# Effects of mechanical stimuli on bone cells for regenerative medicine: A review of recent experimental and computational methods

Emilie Wiedemann-Fodé, Jessica Schiavi-Tritz, Halima Kerdjoudj, Cédric Laurent

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## To cite this version:

Emilie Wiedemann-Fodé, Jessica Schiavi-Tritz, Halima Kerdjoudj, Cédric Laurent. Effects of mechanical stimuli on bone cells for regenerative medicine: A review of recent experimental and computational methods. Medical Engineering & Physics, 2025, 142, pp.104369. 10.1016/j.medengphy.2025.104369. hal-05236576

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Submitted on 3 Sep 2025

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# Effects of mechanical stimuli on bone cells for regenerative medicine: A review of recent experimental and computational methods

Emilie Wiedemann-Fodé<sup>a,b,c,*</sup> <sup>ID</sup>, Jessica Schiavi-Tritz<sup>b,c</sup> <sup>ID</sup>, Halima Kerdjoudj<sup>c</sup>, Cédric Laurent<sup>a,*</sup> <sup>ID</sup>

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## ARTICLE INFO

**Keywords:**

Mechanobiology

Bone regeneration

Stem cells

In silico modelling

Ultrasounds

## ABSTRACT

Mechanobiology integrates biological and mechanical cues to provide a comprehensive understanding of how physical forces influence tissue regeneration, specifically focusing on bone growth and repair. This review presents a comprehensive overview of the latest developments in bone mechanobiology and highlights the remaining scientific and methodological challenges. Following a brief presentation of the challenges facing cell therapy, and in particular the application of different types of mechanical stimuli, the article examines these various processes on cells and tissues such as compressors and bioreactors operating at low frequencies (in the Hz range). Special attention is given to cutting-edge ultrasound techniques, such as the LIPUS method with MHz frequencies and low intensities ranging from 0.5 to 100 mW/cm², and with an emphasis on the emerging application of acoustic levitation with frequencies ranging from 340 kHz to 2.12 MHz permitting non-invasive manipulation of cells and tissues in biological research, with initial beneficial results in cell therapy. Lastly, the review offers a detailed analysis of multi-scale and multi-physics in silico approaches that may contribute to interpret the obtained experimental results. Agent-based models capture the discrete behaviour of individual cells, while continuum models describe tissue mechanics though averaged properties, offering complementary approaches to study complex mechanobiological phenomena. Such approaches hold the potential to drive transformative advances in bone regeneration medicine, providing a roadmap for future research.

## Introduction

Tissue engineering is a pivotal field within regenerative medicine [1], aiming to develop innovative solution to repair and regenerate damaged tissue. A key strategy involves the use of Mesenchymal Stromal Cells (MSCs), along with the application of specific mechanical stimuli to induce their differentiation into targeted phenotype. MSCs and Hematopoietic Stem Cells (HSCs) are primarily found in bone marrow [2], where they play a crucial role in tissue regeneration.

Among the tissues influenced by mechanical stimuli, bone is particularly notable for its remarkable ability to respond and adapt to physical forces. Beyond its mechanical role in enabling body motion and protecting vital organs, the skeleton also plays a key role in the metabolic regulation of skeletal cells [3]. While these various functions are essential, the present contribution primarily focuses on the physiological fate of bone, particularly regarding bone remodelling and stem cell

activity.

Indeed bone, a dynamic and composite material, is constantly being remodelled to repair micro-damage, reshape during growth, and maintain calcium and phosphate homeostasis. This balanced process maintains bone's strength and integrity throughout life and is driven by osteoblasts (formation), osteoclasts (resorption) and osteocytes (Fig. 1). In particular osteocytes serve as the primary mechanosensors and play a central role in sensing mechanical changes within the bone matrix. Such mechanical forces are detected through specialized structures like dentrites or cilia, which act as mechanoreceptors. In the field of mechanobiology [4], a mechanosensor refers to a cell capable of detecting mechanical forces such as pressure, compressive or shear stresses. These forces are converted into biochemical signals, regulating cellular functions such as differentiation and bone homeostasis. Given the complexity of mechanoregulation processes, dozens of comprehensive reviews have been published on the topic, and readers are encouraged to

<footnote><sup>a</sup> LEM3, CNRS URM 7239, University of Lorraine, F-54000 Nancy, France</footnote>

<footnote><sup>b</sup> LRGP, CNRS UMR 7274, University of Lorraine, F-54000 Nancy, France</footnote>

<footnote><sup>c</sup> BIOS, UR 4691, University of Reims Champagne Ardennes, Reims, France</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: emilie.wiedemann-fode@univ-lorraine.fr (E. Wiedemann-Fodé), cedric.laurent@univ-lorraine.fr (C. Laurent).</footnote>
consult these for further details [5-7].

The lacuno-canalicular system allows the dendrites of osteocytes to be connected within the bone structure, which plays a central role in sensing mechanical stimuli and coordinating bone remodelling through their secretion. The figure below (Fig. 2) provides a detailed view of the main structural components of bone, including osteons, lamellae and the lacuno-canalicular system.

However, in the presence of diseases and pathologies, the homeostasis becomes dysregulated, leading to increased skeletal fragility, as observed in disorders such as osteoporosis and osteoarthritis [9,10]. Regenerative medicine plays a crucial role in addressing these challenges, enabling the regeneration of healthy cells and the reconstruction of functional tissues. Various methods in bone engineering – such as scaffold design, stem cell therapy, growth factors, mechanical stimulation, gene therapy, vascularization techniques, and hybrid approaches – each offer unique strategies for promoting bone regeneration [11-14]. Among these, the key role of biomaterials has become increasingly important for bone repair, providing structural support while influencing cellular behaviour. However, fine-turning its architecture and physico-chemical properties to mimic bone's complexity and support vascularization remains a challenge [15-18]. Combinations of these techniques are constantly tested to enhance our understanding of the impact of the mechanical environment [19-24]. The focus of the subsequent sections lies in understanding how stem cells respond to mechanical stimulation when applied to a given biomaterial: the reader interest by recent advances on biomaterials is referred to [25-27].

