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       Movement of organs and tissues can lead to errors in the positioning of X-rays during radiotherapy. Therefore, materials with tissue-equivalent mechanical and radiological properties are needed to mimic organ movement for the optimization of radiotherapy. However, the development of such materials remains a challenge. Alginate hydrogels have properties similar to those of the extracellular matrix, making them promising as tissue-equivalent materials. In this study, alginate hydrogel foams with desired mechanical and radiological properties were synthesized by in situ Ca2+ release. The air-to-volume ratio was carefully controlled to obtain hydrogel foams with defined mechanical and radiological properties. The macro- and micromorphology of the materials were characterized, and the behavior of the hydrogel foams under compression was studied. The radiological properties were estimated theoretically and verified experimentally using computed tomography. This study sheds light on the future development of tissue-equivalent materials that can be used for radiation dose optimization and quality control during radiotherapy.
       Radiation therapy is a common treatment for cancer1. Movement of organs and tissues often leads to errors in the positioning of X-rays during radiation therapy2, which can result in undertreatment of the tumor and overexposure of surrounding healthy cells to unnecessary radiation. The ability to predict the movement of organs and tissues is critical to minimizing tumor localization errors. This study focused on the lungs, since they undergo significant deformations and movements when patients breathe during radiation therapy. Various finite element models have been developed and applied to simulate the motion of human lungs3,4,5. However, human organs and tissues have complex geometries and are highly patient-dependent. Therefore, materials with tissue-equivalent properties are very useful for developing physical models to validate theoretical models, facilitate improved medical treatment, and for medical education purposes.
       The development of soft tissue-mimicking materials to achieve complex external and internal structural geometries has attracted much attention because their inherent mechanical inconsistencies can lead to failures in target applications6,7. Modeling the complex biomechanics of lung tissue, which combines extreme softness, elasticity, and structural porosity, poses a significant challenge in developing models that accurately reproduce the human lung. The integration and matching of mechanical and radiological properties are critical for the effective performance of lung models in therapeutic interventions. Additive manufacturing has proven to be effective in developing patient-specific models, enabling rapid prototyping of complex designs. Shin et al. 8 developed a reproducible, deformable lung model with 3D-printed airways. Haselaar et al. 9 developed a phantom highly similar to real patients for image quality assessment and position verification methods for radiotherapy. Hong et al10 developed a chest CT model using 3D printing and silicone casting technology to reproduce the CT intensity of various lung lesions to evaluate the accuracy of quantification. However, these prototypes are often made of materials whose effective properties are very different from those of lung tissue11.
       Currently, most lung phantoms are made of silicone or polyurethane foam, which do not match the mechanical and radiological properties of real lung parenchyma.12,13 Alginate hydrogels are biocompatible and have been widely used in tissue engineering due to their tunable mechanical properties.14 However, reproducing the ultra-soft, foam-like consistency required for a lung phantom that accurately mimics the elasticity and filling structure of lung tissue remains an experimental challenge.
       In this study, it was assumed that lung tissue is a homogeneous elastic material. The density of human lung tissue (\(\:\rho\:\)) is reported to be 1.06 g/cm3, and the density of the inflated lung is 0.26 g/cm315. A wide range of Young’s modulus (MY) values ​​of lung tissue have been obtained using different experimental methods. Lai-Fook et al. 16 measured the YM of human lung with uniform inflation to be 0.42–6.72 kPa. Goss et al. 17 used magnetic resonance elastography and reported a YM of 2.17 kPa. Liu et al. 18 reported a directly measured YM of 0.03–57.2 kPa. Ilegbusi et al. 19 estimated the YM to be 0.1–2.7 kPa based on 4D CT data obtained from selected patients.
       For the radiological properties of the lung, several parameters are used to describe the interaction behavior of lung tissue with X-rays, including the elemental composition, electron density (\(\:{\rho\:}_{e}\)), effective atomic number (\(\:{Z}_{eff}\)), mean excitation energy (\(\:I\)), mass attenuation coefficient (\(\:\mu\:/\rho\:\)) and the Hounsfield unit (HU), which is directly related to \(\:\mu\:/\rho\:\).
