Abstract
Osteosarcoma is a rare but aggressive bone cancer primarily affecting children and adolescents. Current treatment options are limited by toxicity and reduced efficacy in advanced stages. Pulsed electromagnetic field (PEMF) stimulation has shown promise as a non-invasive anticancer strategy, though inconsistent experimental models and exposure protocols limit translational progress. In the present study, a co-culture spheroid model of osteosarcoma was optimized using human osteosarcoma U2OS cells and bone marrow-derived mesenchymal stem cells (hBMSCs) and used to investigate whether PEMF exposure (1.5 mT, 75 Hz, sinusoidal) enhances spheroid sensitivity to doxorubicin (DOX). The model was characterized by structural integrity, mechanical properties, and functionality: while U2OS monoculture spheroids lacked structural stability, 1:3 MSC-U2OS co-cultures produced compact, stiff spheroids with migratory potential. PEMF stimulation for 3 days at 4 h per day reduced cell metabolic activity and spheroid stiffness and caused the downregulation of several genes associated with proliferation, survival, and invasion. These changes were most evident when combined with low-dose DOX, suggesting altered sensitivity; however, the effect was not uniformly detectable across all assessment methods. Thus, PEMF stimulation induces biological changes consistent with increased chemosensitivity in a subset of conditions, though the effect is subtle and assay-dependent. The developed co-culture model offers a relevant platform for further investigation of PEMF as a modulator of anticancer treatment response.
Keywords: Pulsed electromagnetic field stimulation, Osteosarcoma, Cancer model in vitro, Tumor engineering
Subject terms: Cancer, Cell biology, Oncology, Stem cells
Introduction
Osteosarcoma is the most common primary bone cancer. Being rare—with a global incidence seldom exceeding 5 cases per million in the young population and around 1–4 per million in adults and the elderly1,2—this aggressive type of cancer, nevertheless, poses a heavy problem to society: it affects mainly children and adolescents and has a poor prognosis in metastatic or recurrent cases3,4. As of 2000, osteosarcoma management costs approximately €14.7 billion in Europe and $45 billion in the USA, the latter including metastatic unresectable osteosarcoma per-patient costs ranging from $17,500 to over $100,000, as of 20145,6.
Currently, osteosarcoma is treated using a complex approach, typically consisting of chemotherapy and surgery7,8. The toxicity of chemotherapeutics limits their use, while surgical incision comes along with a risk of residual malignant cells and complications associated with bone tissue loss9. Moreover, as applied to any other type of cancer, osteosarcoma cases are like snowflakes: there are no identical ones that would have a similar molecular pattern10. Altogether, these factors form the need for better therapeutic strategies in alignment with precision medicine trends.
There is emerging evidence of an antineoplastic effect of pulsed electromagnetic field (PEMF) stimulation11,12. PEMF is a non-invasive biophysical stimulation that is already widely used in clinics to manage pain and promote wound healing and bone regeneration, although the mechanisms of its action are still not fully unveiled13–17. Some studies suggest that PEMF can influence drug sensitivity or cancer cell viability18–20. Therefore, PEMF appears to be a promising strategy for osteosarcoma management.
Currently, one of the major problems in the research of anticancer PEMF effects is caused by a lack of uniformity and standards in vitro: in the literature, the exposure parameters vary dramatically, which complicates building a complete understanding of the molecular mechanisms. For instance, Crocetti et al. demonstrated the cytotoxic effect of asymmetric PEMF on human breast adenocarcinoma cell (MCF7) monolayer culture, which was exposed to PEMF of a frequency of 20 Hz and intensity of 3 mT for 60 min per day for up to 3 days21. Another group investigated PEMF potential on breast (MDA-MB-231) and colon cancer (SW-480 and HCT-116) monolayer cultures: apoptosis was observed after 24 and 72 h of PEMF exposure with a frequency of 50 Hz and an intensity of 10 mT22. In both cases, the control groups (not exposed to PEMF stimulation) did not undergo apoptosis. The inhomogeneity in the exposure parameters gets entangled even more when both PEMF stimulation and chemotherapeutic effects are studied. Ruiz-Gomez and co-authors studied the effect of sequential and simultaneous treatment of monolayer adenocarcinoma cell culture by several anticancer drugs (vincristine, mitomycin C, and cisplatin) and PEMF stimulation (1 and 25 Hz, 1.5 mT peak, rectangular), with the conclusion that the simultaneous approach is more efficient in comparison to PEMF stimulation applied after a drug18. In another study, a synergistic cytostatic effect on mouse osteosarcoma cells was demonstrated for another anticancer drug, doxorubicin (DOX), applied immediately after 12 h of PEMF exposure19. Finally, in a chick chorioallantoic membrane model, MCF7-derived tumoroids were affected by DOX when followed immediately by 1 h of 3 mT PEMF stimulation daily for 4 consecutive days20.
As can be seen from the examples above, the inhomogeneity in the exposure parameters may not be the only obstacle to the translatability of the results. Similar to the need for better preclinical models to evaluate anticancer drug efficacy23–25, models investigating the anticancer mechanisms of PEMF do need a certain level of standardization and conformity to clinical relevance. Spheroid-based models seem a robust yet physiologically relevant tool for this aim: they outcompete monolayer cultures owing to an improved mimicking of the tumor microenvironment (they guarantee cell-cell and cell-matrix interactions, and provide gradients of oxygen, nutrients, and drugs) and, at the same time, are relatively controllable26,27.
The goal of this study is, therefore, to demonstrate the potential of PEMF to modulate drug response in an in vitro model of osteosarcoma. As the first step of the study, we optimize a spheroid-based model of osteosarcoma using a co-culture of human osteosarcoma cells (U2OS) and human bone marrow-derived mesenchymal stem cells (hBMSCs). MSCs are part of the bone tumor microenvironment and can influence drug response and tumor behavior28,29; thus, the co-culture of U2OS cells with hBMSCs enhances the relevance of the in vitro model5,30. Then, we apply the optimized osteosarcoma model to test whether PEMF stimulation can increase the sensitivity of osteosarcoma cells to DOX.