To better anticipate cellular behaviour, especially when the biomaterial is not designed and needs to be created, computational models are emerging to simulate the environmental conditions and apply specific mechanical conditions on the virtual scaffold. Such models aim at predicting cell behaviours via the data collected, opening a wide research area known as *in silico* modelling [28,29]. Some of the main strategies reported to integrate recent knowledge in mechanobiology within computational models to improve the understanding of biological response will be described subsequently. Moreover, while substantial data have been gathered concerning the link between a given cyclical load amplitude and the corresponding cell response, little is known about the effect of loading frequency and the techniques available to apply those stimuli.

The present contribution therefore aims to provide a recent and comprehensive review of:

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Cortical bone and cancellous bone. Osteons are cylindrical structures with concentric lamellae in the cortical bone, while cancellous bone has trabeculae with less organized lamellae. Figure reproduced with permission of the author [8].</figcaption></figure>

* The different techniques used to apply a dynamic cyclical loading to cells and tissues with a particular attention on bone tissue, with an extra focus on bioreactors and ultrasound techniques such as acoustic levitation to assess different frequencies, and the associated reported results concerning cellular responses;

* The use of *in silico* approaches and the associated modelling methods to understand and interpret the collected data, based on the mechanical loadings that are simulated.

This contribution aims to broaden the scope of existing literature reviews on the subject, which are typically limited to low-frequency stimuli and focus exclusively either on experimental or computational approaches, but rarely both.

## Part I: experimental protocols and cellular responses

Previous studies highlight that bone cells, especially osteocytes, play a crucial role in the constant remodelling of bone tissue. Among the

<figure><img src="image_6.png" /><figcaption>**Fig. 1.** Mechanotransduction in bone. Bone homeostasis is balanced between bone formation by osteoblasts and bone resorption by osteoclasts, is orchestrated by osteocytes that sense various mechanical stimuli, such as shear force ($\tau$), strain ($\epsilon$), hydrostatic pressure, and bending moment, and send biochemical signals in response to these mechanical changes.</figcaption></figure>
different quoted methods such as stem cell therapy, this contribution focuses on the use of MSCs from the bone marrow to emphasize how mimicking their usual mechanical environment enhances proliferation, viability and differentiation. Such stem cell therapy could avoid allo- geneic rejection from patients, by directly using autologous MSCs from their own bone marrow [30–32].

### The importance of the cell environment

Reported studies in bone mechanobiology aimed to recreate in vitro biomimetic conditions and the mechanical environment of bone cells, to investigate the relations between cellular behaviour at the microscopic scale and its environment [33]. Tissue growth is dynamic since biolog- ical, physical and mechanical parameters constantly evolve over time. Therefore, it is important to understand which mechanical stimuli can be applied to mimic in vivo conditions to obtain the desired environment get positive results, while out-of-range stresses may lead to opposite cell behaviours. Mechanical stimuli can induce osteocyte apoptosis, which increases skeletal fragility [34] however this process can be reversed under specific conditions. Conversely, apoptosis also plays a beneficial role by supporting damage repair and skeletal replacement, although inhibition during necessary repairs may have adverse effects [35].

The in vitro culture of cells requires to reproduce their physiological conditions outside of their natural environment. Recent observations have shown that the microenvironment, or niche, is critical for MSCs well-being regulation, specifically from the bone marrow. In laboratory settings, several parameters are monitored and controlled such as cell proliferation and viability, and the nutrient supply, temperature, and environmental conditions (pH level, oxygen and carbon dioxide levels). Alteration of the culture microenvironment can rapidly degrade their properties and culture productivity, which refers to the effectiveness of cell growth. Different conditions must be respected to mimic niches, which can be classified into two main categories: (i) essential biochemical signals for survival and regeneration and (ii) the physical and mechanical properties of the niche.

The intensification of cell proliferation through external mechanical stimuli may allow to obtain large batches of MSCs in regenerative medicine, mitigating the challenges of painful harvesting and limited availability of autologous cells. The section briefly reviews existing setups known to biologists as “bioreactors”, and introduces acoustic levitation as an alternative and promising method due to its non-contact nature that allows for easily determined boundary conditions. To compare different methods, particular attention will be put on the associated cellular environments, stress states, targeted loading fre- quencies for cyclical loading and the characterization methods that have been used to assess cellular responses together with a brief report of results.

### 2D. *cultures*

Bone cells are mostly cultured in vitro in a 2D static culture envi- ronment on surfaces like glass or plastic substrate [36–38]. Various 2D models exist, such as the sandwich model, which some consider 3D due to the cells being seeded between two ECM or collagen layers [39,40]. However, this model still represents a 2D culture, as cells remain confined to a single plane, unlike true 3D models like the cell sheet, where cells interact in multiple dimensions. ECM can improve cell growth, motility and repair [41], while type I collagen provides physical scaffolding for bone and connective tissues [42]. On the basis of these 2D flat surfaces, micro-patterning, uses lithography to create surface pat- terns that guide cell behaviour, such as migration and differentiation [43]. Combined with mechanical stimulation setups, 2D culture has improved our understanding of osteocytes and bone mechanobiology [44].