       Electron density \(\:{\rho\:}_{e}\) is defined as the number of electrons per unit volume and is calculated as follows:
       where \(\:\rho\:\) is the density of the material in g/cm3, \(\:{N}_{A}\) is the Avogadro constant, \(\:{w}_{i}\) is the mass fraction, \(\:{Z}_{i}\) is the atomic number, and \(\:{A}_{i}\) is the atomic weight of the i-th element.
       The atomic number is directly related to the nature of the radiation interaction within the material. For compounds and mixtures containing several elements (e.g., fabrics), the effective atomic number \(\:{Z}_{eff}\) must be calculated. The formula was proposed by Murthy et al. 20:
       The average excitation energy \(\:I\) describes how easily the target material absorbs the kinetic energy of the penetrating particles. It describes only the properties of the target material and has nothing to do with the properties of the particles. \(\:I\) can be calculated by applying Bragg’s additivity rule:
       The mass attenuation coefficient \(\:\mu\:/\rho\:\) describes the penetration and energy release of photons in the target material. It can be calculated using the following formula:
       Where \(\:x\) is the thickness of the material, \(\:{I}_{0}\) is the incident light intensity, and \(\:I\) is the photon intensity after penetration into the material. \(\:\mu\:/\rho\:\) data can be obtained directly from the NIST 12621 Standards Reference Database. \(\:\mu\:/\rho\:\) values ​​for mixtures and compounds can be derived using the additivity rule as follows:
       HU is a standardized dimensionless unit of measurement of radiodensity in the interpretation of computed tomography (CT) data, which is linearly transformed from the measured attenuation coefficient \(\:\mu\:\). It is defined as:
       where \(\:{\mu\:}_{water}\) is the attenuation coefficient of water, and \(\:{\mu\:}_{air}\) is the attenuation coefficient of air. Therefore, from formula (6) we see that the HU value of water is 0, and the HU value of air is -1000. The HU value for human lungs ranges from -600 to -70022.
       Several tissue equivalent materials have been developed. Griffith et al. 23 developed a tissue equivalent model of the human torso made of polyurethane (PU) to which various concentrations of calcium carbonate (CaCO3) were added to simulate the linear attenuation coefficients of various human organs including the human lung, and the model was named Griffith. Taylor24 presented a second lung tissue equivalent model developed by Lawrence Livermore National Laboratory (LLNL), named LLLL1. Traub et al.25 developed a new lung tissue substitute using Foamex XRS-272 containing 5.25% CaCO3 as a performance enhancer, which was named ALT2. Tables 1 and 2 show a comparison of \(\:\rho\:\), \(\:{\rho\:}_{e}\), \(\:{Z}_{eff}\), \(\:I\) and the mass attenuation coefficients for the human lung (ICRU-44) and the above tissue equivalent models.
       Despite the excellent radiological properties achieved, almost all phantom materials are made of polystyrene foam, which means that the mechanical properties of these materials cannot approach those of human lungs. The Young’s modulus (YM) of polyurethane foam is about 500 kPa, which is far from ideal compared to normal human lungs (about 5-10 kPa). Therefore, it is necessary to develop a new material that can meet the mechanical and radiological characteristics of real human lungs.
       Hydrogels are widely used in tissue engineering. Its structure and properties are similar to the extracellular matrix (ECM) and are easily adjustable. In this study, pure sodium alginate was chosen as the biomaterial for the preparation of foams. Alginate hydrogels are biocompatible and widely used in tissue engineering due to their adjustable mechanical properties. The elemental composition of sodium alginate (C6H7NaO6)n and the presence of Ca2+ allow its radiological properties to be adjusted as needed. This combination of adjustable mechanical and radiological properties makes alginate hydrogels ideal for our study. Of course, alginate hydrogels also have limitations, especially in terms of long-term stability during simulated respiratory cycles. Therefore, further improvements are needed and expected in future studies to address these limitations.
       In this work, we developed an alginate hydrogel foam material with controllable rho values, elasticity, and radiological properties similar to those of human lung tissue. This study will provide a general solution for fabricating tissue-like phantoms with tunable elastic and radiological properties. The material properties can be easily tailored to any human tissue and organ.
       The target air to volume ratio of the hydrogel foam was calculated based on the HU range of human lungs (-600 to -700). It was assumed that the foam was a simple mixture of air and synthetic alginate hydrogel. Using a simple addition rule of individual elements \(\:\mu\:/\rho\:\), the volume fraction of air and the volume ratio of the synthesized alginate hydrogel could be calculated.