To our knowledge, this is the first attempt to investigate the antineoplastic effect of PEMF stimulation in a controlled environment presented by a 3D spheroid co-culture model of osteosarcoma. The results of our work suggest a sensitizing effect of PEMF stimulation of 1.5 mT intensity, 75 Hz frequency, and sinusoidal waveform applied for 3 days, 4 h each, on the tumor cells within the tested conditions.
Materials and methods
Spheroid model optimization
Cell culture and spheroid generation
Human bone marrow-derived stem cells (hBMSCs, hTERT-BMSC clone Y201, immortalized through hTERT lentiviral vectors31, previously isolated and kindly provided by the group of Paul Genever (University of York)) were cultivated in low-glucose (1 g/L) Dulbecco’s modified Eagle’s medium (DMEM, Sigma-Aldrich, USA) supplemented with 15% fetal bovine serum (FBS, Sigma-Aldrich, USA) and 1% penicillin-streptomycin (PS, Invitrogen, USA). Human osteosarcoma cells (U2OS, HTB96, American Type Culture Collection, USA) were cultivated in high-glucose (4.5 g/L) DMEM supplemented with 10% FBS and 1% PS. Both cell lines were kept at 37 °C in a humidified atmosphere containing 5% CO2. Cells were cultivated until 80–90% confluence, detached by trypsin-EDTA (1X, Sigma-Aldrich, USA) solution, harvested, and used for experiments.
For spheroid generation, firstly, wells of a 48-well plate were coated with 150 µL of 1.5% agarose (Bio-Rad Laboratories, USA) solution in sterile conditions and left to disinfect at room temperature (RT) under UV exposure for up to 2 h until complete solidification and cooling down32,33. Then, hBMSCs and U2OS cells were seeded at a concentration of 2.5 × 104 cells per well of the agarose-coated plate in proportions of 1:3 and 3:1, respectively. Cells were incubated in standard conditions in 450 µL of a medium composed of a 1:1 mix of the relevant media mentioned above, which was changed every 2 to 3 days by gentle aspiration. Self-aggregation of the spheroids was monitored by light microscopy, and on the 5th day, the spheroids were harvested for the experiment by gentle pipetting and placed into the wells of a standard culture 48-well plate until full attachment.
Migration assay
Migration of the spheroids was assessed after 24 h upon attachment. Phase-contrast images of spheroids were collected with a camera-equipped light microscope (MC170 HD, Leica Microsystems, Germany), and results were analyzed in the ImageJ software (https://imagej.net/ij/, version 1.54d) with the use of a free toolset for cell invasion analysis (Analyse Spheroid Cell Invasion In 3D Matrix, RRID: SCR_02120434.
Scanning electron microscopy
The superficial morphology of the spheroids was assessed using scanning electron microscopy (SEM). The spheroids were fixed in 2.5% glutaraldehyde (prepared from 25% solution (Merck KGaA, Germany)) for 2 h at RT, then washed with phosphate-buffered saline (PBS) to remove fixative, and dehydrated using an increasing ethanol concentration series (30%, 50%, 70%, 90%, 95%, and 100%, 20 min each). Subsequently, the specimens were submerged in hexamethyldisilazane (HMDS, Alfa Aesar, USA) and left to air-dry overnight. The dehydrated spheroids were mounted onto aluminum stubs using conductive carbon tape, coated with a 10 nm gold layer (DII-29019SCTR SmartCoater, Jeol, Japan), and examined using a scanning electron microscope (JSM-IT500 InTouchScope, Jeol, Japan).
Nanoindentation
For mechanical characterization, stably attached spheroids were rinsed with PBS and fixed with 2.5% glutaraldehyde solution at RT for 2 h. Then, samples were washed with PBS to remove the fixative and left in PBS at 4 °C until analysis. Nanoindentation of live spheroids would be preferable, and engineered cellular structures are often characterized live when feasible35. In our setting, however, this was not practical: nanoindentation of small spheroids is time-consuming and performed in an open system, where stable gas and temperature control cannot be ensured. For reproducibility, all spheroids were subjected to the same fixation protocol. While fixation increases absolute stiffness, it does so uniformly across groups, preserving the validity of relative comparisons36,37. The analysis was performed with Piuma Nanoindenter (Optics11 Life, NL) equipped with a probe of 0.53 N/m stiffness (geo factor in air: 2.6; tip radius: 21.5 μm). The sensitivity of the cantilever was calibrated before testing with the probe immersed in PBS, without contact with the surface, and then by indenting a hard surface (glass Petri dish). Each spheroid was indented by the probe 25 times as a 5 × 5 matrix scan (with dX and dY equal to 5 μm), and each indentation included an approach phase for 1 s, a contact phase at 10,000 nm indentation depth, which was held for 1 s, and a 1-s long retraction phase. Measurement was performed in PBS to minimize attraction forces between the material and the tip, as well as to prevent the spheroid from drying out. The data was optimized by the indentation model on the relevant range (DataViewer Software v2.5.7, https://www.optics11life.com/, Optics11 Life, NL).
Application of the model for PEMF exposure optimization
DOX and PEMF exposure
To expose spheroids to PEMF and DOX, the agarose-coated plates with the fully formed spheroids were first arranged between the coils of a custom-made PEMF generator placed in the incubator (Fig. 1a). PEMF (1.5 mT, 75 Hz, sinusoidal) was applied for a period of 3–4 h once per day for 2 or 3 days. After that, the spheroids were gently transferred to a standard culture 48-well plate for an overnight attachment. Then, the culture medium in the wells with the spheroids stimulated or not stimulated by PEMF was replaced with culture medium containing DOX (Doxorubicin hydrochloride, Thermo Scientific Chemicals, USA) at the concentrations of 0, 0.25, or 0.5 µg/mL—sub-lethal concentrations allowing for downstream analyses38. The scheme of the experiment is illustrated in Fig. 1b.
Fig. 1.
(a) The setup of PEMF exposure. (b) The scheme of the experiment. Created with BioRender (https://app.biorender.com/).
Metabolic activity assay
To estimate the metabolic activity of the cell spheroids, the culture medium was replaced with 1X resazurin solution (alamarBlue HS Cell Viability Reagent, Invitrogen, USA) in culture medium. After incubation in the dark for 3 h, 100 µL of supernatant was transferred into a black opaque 96-well plate and read with a spectrophotometer (Spark, Tecan Trading AG, CH) at 560 and 590 nm excitation and emission wavelengths, respectively.
