Advances in Biology, Biotechnology and Genetics
Volume 3 | Issue 3 | Pages 13-20
Predicting Frequencies to Cause Platelet Apoptosis and Activation
Alireza Shahin-Shamsabadi 1*, Ata Hashemi 1
1 Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, IR. Iran.
Several studies have shown that cells understand different mechanical loadings; and the responses to these loadings are dependent on their health conditions. External loading is also believed to affect behaviour of different cells. In this study natural frequencies and mode shapes of suspended platelets were obtained. Based on available experimental studies, the platelet geometry was considered to be disc-like. Mechanical properties were also taken from the literature and assumed to be homogenous and uniform in the whole platelet. A three dimensional finite element model of the platelet was developed to carry out this study. These results suggest that ultrasounds with frequencies close to the predicted fundamental platelet frequency could activate and induce their aggregation. Furthermore, they show that the larger platelets, present in different syndromes, have lower natural frequencies making them more sensitive to ultrasounds with lower frequencies. The possibility of using these frequencies to induce apoptosis was also proposed..
Keywords: Blood Platelets, Natural Frequency, Mode Shapes, Finite Element Method, Aggregation, Apoptosis
As a connective tissue, blood is a fluid extracellular matrix (ECM) for cells like platelets (thrombocytes) that are suspended in it (Mescher, 2009). Platelets are fragments of megakaryocytes that consist of cytoplasm, membrane, and other organelles. Every day, these cells are produced in large numbers in the bone marrow (Hartwig, 2006). An average number of 120-300 thousand platelets per cubic millimeter exist in a normal person. Disk-like platelets are non-nucleated cells with smooth membranes when not activated (Kumar et al., 2007). Activated platelets play significant roles in hemostasis, wound healing, inflammation, and immune responses. Platelet activation could be the result of an interaction between their receptors and certain biochemical agonists or changes in their membrane in response to different mechanical loadings. The final corollary of platelet activation is their immobilization in platelet-platelet or platelet-vessel wall interactions, called ‘aggregation’ and ‘adhesion’ respectively (Jurk and Kehrel, 2005).
Cells, including platelets, are under the influence of the mechanics of their environment; mechanical stimulation for example, causes platelet activation (Otto et al.). Shear stress has also shown to affect their activation (Miyazaki et al., 1996). One of the other mechanical phenomena that could affect cells is the frequency of loading. Tanaka et. al. (Tanaka et al.) and Shikata et. al. (Shikata et al., 2008) have studied the effect of loading frequency on osteoblasts. These studies have shown that loading frequency affects cell proliferation, gene expression, and even bone matrix formation.
Different studies have previously shown the effect of mechanical and physical factors on cell behavior and fate (Fletcher and Mullins, 2010; Li et al., 2011). Resonance, for example, is believed to affect the life of cells. When a cell is allowed to vibrate on its own after initial disturbance, the frequency of the deformation is called natural frequency. If the loading frequency is close to this frequency, the cell’s oscillation is called resonance (Huang et al., 2000; Gibbs et al., 2011). Natural frequency is a characteristic of structure, which depends on geometry, physical properties, and boundary conditions (Huang et al., 2000). The health condition of a cell is believed to regulate its natural frequency (Molavi Zarandi et al., 2010).
Molavi Zarandi et. al. used finite element analysis to calculate natural frequencies of yeast cells. In their study, they investigated the effect of the cell shape -spherical or ellipsoidal- and presence or absence of the nucleus, on natural frequency (Molavi Zarandi et al., 2010). Wee et. al. also used the same method for modal analysis of osteoblasts. They examined the effect of the Young’s modulus of the cell on its natural frequency (Wee and Voloshin, 2012). In both studies the cells were considered to have been composed of cytoplasm and nucleus, without the details of different filaments and organelles present in the cell.