       Alginate hydrogel foams were prepared using sodium alginate (Part No. W201502), CaCO3 (Part No. 795445, MW: 100.09), and GDL (Part No. G4750, MW: 178.14) purchased from Sigma-Aldrich Company, St. Louis, MO. 70% Sodium Lauryl Ether Sulfate (SLES 70) was purchased from Renowned Trading LLC. Deionized water was used in the foam preparation process. Sodium alginate was dissolved in deionized water at room temperature with constant stirring (600 rpm) until a homogeneous yellow translucent solution was obtained. CaCO3 in combination with GDL was used as a Ca2+ source to initiate gelation. SLES 70 was used as a surfactant to form a porous structure inside the hydrogel. The alginate concentration was maintained at 5% and the Ca2+:-COOH molar ratio was maintained at 0.18. The CaCO3:GDL molar ratio was also maintained at 0.5 during foam preparation to maintain a neutral pH. The value is 26. 2% by volume of SLES 70 was added to all samples. A beaker with a lid was used to control the mixing ratio of the solution and air. The total volume of the beaker was 140 ml. Based on the theoretical calculation results, different volumes of the mixture (50 ml, 100 ml, 110 ml) were added to the beaker to mix with air. The sample containing 50 ml of the mixture was designed to mix with sufficient air, while the air volume ratio in the other two samples was controlled. First, SLES 70 was added to the alginate solution and stirred with an electric stirrer until completely mixed. Then, the CaCO3 suspension was added to the mixture and stirred continuously until the mixture was completely mixed, when its color changed to white. Finally, the GDL solution was added to the mixture to initiate gelation, and mechanical stirring was maintained throughout the process. For the sample containing 50 ml of the mixture, mechanical stirring was stopped when the volume of the mixture stopped changing. For the samples containing 100 ml and 110 ml of the mixture, mechanical stirring was stopped when the mixture filled the beaker. We also attempted to prepare hydrogel foams with a volume between 50 ml and 100 ml. However, structural instability of the foam was observed, as it fluctuated between the state of complete air mixing and the state of air volume control, resulting in inconsistent volume control. This instability introduced uncertainty into the calculations, and therefore this volume range was not included in this study.
       The density \(\:\rho\:\) of a hydrogel foam is calculated by measuring the mass \(\:m\) and volume \(\:V\) of a hydrogel foam sample.
       Optical microscopic images of hydrogel foams were obtained using a Zeiss Axio Observer A1 camera. ImageJ software was used to calculate the number and size distribution of pores in a sample in a certain area based on the obtained images. The pore shape is assumed to be circular.
       To study the mechanical properties of the alginate hydrogel foams, uniaxial compression tests were performed using a TESTRESOURCES 100 series machine. The samples were cut into rectangular blocks and the block dimensions were measured to calculate the stresses and strains. The crosshead speed was set at 10 mm/min. Three samples were tested for each sample and the mean and standard deviation were calculated from the results. This study focused on the compressive mechanical properties of the alginate hydrogel foams since the lung tissue is subjected to compressive forces at a certain stage of the respiratory cycle. The extensibility is of course crucial, especially to reflect the full dynamic behavior of the lung tissue and this will be investigated in future studies.
       The prepared hydrogel foam samples were scanned on a Siemens SOMATOM Drive dual-channel CT scanner. The scanning parameters were set as follows: 40 mAs, 120 kVp and 1 mm slice thickness. The resulting DICOM files were analyzed using MicroDicom DICOM Viewer software to analyze the HU values ​​of 5 cross-sections of each sample. The HU values ​​obtained by CT were compared with theoretical calculations based on the density data of the samples.
       The aim of this study is to revolutionize the fabrication of individual organ models and artificial biological tissues by engineering soft materials. Developing materials with mechanical and radiological properties that match the working mechanics of human lungs is important for targeted applications such as improving medical training, surgical planning, and radiation therapy planning. In Figure 1A, we plotted the discrepancy between the mechanical and radiological properties of soft materials putatively used to fabricate human lung models. To date, materials have been developed that exhibit the desired radiological properties, but their mechanical properties do not meet the desired requirements. Polyurethane foam and rubber are the most widely used materials for fabricating deformable human lung models. The mechanical properties of polyurethane foam (Young’s modulus, YM) are typically 10 to 100 times greater than those of normal human lung tissue. Materials that exhibit both the desired mechanical and radiological properties are not yet known.