Gene expression analysis
Gene expression analysis was applied selectively, following a stepwise experimental approach: conditions that showed measurable changes in cell metabolic activity or spheroid mechanical properties were prioritized for RT-qPCR. Furthermore, analysis did not involve DOX-treated spheroids owing to the RNA yield being insufficient in quality and quantity due to reduced cell viability—a phenomenon reported earlier39. The spheroids in various conditions were compared in the context of the expression of genes associated with aggressiveness and invasiveness of osteosarcoma and its response to biophysical stimuli and drug exposure (Table 1). Total RNA was extracted using TRIzol (Invitrogen, USA) following the manufacturer’s recommendations. The gene expression was analyzed on the synthesized cDNA (iScript cDNA Synthesis Kit, Bio-Rad Laboratories, USA) with a mix for quantitative real-time PCR (SsoAdvanced Universal SYBR Green Supermix, Bio-Rad Laboratories, USA). RPL13A was used as a housekeeping gene. The sequences of forward and reverse primers were designed using the PrimerQuest Tool (https://eu.idtdna.com/pages/tools/primerquest/, IDT, USA) and synthesized by Integrated DNA Technologies (IDT, USA).
Table 1.
Forward and reverse primer sequences.
| Gene | Forward primer | Reverse primer |
|---|---|---|
| BCL2 | 5’-GAA GCA GAA GTC TGG GAA TC-3’ | 5’-CTT CAG CAC TCT CCA GTT ATA G-3’ |
| CDK1 | 5’-CAG TCT TCA GGA TGT GCT TAT G-3’ | 5’-TAC TGA CCA GGA GGG ATA GA -3’ |
| EZR | 5’-AAG ACT ATC GGC CTC CGG G-3’ | 5’-GCC CGG AAC TTG AAC TGG AG-3’ |
| ITGA5 | 5’-GAA TCT CAA CAA CTC GCA AAG-3’ | 5’-CAG TCG CTT ACT GGG AAT AG-3’ |
| MAPK1 | 5’-GTA CAG GAC CTC ATG GAA AC-3’ | 5’-CTC TGA GGA TCT GGT AGA GAA-3’ |
| MMP9 | 5’-TTG ACA GCG ACA AGA AGT G-3’ | 5’-GGC ACT GAG GAA TGA TCT AAG-3’ |
| NOTCH3 | 5’-GAG AGC TGC AGT CAG AAT ATC-3’ | 5’-GCA GGC ACA GTA GAA AGA A-3’ |
| RPL13A | 5’-CTG GAG GAG AAG AGG AAA GA-3’ | 5’-GTC TTG AGG ACC TCT GTG TA-3’ |
| TRPC1 | 5’-GCC AGT CCA GCT CTA ATA ATG-3’ | 5’-CTG AAT TCC ACC TCC ACA AG-3’ |
| WNT5A | 5’-GGA CTT TCT CAA GGA CAG AAG-3’ | 5’-CCT TCG ATG TCG GAA TTG AT-3’ |
Statistical analysis
Each group of samples was represented by at least three biological replicates; results are shown as mean value ± standard deviation. Comparison between groups was performed in Prism (v8, GraphPad Software, https://www.graphpad.com/, USA) using one-way ANOVA, preceded by normal distribution Shapiro–Wilk’s test. For each comparison performed, the difference was determined as significant for p < 0.05. The same statistical approach was applied within fixed DOX concentrations to evaluate the effect of different PEMF exposure durations independently. This approach was chosen to isolate the contribution of PEMF under controlled chemotherapeutic conditions, with interaction effects between PEMF and DOX not being assessed.
Results
Spheroid model optimization
First, the ability of osteosarcoma U2OS cells to form stable spheroids was evaluated. Light microscopy observation revealed that the spheroids tended to disaggregate during culture; moreover, not all spheroids could withstand spontaneous mechanical disruption caused by pipetting. The spheroids formed from hBMSCs or the combination of U2OS and hBMSCs in both 1:3 and 3:1 tested ratios (later on referred to as “MSC-U2OS”), on the contrary, were found to be stable and compact. In contrast to U2OS-only (monoculture) spheroids, their area decreased with time of incubation, not due to disaggregation, but due to the increasing compactness of the spheroids (Fig. 2a).
Fig. 2.
(a), left: U2OS cell spheroid disaggregation monitoring after spheroid maturation, light microscopy, scale bar 500 μm. (a), right: monitoring and area analysis (ImageJ software, data presented as mean area of 3 biological replicates (individual spheroids) ± SD) of cell spheroids formed of hBMSCs and co-culture of U2OS and hBMSCs. (b): Cell spheroid nanoindentation; the distributions of Eff. Young’s modulus (E[eff]) values (in Pa) obtained from matrix scans of 4 biological replicates are shown for hBMSCs, U2OS, and co-culture spheroids; the difference between all groups is significant (p < 0.0001) unless stated otherwise (“ns”). (c), left: SEM images of co-culture spheroids, scale bars on the magnified images—10 μm; (c), right: cell spheroid migration analysis with the migration area indicated with an arrow and outlined in yellow with ImageJ software, scale bar 500 μm.
The mechanical stability of the spheroids was confirmed by nanoindentation analysis (Fig. 2b). The matrix scan revealed that the spheroids formed from hBMSCs only or from the 3:1 ratio of MSC-U2OS are the stiffest (> 40 kPa) and do not vary significantly. The stiffness of co-culture spheroids with predominant U2OS cells was ⁓20 kPa, while that of U2OS spheroids barely reached 3 kPa. So, both ratios of U2OS and hBMSCs co-culture reported suitable values of stiffness to properly study osteosarcoma drug sensitivity in a 3D environment, as previously reported40.