Considering the limited literature available on natural frequency of different cells, the main objective of the present study hence, was to determine the natural frequencies of platelets and their related mode shapes for the first time. Furthermore, the effect of size variation was examined on the fundamental frequency, closely correlating to the health condition. It was hypothesized that the predicted fundamental frequency would be in the range of reported ultrasound frequency needed to cause platelet activation and aggregation (Otto et al., 2001; Poliachik et al., 2001). Moreover, the size enlargement of platelets was expected to reduce their fundamental frequency that could make them more sensitive to ultrasounds with lower frequencies. To carry out this study, a three dimensional (3D) finite element model of a platelet was developed. The platelet geometry and its mechanical properties were obtained from literature (Milton et al., 1985; Polanowska-Grabowska et al., 1992; Radmacher et al., 1996). The size increase employed in the model was based on the work of Milton et. al. (McGarry and Prendergast, 2004), in which a correlation between an increase in size and different syndromes was developed.
To find the natural frequency of platelets, a 3D finite element model of these cells was developed. The geometry of almost all platelets was reported to be the same and was obtained from the literature. Frojmovic et. al. used light microscopy to measure the shape of platelets suspended in an isotonic solution. Differences in dimensions of different healthy platelets present in the human body were observed (Frojmovic and Panjwani, 1976). The geometry and dimensions of the most abundant platelets in human blood used to define the 3D FEA model are presented in Figure 1.
Radmacher et. al. employed atomic force microscopy to show that the viscoelastic behaviour of platelets was negligible compared to their elastic behaviour, allowing the utilization of a linear elastic mechanical model for platelets in the present study (Radmacher et al., 1996). Furthermore, the mechanical model was considered to be isotropic, due to lack of data.
Since the platelet structure does not include a nucleus, which has quite stiffer mechanical properties than those of the cytoplasm and other organelles, it has been modeled as a homogeneous material with uniform mechanical properties equal to that of the cytoplasm. The Young’s modulus, Poisson’s ratio and density of cytoplasm were used in the current work, as presented in Table 1. The reported data on density shows that it varies from 1040 to 1080 Kg/m3 for three groups of platelets in one’s body. However, the higher end data correspond with the most abundant platelets which constitute 47% of the entire population (Polanowska-Grabowska et al., 1992).
SolidWorks® (Premium 2014 x64 SP 0.0) was used on a PC (Intel Core i7-4702MQ CPU, 2.20 GHz with 6 GB RAM on a 64-bit operating system) for developing the model, linear elastic isotropic model type, and performing the finite element analysis for platelet modal analysis and finding the natural frequencies and mode shapes.
A 10-node tetrahedral element was utilized to model platelets. Mesh independency was verified and 11739 elements were found to be suitable for analysis performance. Considering the platelet suspensions in the blood, no boundary condition was applied to the cells, allowing them to have the zero or rigid body modes. Figure 2 shows the meshed finite element model of a platelet with no boundary condition.
The governing equation for un-damped free vibration modal analysis is provided below:
using the exponential solution and replacing and assuming that couldn’t be zero, the equation becomes:
where , and ω stand for mass matrix, spring matrix and frequency, respectively.
Figure 1. (a) Dimensions assigned to the platelet, (b) Cross-section of the 3D finite element model used for the platelet.
Figure 2. Meshed Finite Element Model of a Platelet
Table 1. Mechanical Properties Assigned to Each Cell’s Components
|Young’s modulus (Pa)||100||McGarry et. al.. (McGarry and Prendergast, 2004)|
|Density (kg/m3)||1065||P-Grabowska et. al.. (Polanowska-Grabowska et al., 1992)|
Similar to red blood cells, platelets are floating (or free) cells in the blood and are not attached to any medium (or substrate), i.e. no boundary condition was needed to model them. The free movement of platelets results in six rigid body modes, each with a natural frequency of about zero. The first three of these modes were translations and the other three were rotations. The first eight non-zero frequencies and associated mode shapes of platelets were also calculated and are depicted in Figure 3. The fundamental frequency of normal platelets with a mode shape exhibiting the 1st out-of-plane bending mode was calculated at 39.40 kHz. The 2nd natural frequency representative of the 1st in-plane bending mode was predicted at 58.15 kHz.