Among the reported 2D culture surfaces, the use of spherical microcarriers rather than flat flasks is gaining in popularity for pro- ducing human Mesenchymal Stromal Cells (hMSCs). Benefits include

reduced contamination due to automatic monitoring, with a higher surface-to-volume ratio than microcarrier-free methods [45]. These carriers can be tailored to meet patient needs, providing varying quan- tities of cells for different conditions, such as skeletal disorders and osteogenesis imperfecta [46]. With a diameter of 100 to 250 µm, microcarriers can be developed with different physiochemical proper- ties, for the production of several cell phenotypes and adaptable to bioreactor cultures. However, challenges as the homogenization of nu- trients and oxygen is key as it can alter the proliferation of cells or lead to necrosis of tissues which highlight the need for further research. Reproducibility issues also remain when using primary cells despite using similar protocols [47–49].

### 3D. *cultures*

By removing MSCs from their natural 3D niche, 2D culture can alter growth kinetics and differentiation potential [50] highlighting the need for 3D culture systems that better mimic bone's architecture [51–54]. Different models, such as spheroids, cell sheets, scaffolds or hydrogels simulate the 3D structure [55] allowing forces to be transmitted in an environment that mimics the native bone, unlike 2D cultures. Spheroids, for example, are aggregates of cells that form spheres to expand cell populations for therapies or produce tissue. However they present challenges such as size control and nutrient access [56–59].

Hydrogels with their water absorption capacity and similarity to ECM are of particular interest. They are generally made from natural polymers, cross-linked in networks [60], such as collagen [61], gelatine, alginate [62–65] or chitosan [66], and offer various mechanical prop- erties, biodegradability and low toxicity, making them ideal for many applications [67]. Despite their advantages, hydrogels do not fully recreate bone's physical properties (such as structural, mechanical, and biological) leading to the development of scaffolds to better mimic bone tissue. These scaffolds need features like adjustable porosity [68], me- chanical strength and stiffness [69], cell-matrix-interaction, and distri- bution of ECM factors to support stem cell characteristics. Common scaffold materials range from natural substances like alginate and chi- tosan to synthetic polymers, which allow for controlled physical and mechanical properties, increasingly driven by computational methods to predict their overall properties and meta-material research [70]. For further information, the interested reader may refer to recent dedicated reviews [71–74].

### What kind of mechanical stimuli exists

For mechanobiological studies, the responses of cells to mechanical stimulation are assessed and have been shown to enhance bone forma- tion [75]. Parameters such as amplitude, frequency and the loading sequence (or duty cycle) are critical, especially for high-frequency stimulations like ultrasounds, which can raise harmonic frequencies or may be associated with temperature elevation.

A representation on a frequency scale (Fig. 4) illustrates the various ranges of amplitude of frequencies employed in mechanical stimuli,

<figure><img src="image_7.png" /><figcaption>Fig. 3. Representation of the activation of the acoustic field leading to a displacement of the particles towards the pressure node.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Fig. 4. Frequency range of mechanical stimuli at the macro/micro scale with four different groups: compressor (blue), bioreactor with pulsatile flow (purple), acoustic levitation (green), and ultrasounds (orange).</figcaption></figure>

from low-frequency oscillations to high-frequency vibrations, high-
lighting the diverse mechanical environments to which cells and tissues
are exposed.

Bioreactor are designed to control and monitor the physico-chemical
environment of cells, and may also provide mechanical stimuli to
homogenise the media and study cellular responses. Among these,
"dynamic bioreactors" (or "cyclical bioreactors") apply cyclical loads
(compression, tension, flexion, etc...) to the substrate. Studies show
that proper biochemical and physical signals in such bioreactors pro-
mote stem cell differentiation and ECM production [76,77]. Note-
worthy, a recent automated system which applied mechanical
compression to 3D cell culture at 5 Hz resulted in increased cell prolif-
eration and ALP activity, indicating osteogenic differentiation [78].
Alternatively, another recent study highlighted that dynamic compres-
sion study at 3 Hz enhanced ECM production and improved cell distri-
bution [79].

Alternatively, fluid-flow-based bioreactors aim to simulate the me-
chanical environment caused by fluid flow in the lacuno-canalicular
system [80,81], which is known to constitute a key element in bone
mechanobiology. Rotating walls or fluid perfusion systems have been
proven to enhance cell culture efficiency by generating fluid-induced
shear stress (FSS) [82]. Pulsatile fluid-flow bioreactors, replicating cy-
clic hydrostatic pressure (CHP), have demonstrated the ability to
enhance osteogenic responses in human bone marrow stem cells
(hBMSCs) by promoting Adenosine Triphosphate (ATP) release,
collagen synthesis, and mineral deposition. Notably, even low pressure
(10 kPa) at physiological frequencies (2 Hz) can induce osteogenic
lineage commitment, highlighting the importance of pressure-driven
fluid shear effects in bone mechanobiology [83].