As a final criterion of the co-culture ratio selection, the spheroid migration assay was set up (Fig. 2c): cells in the spheroids composed of a 3:1 ratio of MSC-U2OS did not demonstrate any migration, while the 1:3 MSC-U2OS cell spheroids demonstrated a fast migration from the spheroid to the monolayer, giving a hint at the invasion potential of this co-culture ratio. The findings were in agreement with the superficial morphology analysis (SEM, Fig. 2c): on the magnified areas, it can be observed that a significant number of cells in the 1:3 MSC-U2OS spheroids possess spherical morphology, while the co-culture spheroids with the prevalent amount of hBMSCs contain a large number of flattened cells, as well as cells exhibiting numerous filopodia. This matches the light microscopy observations and is evidence of stronger cell-cell contacts and, possibly, extensive extracellular matrix (ECM) synthesis by hBMSCs, preventing cell migration.
Application of the model for PEMF exposure optimization
To investigate the effect of PEMF stimulation on spheroid sensitivity to DOX, the optimized co-culture spheroid model composed of human osteosarcoma U2OS cells and hBMSCs in a 3:1 ratio was exposed to three PEMF protocols: (i) 2 days (3 h per day), (ii) 3 days (3 h per day), and (iii) 3 days (4 h per day). After PEMF exposure, spheroids were treated with different concentrations of DOX: 0, 0.25, and 0.5 µg/mL.
As shown in Fig. 3a, metabolic activity of the spheroids was assessed using the resazurin reduction assay and reported as RFU. In most conditions, PEMF stimulation did not significantly alter metabolic activity compared to the non-stimulated control. However, spheroids exposed to PEMF for 3 days for 4 h per day showed a significant decrease in RFU values in comparison to the non-stimulated control, both in the absence of DOX and across all tested DOX concentrations, suggesting a measurable response to the longer PEMF exposure in line with previous literature21,22.
Fig. 3.
(a): Metabolic activity of MSC-U2OS 1:3 co-culture cell spheroids after exposure to PEMF (2 d and 3 d, 3 h each, and 3 d, 4 h each) and DOX (0, 0.25 and 0.5 µg/mL); ‘Ctrl’ represents spheroids cultivated without PEMF exposure; the values are presented as mean RFU of a minimum of 3 biological replicates (individual spheroids) ± SD, *Significant differences between ‘PEMF’ and ‘Ctrl’, p < 0.05; **p < 0.01; ***p < 0.001. (b): MSC-U2OS 1:3 co-culture cell spheroid nanoindentation—example of measurement (photo) and stiffness of spheroids; each dot represents Eff. Young’s modulus (Pa) measured during one indentation, *Significant differences between ‘PEMF’ and ‘Ctrl’, p < 0.05, defined using a minimum of 3 biological replicates (individual spheroids). (c) Normalised gene expression in PEMF-exposed co-culture spheroids in relation to spheroids not exposed to PEMF (Ctrl); RPL13A was used as the housekeeping gene; the data are presented as means ± SD of 2− ddCt values of 3 biological replicates.
Figure 3b, presents the mechanical characterization of the spheroids using nanoindentation. An example image of the measurement is included for reference. Quantitative analysis of effective Young’s modulus revealed that a significant decrease in spheroid stiffness was observed only in the group stimulated with PEMF for 3 days, 4 h per day, and treated with 0.25 µg/mL DOX. No significant changes in stiffness were found in spheroids under other conditions in comparison to the non-stimulated group. The results of the nanoindentation of the spheroids exposed to 0.5 µg/mL DOX are not presented due to spheroid integrity loss and the inability to measure with the same probe.
Gene expression analysis was performed selectively on the spheroids under conditions that had shown measurable changes in preceding assays. For this reason, the 2-day, 3 h/day PEMF condition was not included in the analysis. Moreover, the analysis was limited to PEMF-only spheroids due to a gene panel design focused primarily on PEMF-affected pathways, as well as due to insufficient RNA yield and integrity obtained from DOX-treated spheroids, consistent with previous reports of RNA degradation in drug-treated in vitro tumor models39. Thus, RT-qPCR was carried out to identify early transcriptional changes in the spheroids caused by PEMF stimulation alone. As shown in Fig. 3c, two PEMF conditions—3 days at 3 h per day and 3 days at 4 h per day—were compared against a non-stimulated control. Interestingly, the shorter PEMF exposure (3 days, 3 h each) led to a mild upregulation of the majority of the tested genes (including EZR, BCL2, CDK1, TRPC1, ITGA5, NOTCH3, MMP9, and MAPK1). In contrast, when the stimulation duration was increased to 4 h per day, expression levels of these genes were reduced relative to control, suggesting that PEMF duration can influence the direction of gene regulation.
Discussion
In this study, we aimed to develop a physiologically relevant, yet reproducible and controllable, in vitro model of osteosarcoma using a co-culture spheroid approach and to evaluate the effect of PEMF stimulation on tumor cell sensitivity to DOX. The work was structured in two main phases: (1) optimization of a co-culture spheroid model using U2OS osteosarcoma cells and hBMSCs, and (2) application of this model to investigate whether PEMF exposure could modulate the cellular response to DOX.
Spheroid-based models have been employed in cancer research for decades, offering a powerful approach to recapitulate the tumor architecture by enabling cells to grow, interact, and migrate in all three dimensions and better replicate the tumor microenvironment (TME)41,42. Despite their advantages, spheroid generation in practice can be challenging: different cell types and lines vary in their capacity to aggregate, secrete ECM, and form compact, uniform spheroids. In the first stage of this study, we encountered similar difficulties while optimizing a spheroid-based in vitro model of osteosarcoma. Spheroids generated from osteosarcoma U2OS cells alone were consistently loose and fragile, irrespective of the maturation time (Fig. 2a), complicating their use in downstream assays. This instability aligns with previous findings, where U2OS spheroids were described as poorly defined and structurally unstable38,43,44, while stable monoculture spheroids have been generated using other osteosarcoma cell lines, such as SaOS-2, HOS, and MG-6345.