       (A) Schematic representation of the properties of various soft materials and comparison with human lung in terms of density, Young’s modulus and radiological properties (in HU). (B) X-ray diffraction pattern of \(\:\mu\:/\rho\:\) alginate hydrogel with a concentration of 5% and a Ca2+:-COOH molar ratio of 0.18. (C) Range of air volume ratios in hydrogel foams. (D) Schematic representation of alginate hydrogel foams with different air volume ratios.
       The elemental composition of alginate hydrogels with a concentration of 5% and a Ca2+:-COOH molar ratio of 0.18 was calculated, and the results are shown in Table 3. According to the addition rule in the previous formula (5), the mass attenuation coefficient of alginate hydrogel \(\:\:\mu\:/\rho\:\) is obtained as shown in Figure 1B.
       The \(\:\mu\:/\rho\:\) values ​​for air and water were obtained directly from the NIST 12612 standards reference database. Thus, Figure 1C shows the calculated air volume ratios in hydrogel foams with HU equivalent values ​​between -600 and -700 for the human lung. The theoretically calculated air volume ratio is stable within 60–70% in the energy range from 1 × 10−3 to 2 × 101 MeV, indicating good potential for the application of hydrogel foam in downstream manufacturing processes.
       Figure 1D shows the prepared alginate hydrogel foam sample. All samples were cut into cubes with an edge length of 12.7 mm. The results showed that a homogeneous, three-dimensionally stable hydrogel foam was formed. Regardless of the air volume ratio, no significant differences in the appearance of the hydrogel foams were observed. The self-sustaining nature of the hydrogel foam suggests that the network formed within the hydrogel is strong enough to support the weight of the foam itself. Apart from a small amount of water leakage from the foam, the foam also demonstrated transient stability for several weeks.
       By measuring the mass and volume of the foam sample, the density of the prepared hydrogel foam \(\:\rho\:\) was calculated, and the results are shown in Table 4. The results show the dependence of \(\:\rho\:\) on the volume ratio of air. When enough air is mixed with 50 ml of the sample, the density becomes the lowest and is 0.482 g/cm3. As the amount of mixed air decreases, the density increases to 0.685 g/cm3. The maximum p value between the groups of 50 ml, 100 ml and 110 ml was 0.004 < 0.05, indicating the statistical significance of the results.
       The theoretical \(\:\rho\:\) value is also calculated using the controlled air volume ratio. The measured results show that \(\:\rho\:\) is 0.1 g/cm³ smaller than the theoretical value. This difference can be explained by the internal stress generated in the hydrogel during the gelation process, which causes swelling and thus leads to a decrease in \(\:\rho\:\). This was further confirmed by the observation of some gaps inside the hydrogel foam in the CT images shown in Figure 2 (A, B and C).
       Optical microscopy images of hydrogel foams with different air volume contents (A) 50, (B) 100, and (C) 110. Cell numbers and pore size distribution in alginate hydrogel foam samples (D) 50, (E) 100, (F) 110.
       Figure 3 (A, B, C) shows the optical microscope images of the hydrogel foam samples with different air volume ratios. The results demonstrate the optical structure of the hydrogel foam, clearly showing the images of pores with different diameters. The distribution of pore number and diameter was calculated using ImageJ. Six images were taken for each sample, each image had a size of 1125.27 μm × 843.96 μm, and the total analyzed area for each sample was 5.7 mm².
       (A) Compressive stress-strain behavior of alginate hydrogel foams with different air volume ratios. (B) Exponential fitting. (C) Compression E0 of hydrogel foams with different air volume ratios. (D) Ultimate compressive stress and strain of alginate hydrogel foams with different air volume ratios.
       Figure 3 (D, E, F) shows that the pore size distribution is relatively uniform, ranging from tens of micrometers to about 500 micrometers. The pore size is basically uniform, and it decreases slightly as the air volume decreases. According to the test data, the average pore size of the 50 ml sample is 192.16 μm, the median is 184.51 μm, and the number of pores per unit area is 103; the average pore size of the 100 ml sample is 156.62 μm, the median is 151.07 μm, and the number of pores per unit area is 109; the corresponding values ​​of the 110 ml sample are 163.07 μm, 150.29 μm and 115, respectively. The data show that the larger pores have a greater influence on the statistical results of the average pore size, and the median pore size can better reflect the change trend of the pore size. As the sample volume increases from 50 ml to 110 ml, the number of pores also increases. Combining the statistical results of median pore diameter and pore number, it can be concluded that with increasing volume, more pores of smaller size are formed inside the sample.