Ultrasound-based mechanical stimulation uses wave propagation by
placing a piezoelectric transducer in culture media, also generating FSS.
This allows the study of high-frequency stimulation up to several MHz
[84,85]. Ultrasound applications vary in intensity: low intensities (0.5 to
50 mW/cm²) are used for diagnostic, while high ones (0.2 to 100
W/cm²) are applied for therapeutic purposes, such as promoting bone
healing or drug efficiency [86]. Among those techniques, Low-Intensity
Pulsed Ultrasound (LIPUS) is a non-invasive, non-thermal method
particularly effective for fracture repair, as it causes micromechanical
stress at the fracture site and promotes bone formation, notably through

intramembranous and endochondral ossification [87]. Recent reviews
highlight LIPUS applications for stem cells and bone, improving prolif-
eration, migration, and osteogenesis [88–91]. Xie et al. studied LIPUS on
hBMSCs using intensities at 30, 40, 50, 60 and 70 mW/cm² over 4 days,
with parameters of 1.5 MHz frequency, 20 % duty cycle and 1 kHz pulse
repetition frequency. Optimal intensities were at 50 or 60 mW/cm² for 5
or 10 min daily, resulting in increased ultimate load and stiffness
compared to controls. Flow cytometry confirmed specific MSC markers,
and cells cultured in osteogenic medium, a significant calcium produc-
tion. The underlying causes of such positive effects require further
investigation since the local mechanical environment related to such
loading protocols is largely unknown.

Although studies show some effectiveness of ultrasound stimulation
on cell culture, wound healing and anti-inflammatory effects, there are
still limitations and controversies. Results remain inconsistent due to the
diversity of parameters tested (intensity, frequency, exposure time). The
cell type is also a parameter to be considered, as their reactions are
particularly sensitive and can various to different results going from
bone cells to neural cells [92]. While promising, the LIPUS method still
lacks widespread clinical validation for many applications and therefore
highlight the need for better standardization of protocols.

These common methods for mechanical stimulation applied via
substrates often result in heterogeneous microscale stress fields that are
difficult to control (highlighting the interest of associated *ad hoc*
computational methods, mentioned in the next section). To address this,
levitation is a non-contact technique and has gained popularity for
controlled particle manipulation in a precise environment. Various
levitation techniques exist including magnetic [93], optical [94], elec-
tric [95], aerodynamic [96] and acoustic levitation. Among these,
acoustic levitation is increasingly being used in cell culture experiments
due to its unique advantages including the ability to create 3D culture
environments, reduced contamination risk and cost-effectiveness [97,
98]. It uses high-intensity sound waves to suspend objects by balancing
gravity and acoustic radiation pressure. A piezoelectric transducer
generates ultrasonic waves, which when reflected, create "standing
waves". Particles, including cells, are drawn to pressure nodes where
movement ceases (Fig. 3), enabling controlled manipulation [99–102].

Acoustic levitation has numerous biological applications, including
cell trapping [103], cell sorting [104], cell differentiation [105] and cell
proliferation [106]. In fact, it has been used to organize epithelial and fibroblast cells to recreate multi-layered tissues [104]. Initially, epithelial cells aggregated, but adjusting the conditions (1.95 to 2.12 MHz for 2 h) allowed them to form sheets on fibroblasts, promoting intercellular communication. Similarly, acoustic levitation has been shown to support the formation of 3D brain-like tissue by promoting the differentiation of human Embryonic Stem Cells (hESCs) at 380 kHz and 640 kHz into neurons [105], showing enhanced cell activity and stability after levitation. It also positively influences cell differentiation as demonstrated with the formation of spheroids at 2 MHz with adipose tissue-derived MSCs [106] which enhanced their differentiation into osteoblast and no adverse effects were reported on surface markers. In another study [103], similar to the previous study, hMSCs spheroids were rapidly formed at 1.6 MHz while maintaining the viability of cells. In addition, they showed that levitation promoted angiogenesis by upregulating paracrine factors essential for blood vessel formation which is essential for vascularized tissues like bone. Despite its potential for mechanical stimulation of cells, acoustic levitation remains underexplored in bone cell studies. Moreover, and uppermost, leveraging it for cyclic, non-contact mechanical stimulations across various frequencies could offer valuable insights into bone cell responses, a research gap worth addressing in future studies.

However, the examples quoted only focus on small volumes, and it is still difficult to control larger cell populations or tissue samples. Due to variations in acoustic pressure fields, it can lead to unpredictable cell drifting. Even if the results are conclusive, too much exposure could have the opposite effect, causing stress and even cell death, which has not been deeply investigated so far. Further testing is therefore required to fully understand the potential effects on membrane integrity, gene expression and viability. From a material point of view, even if the process itself is fairly simple, it requires precise tuning of frequency, intensity, and chamber conditions. Therefore, devices can be expensive and sensitive to temperature, humidity, and medium composition, and there is uppermost a need to scale-up the currently available devices in order to tend towards easier clinical application. The next section sets out some methodological considerations about the common methods reported for characterization of cellular response after the application of mechanical stimulation.

### Effect of mechanical stimuli on cell's phenotype

Methods like viability tests and gene expression analysis are generally adopted to help assess cellular responses to mechanical stimuli (viability, proliferation, differentiation). Viability assays focus on specific markers, like mitochondrial function and apoptosis [107]. Gene expression analysis, critical in cell differentiation, helps define the lineage and differentiation phases in cells are [108]. Mechanical stimulation such as LIPUS at 1 MHz on MSC, have shown to induce ECM mineralisation and increase osteogenesis-related gene expression [91]. Similarly, mechanical loading at 5 Hz on MSC revealed osteogenic differentiation through analyses of bone markers, sclerostin and Young's modulus of the scaffold [78]. After LIPUS simulation at 1.5 Hz, the secretome was analysed to confirm the promotion of osteogenic differentiation [90] by assessing proteins such as ALP and sclerostin for osteoblasts and osteocytes, respectively [109].

These diverse methods help to establish links between mechanical stimuli to cellular responses (Table 1). In general, current research remains largely fundamental, focusing not quite yet on developing new therapeutic systems but rather on deepening our understanding of its mechanisms and biological impact. This link may make use of computational models to better understand stresses in tissues under a given macroscopic loading, which constitutes the focus of the next section.