Moreover, the non-zero natural frequencies of the abnormal platelets i.e. those 10-20% bigger than the normal size- were calculated. To our knowledge, there is no published data available on the exact measurements of the geometry and mechanical properties of abnormal platelets. Therefore, due to this limitation, this study only considered the effect of size increase and, accordingly, estimated the first eight natural frequencies. The frequencies of normal platelets and those related with size increase are tabulated in Table 2. Overall, all the computed frequencies indicate a reduction of 9% & 16%, for a size increase of 10% & 20%, respectively. The mode shapes for these three groups of platelets remained the same. Contrary to the geometry, changes in mechanical properties of the platelets, such as Young’s modulus, by as much as 20% has had little effect on the calculated frequencies, while keeping the geometry the same.
Table 2. Effect of Platelet Size on Natural Frequency
|Frequency Mode||Natural Frequency, report all in kHz|
|Normal Cell||Cell With 10% Increase in Size||Cell With 20% Increase in Size|
Figure 3. Different Shape Modes of the Platelet
Figure 4. Effect of Natural Frequency on the Inside of the Cell; Cross-section of the Platelet in Different Modes
It has been proposed that Platelet activation leading to clot formation may be the result of chemical agents and mechanical stimulation (Otto et al., 2001). Different studies have shown that mechanical stimulation without chemical agonists could result in platelet activation. Miyazaki et. al. have shown the effect of mechanical shear stress on platelet activation (Miyazaki et al., 1996). Williams et. al. have indicated that mechanical irritation has a similar effect (Williams et al., 1998). Other studies have shown that ultrasound stimulation of platelets in the range of 1 MHz could also cause the activation of platelets, but this happens more readily as the frequency decreases to the range of 20-30 kHz. Williams et. al. have used a 25 kHz ultrasound device in order to activate platelets as a result of structural damage to mammalian platelets (Williams and Chater, 1980). A more recent study has used a 35 kHz ultrasound device for 5 seconds in order to activate platelets in the absence of any kind of chemical agent (Otto et al., 2001). Our findings are consistent with these studies. The first calculated natural frequency for a platelet in this study was 39.4 kHz, which is close to the frequency used in Otto et. al’s study to activate platelets. This platelet activation could be related to the structural damage, and more precisely, damage to the platelet membrane, caused by the resonance initiated by ultrasound exposure.
As discussed earlier, an increase in the size of platelets has been reported in different syndromes (Milton et al., 1985). Based on our findings, the greater the size increase, the more the natural platelet frequency decreases. Using a micropipette aspiration method, White et. al. showed that abnormal platelets displayed more deformation than normal ones (White et al., 1984). This decrease in elasticity is consistent with the decrease in natural frequency predicted in the current study, and agrees well with Wee et. al.’s findings; where in the natural osteoblast frequency was demonstrated to have increased with Young’s modulus.
Moreover, cells respond to mechanical stimulation and environmental conditions. This also applies to platelets, as indicated by several studies that claim mechanical stimuli may cause platelet activation as well as its apoptosis. According to these studies, mechanical irritation of some of the proteins on the outside of the platelet membrane causes the loss of their adhesion, as well their activation (Chaqour et al., 1999; Ruggeri et al., 2006; Cranmer et al., 2011; Yin et al., 2011). The mechanical stimulation used included the mechanical stretch of platelets which results in structural damage and loss of integrity of platelets. As presented in Figure 4, in all modes except for mode 4, the relative traction of the membrane was larger than the inside of the cell. This suggests that using these frequencies against platelets influences mostly the membrane, which may cause their activation. Furthermore, Leytin showed that biomechanical rheological forces could also cause platelet apoptosis, in some cases due to mitochondrial responses (Leytin, 2012). The mode shape 4 could be used to speculate this phenomenon in which the most affected part of the platelet is inside the cell. This frequency could activate the intracellular organelles in unleashing chemical agonists stored in these areas, such as the so-called ‘killer protein’ (Josefsson et al., 2012), to ultimately lead to platelet apoptosis. Although there is no experimental data that could be used to validate these predictions, they can be examined experimentally, which is the most exciting point about a model (Sedwick, 2014). These findings may suggest that, similar to all cells, platelets responses to mechanical loadings could be used in different relevant diagnoses and therapeutic procedures.
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