To address this limitation and better replicate TME, we explored a co-culture strategy by combining U2OS cells with hBMSCs. This approach not only aimed to improve spheroid stability through enhanced ECM production but also introduced a biologically relevant stromal component. Indeed, hBMSCs are key players in manipulating the osteosarcoma TME and have been shown to influence tumor progression30,46. Freeman and co-authors previously reported the development of MSC-osteosarcoma co-culture spheroids to model different stages of disease development and highlighted the interplay between tumor cells and stromal components5. In our study, in comparison to monoculture U2OS cell spheroids, hBMSCs-containing spheroids showed a progressive decrease in their area over time due to increased compaction (Fig. 2a), which can be attributed to the robust cell-cell interactions and ECM remodeling promoted by these cells. Of the two tested co-culture ratios, the combination containing one part of hBMSCs and three parts of U2OS (1:3) proved optimal. This co-culture ratio not only ensured structural integrity and stiffness (20 kPa in contrast to 3 kPa of monoculture U2OS spheroids, Fig. 2b) but also exhibited active cell migration from the spheroid to the surrounding culture surface (Fig. 2c), suggesting a higher invasion potential compared to spheroids with the inverse (3:1) cell ratio. This latter type of spheroids appeared to produce excessive ECM, reflected also in their high stiffness (40 kPa), limiting migration. The morphological underpinnings of these different migratory behaviors were elucidated by SEM analysis. In the highly migratory 1:3 MSC-U2OS co-culture spheroids, a significant number of cells maintained a spherical morphology, indicative of looser cell-cell associations; whereas in the non-migratory 3:1 MSC-U2OS co-culture spheroids, a high number preserved their flattened morphology and numerous filopodia.
Summarising the first step of the study, our results confirmed that incorporating hBMSCs facilitated the formation of compact, structurally stable spheroids, characterized by dense cellular packing and elevated stiffness as demonstrated by scanning electron microscopy and nanoindentation analysis. Together with their favorable mechanical properties, the invasion potential of 1:3 MSC-U2OS spheroids makes them a suitable and functionally relevant model for our further applications.
Recently, bioelectromagnetics research has grown, along with its various clinical applications, including cancer therapies11. In particular, studies on PEMF, primarily at very low frequencies (below 1000 Hz and 100 Gs), highlighted their strong penetration and non-thermal effects on cells. These effects alter the trajectories of charged particles and modify membrane potentials, ultimately influencing cell membrane permeability and the regulation of specific ions, which explains why PEMF studies related to cancer primarily focus on their ability to inhibit cell proliferation, directly induce cell death, alter the cell cycle, and affect molecular pathways47. In the second part of the study, we used the optimized co-culture (1:3) osteosarcoma model to explore whether PEMF stimulation could modulate spheroid metabolic activity and mechanical properties, with or without DOX exposure. Among the tested PEMF protocols, only the 3-day, 4-h daily exposure led to measurable biological effects. This condition resulted in a statistically significant reduction in spheroid metabolic activity as assessed by resazurin reduction assay—both in the absence of DOX and across all tested concentrations (Fig. 3a). This result was further supported by nanoindentation analysis, which showed a significant reduction in stiffness only under the same PEMF condition and at 0.25 µg/mL DOX (Fig. 3b). This finding may indicate an alteration of the spheroid’s physical properties, likely due to cytoskeletal reorganization or ECM remodeling.
To better understand the influence of PEMF stimulation in the absence of DOX treatment, we performed gene expression analysis of the stimulated and non-stimulated co-culture osteosarcoma spheroids. Interestingly, it revealed a divergent transcriptional response depending on exposure duration. The 3-day, 3-h stimulation slightly upregulated the majority of tested genes, while the 4-h exposure resulted in their downregulation (Fig. 3c). One of the reported effects of PEMF therapy in cancer is the induction of apoptosis. BCL-2 family of proteins overexpression in tumor cells inhibits their apoptosis48. In our study, we showed that increasing the exposure of 1:3 MSC-U2OS co-culture spheroids to PEMF stimulation by 4 h for 3 days causes downregulation of BCL-2 gene expression. Radeva and Berg studied the lethal response of cancer cell lines and normal human lymphocytes to PEMF (35 mT peak, 50 Hz, sinusoidal) therapy for 4 h49. The authors were able to identify that PEMF therapy enhances necrosis, and its effectiveness was found to be influenced by factors such as the surrounding medium, pH, conductivity, and temperature.
Another molecule involved in tumor cell survival is EZR, which plays a crucial role in the formation of specialized membrane areas50, alters the infiltration ability of cancer cells, and promotes cancer progression51,52. In our study, the expression level of EZR showed a pattern similar to that of BCL-2, suggesting that increasing daily exposure to PEMF may cause an improvement in metastatic prognosis. Several studies focused on the cell cycle effect of PEMF demonstrated that it can modify the binding of calcium ions (Ca2+) to calcium-calmodulin (CaM), resulting in a twofold increase in binding kinetics when observed in cell-free enzymatic preparations53. In our study, the expression of TRPC1 of the TRP ion channel family was higher in the 3-h PEMF stimulation in comparison to the 4-h one. The activation of the members of the TRPC family, non-selective cation channels, causes the TRPC1 to form a Ca2+-permeable channel. The role of Ca2+ in cancer cells is multifaceted; therefore, disruptions to calcium homeostasis can directly alter the initiation and progression of cancer54. Thus, our results may suggest that increasing the time of exposure to PEMF therapy can reduce Ca2+ influx, which negatively impacts the proliferation and invasion of cancer that is commonly associated with a higher intracellular Ca2+ uptake55. Another cell cycle regulator is the protein kinase CDK-1, which, in our study, was also downregulated in the 4-h PEMF therapy in comparison to the 3-h one. Since CDKs are crucial in cancer cell cycle progression and tumorigenesis56, this downregulation of CDK-1 may suggest a potential therapeutic effect of the 4-h PEMF therapy, since inhibiting CDK-1 activity can disrupt uncontrolled cancer cell proliferation and potentially induce cell cycle arrest or senescence.