<caption>**Table 1**</caption>

Summary of Experimental Conditions and Findings: This table presents key ex- cepts from various studies regarding the cell culture medium, mechanical stimulation methods, and observed results (same colour codes as Fig. 4).

<table><thead><tr><th>Cell medium/ subtract</th><th>Mechanical stimuli parameters</th><th>Results</th><th>References</th></tr></thead><tbody><tr><td>3D bioprinted hBMSCs cell-laden Graphene Oxide (GO) composite scaffold with osteogenic medium</td><td>Loading frequency of 5 Hz with a 1 % sinusoidal strain, for 5 min/per day and 5 days/for 3 groups: No Loading – Mechanical Loading day 1 – ML day 21</td><td>Increased organoid mineral density, organoid stiffness, osteoblast and osteocyte differentiation, collagen I maturation, lacuno-canalicular network formation and Yes-Associated Protein expression for ML01</td><td>[78]</td></tr><tr><td>Bio-derived cancellous bone scaffold, seeded with human fetal osteoblastic cell line</td><td>Cyclic compression at 1000 microstrain, at 3 Hz for 3 min/day for 24 days</td><td>Increased of osteoblast numbers by 36 % in 24 days, increased extracellular matrix deposition</td><td>[79]</td></tr><tr><td>Spheroids of hBMSCs cultured in standard growth medium or chondrogenic medium for 21 days, and then in osteogenic media for 21 days</td><td>Hydrostatic Pressure (HP) at 10 MPa, 1 Hz for 1 h/day for 3 weeks</td><td>Early bone formation (ALP activity) for growth medium + HP day 21 Late-stage mineralization (calcium) for chondrogenic medium + HP day 42 Collagen and bone matrix proteins for chondrogenic medium + HP day 21</td><td>[80]</td></tr><tr><td>Osteocytes, osteoblasts and periosteal fibroblasts isolated from fetal chicken then seeded on polylysine-coated glass slides with culture medium</td><td>Pulsatile fluid flow at 5 Hz with mean shear stress of 0.7 Pa for 1 h</td><td>Significant inhibition of osteoclast differentiation, and reduced bone resorption signalling via soluble factors produced by osteocytes</td><td>[81]</td></tr><tr><td>hBMSCs cultured on fibronectin coated glass slides</td><td>Cyclic Hydrostatic Pressure (CHP) of 10 kPa, 100 kPa and 300 kPa at 0.5 Hz, 1 Hz and 2 Hz for 1 h, 2 h and 4 h</td><td>At low pressure/ frequency, hMSCs differentiate towards an osteogenic phenotype; Collagen synthesis and mineral deposition at all magnitudes. Best pro-osteogenic response at the highest frequency of 2 Hz</td><td>[83]</td></tr><tr><td>rBMSCs in 24 well-plates, cultivated with osteogenic medium</td><td>Ultrasounds of 3.6 MHz at 30 mW/cm², 20 min/day with a 27.8 % duty cycle for 7 days</td><td>Increased osteogenic markers with osteopontin (OPN), Collagen-1, Runx2 (osteoblast-specific transcription factor) and E11 protein (early osteocyte marker) No apoptosis reported</td><td>[84]</td></tr></tbody></table>

(continued on next page)
<table><caption>**Table 1 (continued)**</caption><thead><tr><th>Cell medium/ subtract</th><th>Mechanical stimuli parameters</th><th>Results</th><th>References</th></tr></thead><tbody><tr><td>rBMSCs from the 3-month and 12-month old animals, seed in a 24-well plates with adipogenic or osteogenic medium</td><td>FLIPUS of 3.6 MHz at 11.7 or 44.5 mW/cm² for 20 min/day for 14 days</td><td>At 11.7 mW/cm² enhanced OCN gene expression and ECM mineralization for rBMSC of the 3-month animal, but decreased Runx2 expression by the cell of the 12-month old animal after 7 days of stimulation<br>At 44.5 mW/cm², enhanced Runx2 expression for the 12-month cells after day 14 of stimulation</td><td>[85]</td></tr><tr><td>hBMSCs in 6 or 96 well-plates with a medium containing cell growth inhibitor</td><td>LIPUS at 1.5 MHz, with a 20 % duty cycle and at 30–40–50–60–80 mW/cm² for 5, 10 and 20 min / day during 4 days</td><td>No differentiation but high expression of stem cell markers<br>50–60 mW/cm² for 5–10 min/day promotes proliferation<br>≥50 mW/cm² for 20 min/day inhibits growth</td><td>[89]</td></tr><tr><td>rBMSCs in a 6 well-plate, then re-plated in osteogenic or adipogenic medium</td><td>LIPUS at 1.5 MHz and 30 mW/cm² for 20 min/d and 3 days, then split into wells with bone healing inhibitor (UAG) or without (UG)</td><td>UG enhanced MSC migration and fracture healing<br>Ultrasound with or without inhibitor provided better bone healing outcomes than control group</td><td>[90]</td></tr><tr><td>rBMSCs suspension seeded on two titanium specimens (polished and Sandblasted, Large-grit, Acid-etched)</td><td>LIPUS at 1 MHz and 100 mW/cm² for 10min</td><td>Increased cell proliferation, ALP activity, ECM mineralization as well as up-regulated osteogenic genes and proteins (OPN, BMP-2, Runx2)</td><td>[91]</td></tr><tr><td>hBMSCs for 2D culture and in the anti-gravity bioreactor</td><td>Anti-gravity bioreactor at a resonance frequency of 1.6 MHz for 12 h</td><td>Spheroids aggregation, with increased angiogenic paracrine factors, improved therapeutic efficacy and attenuation of fibrosis and inflammation</td><td>[103]</td></tr><tr><td>Epithelial cells and fibroblastic cells</td><td>Acoustofluidic bioreactor at 1.95 to 2.12 MHz for 24 h</td><td>Optimal levitation of 2 h for the formation of stable cell sheet with Ca²⁺ Functional epithelial barrier without mixing layers</td><td>[104]</td></tr><tr><td>Embryonic stem cells derived from neuro-progenitors in a fibrin hydrogel, then placed in a neuronal</td><td>Bio-acoustic levitational assembly at 340 kHz and 680 kHz for 10 min until polymerization of the gel</td><td>Early neural precursor marker expression<br>After a week in neural differentiation medium, differentiation still</td><td>[105]</td></tr></tbody></table>

