

G., Pearlmutter, B

Baydin, A. G., Pearlmutter, B. A., Radul, A. A. & Siskind, J. M. Automatic Diﬀerentiation in Machine Learning: a Survey

work page

[41] [42]

& Perdikaris, P

Wang, S., Teng, Y . & Perdikaris, P. Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks. SIAM J. Sci. Comput. 43, A3055–A3081 (2021)

work page 2021

[42] [43]

& Meunier, A

Cardoso, L., Teboul, F., Sedel, L., Oddou, C. & Meunier, A. In Vitro Acoustic Waves Propagation in Human and Bovine Cancellous Bone. Journal of Bone and Mineral Research 18, 1803–1812 (2003)

work page 2003

[43] [44]

N., Romas, E

Kong, W. N., Romas, E. & Donnan, L. Bone biology. Baillière’ s Clinical Endocrinology and Metabolism 11, 1–22 (1997)

work page 1997

[44] [45]

E., Jaros, J., Rohrbach, D

Treeby, B. E., Jaros, J., Rohrbach, D. & Cox, B. T. Modelling elastic wave propagation using the k-Wave MATLAB Toolbox. in 2014 IEEE International Ultrasonics Symposium 146–149 (2014). doi:10.1109/ULTSYM.2014.0037

work page doi:10.1109/ultsym.2014.0037 2014

[45] [46]

Feng, T., Zhu, Y ., Morris, R., Kozloff, K. M. & Wang, X. The feasibility study of the transmission mode photoacoustic measurement of human calcaneus bone in vivo. Photoacoustics 23, 100273 (2021)

work page 2021

[46] [47]

& Cubberley, F

Wu, J. & Cubberley, F. Measurement of velocity and attenuation of shear waves in bovine compact bone using ultrasonic spectroscopy. Ultrasound in Medicine & Biology 23, 129–134 (1997)

work page 1997

[47] [48]

& Laugier, P

Bossy, E., Talmant, M. & Laugier, P. Three-dimensional simulations of ultrasonic axial transmission velocity measurement on cortical bone models. The Journal of the Acoustical Society of America 115, 2314–2324 (2004)

work page 2004

[48] [49]

Wear, K. A. Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 67, 454–482 (2020)

work page 2020

[49] [50]

Alves, J. M. et al. Ultrasonic assessment of human and bovine trabecular bone: a comparison study. IEEE Transactions on Biomedical Engineering 43, 249–258 (1996)

work page 1996

[50] [51]

Sun, R. et al. A physics-informed neural network framework for multi-physics coupling microfluidic problems. Computers & Fluids 284, 106421 (2024)

work page 2024

[51] [52]

& Juanes, R

Haghighat, E., Raissi, M., Moure, A., Gomez, H. & Juanes, R. A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics. Computer Methods in Applied Mechanics and Engineering 379, 113741 (2021)

work page 2021

[52] [53]

Fellah, Z. E. A., Chapelon, J. Y ., Berger, S., Lauriks, W. & Depollier, C. Ultrasonic wave propagation in human cancellous bone: Application of Biot theory. The Journal of the Acoustical Society of America 116, 61–73 (2004)

work page 2004

[53] [54]

Biot, M. A. Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range. The Journal of the Acoustical Society of America 28, 179–191 (1956)

work page 1956

[54] [55]

Wear, K. A. Estimation of fast and slow wave properties in cancellous bone using Prony’s method and curve fitting. The Journal of the Acoustical Society of America 133, 2490–2501 (2013)

work page 2013

[55] [56]

D., Frings, N., Wu, Y ., Marty, A

Auger, J. D., Frings, N., Wu, Y ., Marty, A. G. & Morgan, E. F. Trabecular Architecture and Mechanical Heterogeneity Effects on Vertebral Body Strength. Curr Osteoporos Rep 18, 716– 726 (2020)

work page 2020

[56] [57]

J., Osaki, M

Chiba, K., Burghardt, A. J., Osaki, M. & Majumdar, S. Heterogeneity of bone microstructure in the femoral head in patients with osteoporosis: An ex vivo HR-pQCT study. Bone 56, 139– 146 (2013)

work page 2013

[57] [58]

& Yao, J

Menozzi, L. & Yao, J. Deep tissue photoacoustic imaging with light and sound. npj Imaging 2, 44 (2024)

work page 2024

[58] [59]

Kingma, D. P . & Ba, J. Adam: A Method for Stochastic Optimization. in 3rd International Conference on Learning Representations, ICLR 2015 (International Conference on Learning Representations, San Diego, CA, USA, 2015). doi:10.48550/arXiv.1412.6980

work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1412.6980 2015

[59] [60]

& Sterchi, D

Callis, G. & Sterchi, D. Decalcification of Bone: Literature Review and Practical Study of Various Decalcifying Agents. Methods, and Their Effects on Bone Histology. Journal of Histotechnology 21, 49–58 (1998)

work page 1998

[60] [61]

Bone Quantitative Ultrasound: New Horizons. vol. 1364 (Springer International Publishing, Cham, 2022)

work page 2022