In this work, ITGA5, NOTCH3, MMP9, and MAPK1 were evaluated as members of signaling pathways directly involved in cell adhesion, cell-cell connections, ECM remodeling, and mechanotransduction, respectively. To start with, ITGA5, a member of the integrin family, is upregulated in multiple tumors, and this upregulation can promote cancer progression57. Despite discrepancies in its role in osteosarcoma, studies showed that dysregulation of ITGA5 can be linked to osteosarcoma progression58. Similarly, several studies showed that molecules in the Notch signaling family are found in abnormally high amounts in most osteosarcoma patients. This overexpression is directly linked to a higher chance of disease relapse, metastasis, and unfavorable clinical outcomes59. Working on another front, studies showed that the MMPs, a proteolytic enzyme family, are also key players in cancer progression and metastasis60,61. Furthermore, the MAPK signaling pathway was also evaluated in osteosarcoma and was shown to be associated with osteosarcoma development, progression, and a low survival rate62,63. In our study, we selected MAPK1 as a mechanotransduction-related molecular marker since we applied PEMF therapy. Our results showed that ITGA5, NOTCH3, MMP9, and MAPK1 demonstrated a pattern similar to the previously discussed genes, in which the 4-h PEMF stimulation resulted in a considerably significant downregulation in comparison to the 3-h stimulation.
Thus, this work demonstrates that an adequate duration of PEMF therapy, specifically 4 h in 3 consecutive days, can cause a considerable decrease in the expression of genes directly linked to osteosarcoma progression, suggesting a potential therapeutic benefit in mitigating disease advancement, even in the absence of DOX to which the sensitivity of tumor cells does not appear to be significantly increased by exposure to PEMF under the conditions tested here.
Being preliminary, this study has limitations that also outline directions for future work. First, although co-culturing U2OS cells with MSCs improved spheroid stability and physiological relevance, we did not analyze potential changes in the cellular composition of the spheroids after PEMF and/or DOX exposure. Monitoring shifts in the U2OS-MSC ratio would provide valuable insight into which cell population is mainly affected. Second, our findings are based on a single osteosarcoma cell line (U2OS) and a single chemotherapeutic agent (DOX), which may limit the applicability of the results to other drugs and osteosarcoma subtypes. Finally, the experimental design included only a limited number of PEMF exposure regimens (2–3 days, 3–4 h per day), two DOX concentrations, and a single sequence of treatment (PEMF → DOX). As this proof-of-concept study was not intended to capture interaction effects between PEMF and DOX, statistical comparisons were performed within fixed DOX concentrations to isolate the contribution of PEMF independently. While appropriate for the exploratory scope, future studies should broaden both PEMF and DOX conditions, as well as explore a different exposure sequence (PEMF → DOX), complemented with additional readouts, which would enable a full factorial design and a deeper understanding of the cellular mechanisms underlying PEMF-drug interactions.
Conclusion
This study presents a robust co-culture spheroid model of osteosarcoma suitable for evaluating tumor responses to external stimuli such as PEMF. Although PEMF stimulation did not consistently enhance DOX efficacy across all tested assays, it did modulate metabolic activity and stiffness in a manner suggestive of altered chemosensitivity. Gene expression analysis, conducted in the absence of DOX, revealed exposure-dependent transcriptional changes affecting genes related to survival, proliferation, and invasion. These findings highlight the need for deeper evaluation and more refined and standardized experimental designs to fully understand the therapeutic potential of PEMF in oncology.
Author contributions
K.M.: Formal Analysis, Investigation, Methodology, Visualization, Writing—original draft, Writing—review & editing. F.D.: Conceptualization, Investigation, Writing—original draft, Writing—review & editing. V.R. and M.A.: Formal Analysis, Investigation, Writing—original draft, Writing—review & editing. S.S.: Conceptualization, Methodology, Writing—review & editing. A.C.: Funding acquisition, Resources, Writing—review & editing. L.R.: Conceptualization, Funding acquisition, Resources, Writing—review & editing.
Funding
The authors acknowledge financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 860462 (PREMUROSA).
Data availability
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
Declarations
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
- 1.Mirabello, L., Troisi, R. J. & Savage, S. A. International osteosarcoma incidence patterns in children and adolescents, middle ages and elderly persons. Int. J. Cancer125, 229–234 (2009). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 2.Lai, J., Li, X., Liu, W., Liufu, Q. & Zhong, C. Global, regional, and National burden and trends analysis of malignant neoplasm of bone and articular cartilage from 1990 to 2021: A systematic analysis for the global burden of disease study 2021. Bone188, 117212 (2024). [DOI] [PubMed] [Google Scholar]
- 3.Misaghi, A., Goldin, A., Awad, M. & Kulidjian, A. A. Osteosarcoma: A comprehensive review. SICOT J.4, (2018). [DOI] [PMC free article] [PubMed]
- 4.Shoaib, Z., Fan, T. M. & Irudayaraj, J. M. K. Osteosarcoma mechanobiology and therapeutic targets. Br. J. Pharmacol.179, 201–217 (2022). [DOI] [PMC free article] [PubMed]
- 5.Freeman, F. E., Burdis, R., Mahon, O. R., Kelly, D. J. & Artzi, N. A. Spheroid model of early and late-stage osteosarcoma mimicking the divergent relationship between tumor elimination and bone regeneration. Adv. Healthc. Mater.11, (2022). [DOI] [PubMed]
- 6.Cornelio, N. & Burudpakdee, C. A. Guideline-Based Estimate of health care resource use and cost of metastatic unresectable osteosarcoma. Value Health17, A629–A630 (2014). [DOI] [PubMed]