<table><caption>**Table 1 (continued)**</caption><thead><tr><th>Cell medium/ subtract</th><th>Mechanical stimuli parameters</th><th>Results</th><th>References</th></tr></thead><tbody><tr><td>differentiation media<br>hMSCs from adipose-tissue placed in adipocytic or osteoblastic medium after levitation</td><td>Acoustic levitation at 2 MHz for 24 h creating layers of cells at pressure nodes, with a perfused culture medium without altering the cells positions</td><td>ongoing but not complete<br>Spheroid formation and aggregation occurred, with potential for osteoblastic differentiation</td><td>[106]</td></tr></tbody></table>

## Part II: in silico modelling

For biomechanical characterization and mechanobiological insights, computational simulations have been crucial to understand the mechanical properties of bone or the local distribution of stresses and strains. Such computational models could link mechanical stimuli to biological responses, which facilitates the development and evaluation of mechanobiological models and provides insights into pathologies and their mechanical underpinnings including bone growth, ossification and degradation supported by experimental results [110]. They also may predict medical outcomes such as the evolution of pathologies and growth outcomes based on clinical data (bone shape, loading history) [111]. In surgical operations, computational models help to establish personalized protocols adapted to specific pathologies reducing the length of the surgery [112].

Advances in numerical methods and computing capacities have facilitated the emergence of complex models which now may account for bone multiscale composition, microstructure and material properties, non-mechanical phenomena (e.g., piezoelectric, magnetic, chemical) and fluid-structure interactions in the lacuno-canalicular network. Numerous reviews exist on computational bone modelling [112–115]. The following sections focus on the computational methods that elucidate the relations between external mechanical loading, cellular mechanical environments, and cellular responses following the mechanobiological phenomena.

Different experiments [116,117], can be replicated in computational models, generally focusing on FSS or solid substrate stresses. Some models recreate the stimulus of the fluid surrounding the osteocytes, while others predict stimuli related to bone deformation under external load. For stimulations induced by external mechanical loading, the Finite Element Method (FEM) solves elasticity equations, while Computational Fluid Mechanics (CFD) addresses fluid flow stimuli by solving flow equations. Difficulties arise when both the solid and fluid responses are modelled and coupled (fluid-structure interactions, or FSI) and when increasing degree of complexity of solid behaviour (anisotropy, damage, viscoelasticity, ...) of fluid behaviour (non-Newtonian) are taken into account. Approaches adapted to model acoustic pressure or wave propagation are less straightforward and lack consensus. These different points will be described in the following sub-sections.

### The use of finite element method to predict solid-phase stimuli

FEM has become the predominant tool in mechanical engineering for solving continuum mechanics equations for solids. It divides complex systems into smaller elements connected at nodes, discretizing continuous equations and applying boundary conditions like pressure, forces, temperature, or displacements. Mechanical fields (stresses and strains) are calculated for each element according to its respective behaviour, providing input for mechanobiological models [118]. FEM has been used extensively over two decades to link external loads to the cellular microenvironment, offering insights into local stimuli sensed by
osteocytes, and aiding in the interpretation of biological data. Numerous reviews detail these studies [119–122]. Today's simulations can involve millions of elements with sophisticated constitutive laws, accurately reproducing experimental results. However, FEM primarily addresses solid mechanics, while CFD is more adapted to a spatial description of the continuum and therefore to fluid mechanics. In mechanobiology, both solid and fluid phases contribute to the stimuli cells respond to, necessitating the integration of FEM and CFD for modelling fluid-structure interactions.

## Fluid-structure interactions, the use of CFD with FEM

FSI are critical for understanding how osteocytes respond to mechanical stimuli at both cellular and tissue levels. These interactions involve the coupling of fluid flow and structural deformation, typically modelled by integrating Computational Fluid Dynamics (CFD), based on the Finite Volume Method (FVM), with Finite Element Method (FEM), as illustrated below (Fig. 5). This approach has been employed to simulate osteocytes subjected to fluid flow in the lacuno-canalicular system (LCS) [123–126], predicting velocity, pressure and shear stress distribution. The geometry of osteocytes impacts fluid flow as well, with studies using simplified geometries yielding different stress/strain values than those obtained from imaging [127]. FSI models predict fluid flow velocity, pressure and shear stress on cells with varying geometries. These models demonstrate that fluid velocity and WSS are highly dependent on structural features such as canalicular spacing and surface roughness, which modulate the mechanical environment experienced by osteocytes [128].

At the cellular level, simulations of fluid-induced forces have been used to predict osteogenic responses under mechanical loading [28]. For example, Verbruggen et al. [129] performed 3D reconstructions of osteocytes with images from confocal microscopy to simulate fluid flow during intense physical activity. By assigning mechanical properties, such as Young's modulus and Poisson ratio, to both the ECM and the cell body, their model demonstrated that the highest velocities and shear stresses within the osteocyte canaliculi, influenced by surface roughness, highlighting the role of the canalicular structure in osteocyte

mechanotransduction and bone growth.