       The mechanical test data are shown in Figures 4A and 4D. Figure 4A shows the compressive stress-strain behavior of the prepared hydrogel foams with different air volume ratios. The results show that all samples have similar nonlinear stress-strain behavior. For each sample, the stress increases faster with increasing strain. An exponential curve was fitted to the compressive stress-strain behavior of the hydrogel foam. Figure 4B shows the results after applying the exponential function as an approximating model to the hydrogel foam.
       For the hydrogel foams with different air volume ratios, their compressive modulus (E0) was also studied. Similar to the analysis of the hydrogels, the compressive Young’s modulus was investigated in the range of 20% initial strain. The results of the compression tests are shown in Figure 4C. The results in Figure 4C show that as the air volume ratio decreases from sample 50 to sample 110, the compressive Young’s modulus E0 of the alginate hydrogel foam increases from 10.86 kPa to 18 kPa.
       Similarly, the complete stress-strain curves of the hydrogel foams, as well as the ultimate compressive stress and strain values, were obtained. Figure 4D shows the ultimate compressive stress and strain of the alginate hydrogel foams. Each data point is the average of three test results. The results show that the ultimate compressive stress increases from 9.84 kPa to 17.58 kPa with decreasing gas content. The ultimate strain remains stable at about 38%.
       Figure 2 (A, B, and C) shows the CT images of hydrogel foams with different air volume ratios corresponding to samples 50, 100, and 110, respectively. The images show that the formed hydrogel foam is almost homogeneous. A small number of gaps were observed in samples 100 and 110. The formation of these gaps may be due to the internal stress generated in the hydrogel during the gelation process. We calculated the HU values ​​for 5 cross sections of each sample and listed them in Table 5 along with the corresponding theoretical calculation results.
       Table 5 shows that the samples with different air volume ratios obtained different HU values. The maximum p value between the 50 ml, 100 ml and 110 ml groups was 0.004 < 0.05, indicating the statistical significance of the results. Among the three samples tested, the sample with 50 ml mixture had the radiological properties closest to those of human lungs. The last column of Table 5 is the result obtained by theoretical calculation based on the measured foam value \(\:\rho\:\). By comparing the measured data with the theoretical results, it can be found that the HU values ​​obtained by CT scanning are generally close to the theoretical results, which in turn confirms the air volume ratio calculation results in Figure 1C.
       The main objective of this study is to create a material with mechanical and radiological properties comparable to those of human lungs. This objective was achieved by developing a hydrogel-based material with tailored tissue-equivalent mechanical and radiological properties that are as close as possible to those of human lungs. Guided by theoretical calculations, hydrogel foams with different air volume ratios were prepared by mechanically mixing sodium alginate solution, CaCO3, GDL and SLES 70. Morphological analysis showed that a homogeneous three-dimensional stable hydrogel foam was formed. By changing the air volume ratio, the density and porosity of the foam can be varied at will. With the increase of the air volume content, the pore size slightly decreases and the number of pores increases. Compression tests were conducted to analyze the mechanical properties of the alginate hydrogel foams. The results showed that the compressive modulus (E0) obtained from the compression tests is in the ideal range for human lungs. E0 increases as the air volume ratio decreases. The values ​​of the radiological properties (HU) of the prepared samples were obtained based on the CT data of the samples and compared with the results of theoretical calculations. The results were favorable. The measured value is also close to the HU value of human lungs. The results show that it is possible to create tissue-imitating hydrogel foams with an ideal combination of mechanical and radiological properties that mimic the properties of human lungs.
       Despite the promising results, the current fabrication methods need to be improved to better control the air volume ratio and porosity to match predictions from theoretical calculations and real human lungs at both global and local scales. The current study is also limited to testing the compression mechanics, which limits the potential application of the phantom to the compression phase of the respiratory cycle. Future research would benefit from investigating tensile testing as well as the overall mechanical stability of the material to assess potential applications under dynamic loading conditions. Despite these limitations, the study marks the first successful attempt to combine radiological and mechanical properties in a single material that mimics the human lung.
       The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request. Both experiments and datasets are reproducible.
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