- 7.Jafari, F. et al. Osteosarcoma: A comprehensive review of management and treatment strategies. Ann. Diagn. Pathol.49, 151654. 10.1016/j.anndiagpath.2020.151654 (2020). [DOI] [PubMed]
- 8.Zhao, X., Wu, Q., Gong, X., Liu, J. & Ma, Y. Osteosarcoma: A review of current and future therapeutic approaches. BioMed. Eng. Online20. 10.1186/s12938-021-00860-0 (2021). [DOI] [PMC free article] [PubMed]
- 9.Brookes, M. J. et al. Surgical advances in osteosarcoma. Cancers13, 1–26. 10.3390/cancers13030388 (2021). [DOI] [PMC free article] [PubMed]
- 10.Fortunato, A. et al. Natural selection in cancer biology: From molecular snowflakes to trait hallmarks. Cold Spring Harb Perspect. Med.7, a029652 (2017). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 11.Vadalà, M. et al. Mechanisms and therapeutic effectiveness of pulsed electromagnetic field therapy in oncology. Cancer Med.5, 3128–3139 (2016). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 12.Mansourian, M. & Shanei, A. Evaluation of pulsed electromagnetic field effects: A systematic review and meta-analysis on highlights of two decades of research in vitro studies. Biomed Res. Int.2021 (2021). [DOI] [PMC free article] [PubMed]
- 13.Azadian, E., Arjmand, B., Khodaii, Z. & Ardeshirylajimi, A. A comprehensive overview on utilizing electromagnetic fields in bone regenerative medicine. Electromagn. Biol. Med.38, 1–20 (2019). [DOI] [PubMed] [Google Scholar]
- 14.Roberti, R. et al. High-intensity, low-frequency pulsed electromagnetic field as an odd treatment in a patient with mixed foot ulcer: A case report. Reports5, 3 (2022). [Google Scholar]
- 15.Strauch, B., Herman, C., Dabb, R., Ignarro, L. J. & Pilla, A. A. Evidence-based use of pulsed electromagnetic field therapy in clinical plastic surgery. Aesthet. Surg. J.29, 135–143 (2009). [DOI] [PubMed] [Google Scholar]
- 16.Iannitti, T., Palmieri, B., Fistetto, E. & Rottigni. Pulsed electromagnetic field therapy for management of osteoarthritis-related pain, stiffness and physical function: Clinical experience in the elderly. Clin. Interv. Aging128910.2147/CIA.S35926 (2013). [DOI] [PMC free article] [PubMed]
- 17.Hug, K. & Röösli, M. Therapeutic effects of whole-body devices applying pulsed electromagnetic fields (PEMF): A systematic literature review. Bioelectromagnetics33, 95–105 (2012). [DOI] [PubMed] [Google Scholar]
- 18.Ruiz-Gómez, M. J. et al. Influence of 1 and 25 Hz, 1.5 mT magnetic fields on antitumor drug potency in a human adenocarcinoma cell line. Bioelectromagnetics23, 578–525 (2002). [DOI] [PubMed] [Google Scholar]
- 19.MURAMATSU, Y., MATSUI, T., DEIE, M. & SATO, K. Pulsed electromagnetic field stimulation promotes anti-cell proliferative activity in Doxorubicin-treated mouse osteosarcoma cells. Vivo (Brooklyn)31, 61–68 (2017). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 20.Tai, Y. K. et al. Modulated TRPC1 expression predicts sensitivity of breast cancer to doxorubicin and magnetic field therapy: Segue towards a precision medicine approach. Front. Oncol.11 (2022). [DOI] [PMC free article] [PubMed]
- 21.Crocetti, S. et al. Low intensity and frequency pulsed electromagnetic fields selectively impair breast cancer cell viability. PLoS One8, e72944 (2013). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 22.Filipovic, N. et al. Electromagnetic field investigation on different cancer cell lines. Cancer Cell. Int.14, 84 (2014). [Google Scholar]
- 23.Rodrigues, J., Heinrich, M. A., Teixeira, L. M. & Prakash, J. 3D in vitro model (R)evolution: Unveiling Tumor–Stroma interactions. Trends Cancer7, 249–264 (2021). [DOI] [PubMed] [Google Scholar]
- 24.Zushin, P. J. H., Mukherjee, S. & Wu, J. C. FDA modernization act 2.0: Transitioning beyond animal models with human cells, organoids, and AI/ML-based approaches. J. Clin. Invest.133 (2023). [DOI] [PMC free article] [PubMed]
- 25.Kim, S. Y., van de Wetering, M., Clevers, H. & Sanders, K. The future of tumor organoids in precision therapy. Trends Cancer10.1016/j.trecan.2025.03.005 (2025). [DOI] [PubMed] [Google Scholar]
- 26.Pinto, B., Henriques, A. C., Silva, P. M. A. & Bousbaa, H. Three-dimensional spheroids as in vitro preclinical models for cancer research. Pharmaceutics12, 1186 (2020). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 27.Domingues, M. F., Silva, J. C. & Sanjuan-Alberte, P. From spheroids to bioprinting: A literature review on biomanufacturing strategies of 3D in vitro osteosarcoma models. Adv Ther. (Weinh)7, (2024).
- 28.Baxter-Holland, M. & Dass, C. R. Doxorubicin, mesenchymal stem cell toxicity and antitumour activity: Implications for clinical use. J. Pharm. Pharmacol.70, 320–327 (2018). [DOI] [PubMed] [Google Scholar]
- 29.Burgos-Panadero, R. et al. The tumour microenvironment as an integrated framework to understand cancer biology. Cancer Lett.461, 112–122 (2019). [DOI] [PubMed] [Google Scholar]
- 30.Cortini, M. et al. Endogenous extracellular matrix regulates the response of osteosarcoma 3D spheroids to doxorubicin. Cancers (Basel)15, 1221 (2023). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 31.James, S. et al. Multiparameter analysis of human bone marrow stromal cells identifies distinct immunomodulatory and differentiation-competent subtypes. Stem Cell. Rep.4, 1004–1015 (2015). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 32.Whitehouse, L., Do, T. & Thomson, N. Optimising dental pulp stem cell adhesion on agarose scaffolds for in vitro dentinogenesis. Fac. Dent. J.15, 112–117 (2024). [Google Scholar]
- 33.Zhang, Q. Spheroid culture of human periodontal ligament stem cells on agarose enhances stemness and osteogenic differentiation potential. Am. J. Transl. Res.17, 5257–5270 (2025). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 34.Bäcker, V. Analyze spheroid cell invasion in 3D matrix, RRID:SCR_021204. https://github.com/MontpellierRessourcesImagerie/imagej_macros_and_scripts/wiki/Analyze-Spheroid-Cell-Invasion-In-3D-Matrix (2012).