At the tissue scale, combining FEM and CFD within FSI frameworks has enabled the investigation of scaffolds under mechanical stimulation [130–134]. These models reveal the heterogeneity of mechanical microenvironments, identifying regions with varying strain and a dynamic balance between tension and compression. Such analyses may enable to optimize scaffold design or dynamic culture conditions for bone tissue engineering, as they allow for the control of parameters like flow velocity and strain rates. Mechanoregulation models, including the pioneering framework by Prendergast [135], link mechanical stimuli to tissue differentiation, offering a comprehensive view of how mechanical forces guide tissue differentiation. In dynamic culture systems, FSI models can be employed to study bone explants under osteogenic stimuli. These simulations demonstrate mechanical loading generates localized mechanical environments that significantly influence bone adaptation [136]. Compressive strains and shear stresses in the marrow were quantified, with higher surface strains in bone and increased shear stress near the surface in explants (difference higher than 1 % compared to <0.1 % in bone marrow). These insights are crucial for designing bioreactors and scaffolds to replicate these mechanical conditions, enhancing the efficacy of bone tissue engineering by targeting specific regions for optimized growth and resorption control.

## Stimulation by acoustic pressure or wave propagation: proposed computational approaches

Experimental studies based on the propagation of acoustic waves (resulting in vibration and levitation), have increased in the last two decades. Accordingly, computational methods aiming at predicting the mechanical environment during vibration-induced stimulation are emerging. Particularly, LIPUS device has been used to computationally explore mechanotransduction at high frequencies, which differ from typical low-frequency mechanical stimuli like walking or running [137]. A 2D cortical model incorporating a 1 MHz ultrasound signal evaluated different flow models to describe WSS in the lacuno-canalicular network. These simulations demonstrated that frequencies exceeding physiological loading ranges (0–20 Hz) can activate osteocyte biological

<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Comparison between FEM and CFD methods on the macro/micro scale. a) Simulation of a scaffold with a more detailed close-up showing the porosity used in the study with CFD of a Representative Volume Element (RVE) of the scaffold's microstructure, illustrating fluid flow and transport characteristics within the porous architecture. Adapted from Zhao et al. [134] License Creative Commons Attribution 4.0 b) Progression from an idealized bone cell model (top-left) to a more complex and precise representation (top-right) and further advancements include CFD models (bottom-left) evolving toward FSI techniques, enabling the prediction of velocities and shear stresses (bottom-right). Adapted from Girogi et al. [28] License Creative Commons Attribution 4.0.</figcaption></figure>
responses. It also provides insight into how ultrasound might be
spatially and temporally optimized in an in-dish ultrasonic bioreactor to
influence cellular behaviour. Similarly, ultrasound propagation in a 3D
fluid medium was modelled to quantify acoustic fields under varying
water levels and with absorbing devices designed to prevent wave
reflection. Similar studies explored the use of absorbent layers to
modulate the acoustic field [138]. These two articles highlight the role
of ultrasound in enhancing *in silico* models for studying cell and tissue
responses to mechanical stimuli. The second article, examining cortical
bone with varied porosities, extends this by showing how ultrasound
interacts with complex tissue structures, addressing how mechanical
forces influence bone at multiple porosity levels. Together these articles
showcase the versatility and precision of ultrasound in computational
models, supporting its potential as a non-contact, adaptable stimulus for
simulating biological responses in various tissue engineering contexts. In
summary, computational studies using ultrasounds or high frequencies
are emerging to address gaps in understanding how bone cells respond
to vibration-induced stimuli. These studies mainly quantify stimuli from
macroscopic loading in 3D substrates to aid biological interpretation. To
better understand cellular activation under stimulation, numerical
methods are being developed focusing on single cells or cell groups to
head towards predictive simulations of the cellular response to a given
mechanical environment.

Computational models of the cellular response: agent-based methods vs
continuum approaches

Cellular response to mechanical stimuli is modelled using two
prominent modelling frameworks: either continuum approaches
[139–141] or agent-based models (ABM) [142–144]. Continuum ap-
proaches use partial differential equations (PDEs) to model cell-density
fields and tissue-level phenomena. In contrast, ABMs explicitly represent
individual cells and their interactions, offering detailed insights into
cellular behaviours at the microscale but at a higher computational cost
[145]. Both frameworks have been instrumental in advancing the un-
derstanding of how mechanical stimuli influence cellular and tissue
dynamic, with each offering unique strengths and limitations.

Continuum models are particularly well-suited for large-scale simu-
lations, as they efficiently describe the mechanical and biochemical
behaviour of tissues under various loading conditions. These models can
incorporate tissue-specific properties, such as anisotropy and heteroge-
neity to simulate stress-strain distributions and fluid dynamics. In the
context of tissue engineering, *in silico* models predict 2D and 3D cell
growth depending on scaffold geometry, where features like pore size
and curvature may impact the predicted growth. Studies utilizing level
set (LS) methods have demonstrated that cell growth in scaffolds with
hexagonal pores tends to be faster compared to those with triangular
pores, emphasizing the critical role of pore geometry in designing
effective tissue engineering scaffolds [146–149]. Beyond mechanical
properties, continuum models often incorporate nutrient gradients to
simulate the interplay between biochemical factors and cell growth.
Nutrient availability is a key determinant of cell proliferation, as models
have shown that higher cell density observed near scaffold core where
nutrient levels are more abundant [150]. Carlier et al. extended this
approach by integrating *in vivo-in silico* methods to study bone healing.
Their model incorporated blood vessel formation, oxygen supply and
growth factors, providing a comprehensive framework for understand-
ing bone repair dynamics [151].

On the other hand, ABMs capture the heterogeneity and stochastic
nature of cellular behaviours. By modelling individual cells as discrete
agents with specific behavioural rules, ABMs can simulate a wide range
of biological processes including proliferation, migration, apoptosis and
differentiation. Open-source platforms like "PhysiCell" [152], simulate
cell interactions in dynamic tissues offering submodels for processes
such as necrosis, and cell cycle regulation. Similarly, tools like Compu-
Cell3D [153] and Mopheus [154], are used to model multicellular

systems, with applications ranging from biomimetic bone tissue fabri-
cation to endothelial cell self-organization [155].

Despite their advantages, both model types have significant limita-
tions. Continuum models, while efficient at the tissue scale, cannot
accurately represent the detailed cellular-level responses to mechanical
stimuli and the complex interactions between cells, making them less
suitable for studying mechanotransduction at the individual cell level.
Additionally, they rely on simplified assumptions of uniform material
properties, which may not capture the complexities of biological tissues.
As for ABMs, while offering a high level of detail at the cellular level,
they are computationally expensive especially for large-scale simula-
tions and often lack integration of mechanical stimuli, limiting their
ability to fully simulate the mechanical environments that influence
cellular behaviour. Both approaches also face challenges in accurately
modelling the perception of mechanical changes by cells and integrating
these effects into the overall system dynamics. The following figure re-
sumes the advantages and disadvantages of both methods (Fig. 6).

Despite these challenges, both continuum and agent-based models enhance the understanding or biological systems. Further research is needed to integrate mechanical stimuli more effectively and to address the remaining questions about mechanotransduction and the perception of mechanical changes in cells. Additionally, validating these models with experimental data remains a critical challenge, as it ensures their reliability and usability in clinical applications, while also addressing uncertainties and improving their predictive accuracy [156].

**Conclusion and future directions**

This article explores the advantages of the combined experimental
and computational approaches to enhance our understanding of bone
mechanobiology. By integrating experimental results with advanced *in
silico* modelling, a comprehensive framework may be designed to
explain the complex and still partially unknown links between the me-
chanical environments and the behaviour of bone cells.

On the experimental side, mechanical stimuli such as fluid shear
stress, cyclic mechanical loading, and acoustic pressure have been
applied on cells to mimic the conditions experienced in their native
environments. Although these stimuli are crucial for understanding how
mechanotransduction pathways are activated, particularly in MSCs and
osteocytes, with positive effects on promoting osteogenic differentiation
or enhancing tissue formation, the macro-micro links are still unclear
and need to be clarified. This would include repeating the several ex-
periments with a frequency sweep and establishing a comprehensive
database of cellular responses to each case.

In addition, computational models have been developed to predict
cellular responses under a given mechanical environment, providing a
deeper understanding of how mechanical forces and fluid flow at both
macroscopic and microscopic levels affect bone tissue. In addition, these
models allow greater freedom with a wide range of parameters, such as
scaffold geometry, pore size and material properties without material
and experimental constraints, making analyses more flexible and in-
depth. Nevertheless, the numerical database needs to be completed to
better manage and include these biological behaviours and pathways as
well as physico-chemical factors such as hydration, cross-linking, and
diffusion capacity. Moreover, most studies focus on either solid me-
chanics or fluid dynamics, but investigating both simultaneously would
provide a more comprehensive and realistic understanding of their
combined effects on cellular behaviour. Thus, more future studies
should be carried out with both fields to establish a complete mechano-
biological understanding.

Ultrasound stimulation is generated a growing interest as it is ad-
vantageous in increasing cellular responses such as proliferation, dif-
ferentiation and matrix production. Indeed, it is a non-invasive and
localised method of application, with complementary numerical studies
suggesting that appropriate adjustment of parameters such as duty cycle
and frequency could optimize these cellular effects, leading to better
<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Advantages and disadvantages of continuum and agent-based models. A) Continuum-based model: description of a fracture healing process at different biological scales: cellular level (chondrocytes), tissue level (fibrous tissue, bone matrix) and vascular system (oxygen tension, active vasculature). Adapted from Carlier et al. [151]. Creative Commons License (CC BY) b) Agent-based model: micro-MPA model that simulates bone tissue dynamics by integrating cells, mechanical signals, cytokines, minerals, oxygen and vascular growth with processes based on local conditions. Adapted from Kendall et al. [142] Creative Commons Attribution License (CC BY).</figcaption></figure>

osteogenic results. Therefore, it is highly interesting and advisable to continue along this path in order to improve current medical techniques in bone repair and regeneration, as well as in cell therapy.

Ultimately, the combination of experimental and computational techniques represents a promising path forward in the field of bone tissue regeneration, offering new insights and more effective strategies for promoting bone repair and regeneration in future clinical trials.

### Clinical status

Clinical trials using ultrasounds have been carried out on a population of adult patients with fractures showing a reducing fracture union without impacting the functional recovery or with enhanced bone healing [157,158]. As for the use of acoustic levitation, studies have been published over the past year on different cell types, showing conclusive results on the use of this bioprocess [159,160] but still remains far from direct clinical applications up to day. At the contrary, clinical trials involving ultrasound techniques such as LIPUS on fractures exist but are still scarce and resulted in contradictory results, also involving side effects [161]. Thus, further clinical trials must be carried out on patients in order to gain a better understanding of the effects of ultrasound on their health and recovery.

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## Acknowledges

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