- 35.Efremov, Y. M. et al. Mechanical properties of cell sheets and spheroids: The link between single cells and complex tissues. Biophys. Rev.13, 541–561 (2021). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 36.Kim, S. O., Kim, J., Okajima, T. & Cho, N. J. Mechanical properties of paraformaldehyde-treated individual cells investigated by atomic force microscopy and scanning ion conductance microscopy. Nano Converg.4, 5 (2017). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 37.Targosz-Korecka, M., Daniel Brzezinka, G., Danilkiewicz, J., Rajfur, Z. & Szymonski, M. Glutaraldehyde fixation preserves the trend of elasticity alterations for endothelial cells exposed to < scp > TNF ‐α. Cytoskeleton72, 124–130 (2015). [DOI] [PubMed] [Google Scholar]
- 38.Baek, N., Seo, O. W., Kim, M., Hulme, J. & An, S. S. A. Monitoring the effects of doxorubicin on 3D-spheroid tumor cells in real-time. Onco Targets Ther.9, 7207–7218 (2016). [DOI] [PMC free article] [PubMed]
- 39.Butler, P. et al. RNA disruption is a widespread phenomenon associated with stress-induced cell death in tumour cells. Sci. Rep.13, 1711 (2023). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 40.Lin, Y. et al. Osteosarocma progression in biomimetic matrix with different stiffness: Insights from a three-dimensional printed gelatin methacrylamide hydrogel. Int. J. Biol. Macromol.252, 126391 (2023). [DOI] [PubMed] [Google Scholar]
- 41.Rodrigues, J., Sarmento, B. & Pereira, C. L. Osteosarcoma tumor microenvironment: The key for the successful development of biologically relevant 3D in vitro models. In Vitro Models. 10.1007/s44164-022-00008-x (2022). [DOI] [PMC free article] [PubMed]
- 42.Sutherland, R. M. Cell and environment interactions in tumor microregions: The multicell spheroid model. Sci. (1979). 240, 177–184 (1988). [DOI] [PubMed] [Google Scholar]
- 43.Baek, N., Seo, O. W., Lee, J., Hulme, J. & An, S. S. A. Real-time monitoring of cisplatin cytotoxicity on three-dimensional spheroid tumor cells. Drug Des. Devel Ther.10, 2155–2165 (2016). [DOI] [PMC free article] [PubMed]
- 44.Panczyszyn, E. et al. FSP1 is a predictive biomarker of osteosarcoma cells’ susceptibility to ferroptotic cell death and a potential therapeutic target. Cell. Death Discov.10, 87 (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 45.Rimann, M. et al. An in vitro osteosarcoma 3D microtissue model for drug development. J. Biotechnol.189, 129–135 (2014). [DOI] [PubMed] [Google Scholar]
- 46.Chang, X., Ma, Z., Zhu, G., Lu, Y. & Yang, J. New perspective into mesenchymal stem cells: Molecular mechanisms regulating osteosarcoma. J. Bone Oncol.29, 100372 (2021). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 47.Xu, W. et al. Pulsed electromagnetic therapy in cancer treatment: Progress and outlook. VIEW3 (2022).
- 48.Qian, S. et al. The role of BCL-2 family proteins in regulating apoptosis and cancer therapy. Front. Oncol.12, (2022). [DOI] [PMC free article] [PubMed]
- 49.Radeva, M. & Berg, H. Differences in lethality between cancer cells and human lymphocytes caused by LF-electromagnetic fields. Bioelectromagnetics25, 503–507 (2004). [DOI] [PubMed] [Google Scholar]
- 50.Gautreau, A., Poullet, P., Louvard, D. & Arpin, M. Ezrin, A plasma membrane–microfilament linker, signals cell survival through the phosphatidylinositol 3-kinase/Akt pathway. Proc. Natl. Acad. Sci.96, 7300–7305 (1999). [DOI] [PMC free article] [PubMed]
- 51.Akter, S. et al. Comprehensive in Silico characterization of nonsynonymous SNPs in the human Ezrin (EZR) gene and their role in disease pathogenesis. Biochem. Biophys. Rep.42, 101972 (2025). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 52.Khanna, C. et al. The membrane-cytoskeleton linker Ezrin is necessary for osteosarcoma metastasis. Nat. Med.10, 182–186 (2004). [DOI] [PubMed] [Google Scholar]
- 53.Markov, M. S. Pulsed electromagnetic field therapy history, state of the art and future. Environmentalist27, 465–475 (2007). [Google Scholar]
- 54.Elzamzamy, O. M., Penner, R. & Hazlehurst, L. A. The role of TRPC1 in modulating cancer progression. Cells9, 388 (2020). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 55.Bruce, J. I. E. & James, A. D. Targeting the calcium signalling machinery in cancer. Cancers (Basel)12, 2351 (2020). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 56.Wang, Q., Bode, A. M. & Zhang, T. Targeting CDK1 in cancer: Mechanisms and implications. NPJ Precis. Oncol.7, 58 (2023). [DOI] [PMC free article] [PubMed]
- 57.Pang, X. et al. Targeting integrin pathways: Mechanisms and advances in therapy. Signal. Transduct. Target. Ther.8, 1 (2023). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 58.Yang, J. & Wang, N. Analysis of the molecular mechanism of osteosarcoma using a bioinformatics approach. Oncol. Lett.12, 3075–3080 (2016). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 59.Shi, Q. et al. Notch signaling pathway in cancer: From mechanistic insights to targeted therapies. Signal. Transduct. Target. Ther.9, 128 (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 60.Egeblad, M. & Werb, Z. New functions for the matrix metalloproteinases in cancer progression. Nat. Rev. Cancer2, 161–174 (2002). [DOI] [PubMed] [Google Scholar]
- 61.Kido, A. et al. Overexpression of matrix metalloproteinase (MMP)-9 correlates with metastatic potency of spontaneous and 4-hydroxyaminoquinoline 1-oxide (4-HAQO)-induced transplantable osteosarcomas in rats. Cancer Lett.137, 209–216 (1999). [DOI] [PubMed] [Google Scholar]
- 62.Ji, Z., Shen, J., Lan, Y., Yi, Q. & Liu, H. Targeting signaling pathways in osteosarcoma: Mechanisms and clinical studies. MedComm (Beijing)4, (2023). [DOI] [PMC free article] [PubMed]
- 63.Cai, X. & Zhu, S. Prognosis-related VDAC1 regulates the proliferation and apoptosis of osteosarcoma cells via the MAPK signaling pathway. Genomics115, 110595 (2023). [DOI] [PubMed] [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.



