Motion and twisting of magnetic particles ingested by alveolar macrophages in the human lung: effect of smoking and disease
© Möller et al; licensee BioMed Central Ltd. 2006
Received: 15 March 2006
Accepted: 15 May 2006
Published: 15 May 2006
Magnetic microparticles being ingested by alveolar macrophages can be used as a monitor for intracellular phagosome motions and cytoskeletal mechanical properties. These studies can be performed in the human lung after voluntary inhalation. The influence of cigarette smoking and lung diseases on cytoskeleton dependent functions was studied.
Spherical 1.3 μm diameter ferrimagnetic iron oxide particles were inhaled by 17 healthy volunteers (40 – 65 years), 15 patients with sarcoidosis (SAR), 12 patients with idiopathic pulmonary fibrosis (IPF), and 18 patients with chronic obstructive bronchitis (COB). The retained particles were magnetized and aligned in an external 100 mT magnetic field. All magnetized particles induce a weak magnetic field of the lung, which was detected by a sensitive SQUID (superconducting quantum interference device) sensor. Cytoskeletal reorganizations within macrophages and intracellular transport cause stochastic magnetic dipole rotations, which are reflected in a decay of the magnetic lung field, called relaxation. Directed phagosome motion was induced in a weak magnetic twisting field. The resistance of the cytoplasm to particle twisting was characterized by the viscosity and the stiffness (ratio between stress to strain) of the cytoskeleton.
One week after particle inhalation and later macrophage motility (relaxation) and cytoskeletal stiffness was not influenced by cigarette smoking, neither in healthy subjects, nor in the patients. Patients with IPF showed in tendency a faster relaxation (p = 0.06). Particle twisting revealed a non-Newtonian viscosity with a pure viscous and a viscoelastic compartment. The viscous shear was dominant, and only 27% of the shear recoiled and reflected viscoelastic properties. In patients with IPF, the stiffness was reduced by 60% (p < 0.02). An analysis of the shear rate and stress dependence of particle twisting allows correlating the rheological compartments to cytoskeletal subunits, in which microtubules mediate the pure viscous (non-recoverable) shear and microfilaments mediate the viscoelastic (recoverable) behavior. The missing correlation between relaxation and particle twisting shows that both stochastic and directed phagosome motion reflect different cytoskeletal mechanisms.
Faster relaxation and a soft cytoskeleton in patients with IPF indicate alterations in cytoskeleton dependent functions of alveolar macrophages, which may cause dysfunction's in the alveolar defense, like a slower migration, a retarded phagocytosis, a disturbed phagosome lysosome fusion and an impaired clearance.
The lungs with about 140 m2 surface area  represent the organ of the human body with the biggest contact area to the environment. Every breath transports many environmental particles into the lungs, which are partially removed and deposited. The different areas of the lung have different mechanisms of deposition and clearance . Clearance from the airway is primarily due to mucociliary transport, where most particles are removed within 24 h from the lungs. The alveolar region is not covered by a mucus layer. Alveolar macrophages are resident in each of the alveoli and phagocytize foreign materials. Phagocytosis transfers the microparticles into phagosomes of the macrophage. After fusion with lysosomes ingested particles, bacteria or viruses are digested due to acidic pH within phagolysosomes and the release of reactive substances, such as oxygen radicals [3–5]. The cytoskeleton of AM is crucially involved in these defense reactions, including locomotion and cell migration, phagocytosis, intracellular transport, phagosome-lysosome fusion and signal transduction [6–8].
Magnetopneumography (MPG) uses ferrimagnetic iron oxide particles as a tracer to investigate the long-term clearance from the alveolar region of the human lungs [9–12]. These particles are non-toxic and non-cancinogenic , and can be inhaled and detected by sensitive magnetic field sensors. Because of the chemical stability, these particles can be used as a probe for intracellular phagosome motions and cytoskeletal integrity. Permanent cytoskeletal reorganizations and the intracellular transport cause a randomization of the magnetic dipole particles, which is reflected in a decay of the magnetic lung field and is called relaxation. Relaxation is an in vivo measure of macrophage motility, which is important in several defense reactions, like cell migration, phagocytosis, phagosome – lysosome fusion etc. Directed (external) phagosome motions are induced in a weak magnetic twisting field in order to investigate the mechanical properties of the cytoskeleton. Application of continuous and discrete twisting stress yields the rheological properties of the cytoskeleton, which reflects the integrity of the cytoskeleton and the role of the different cytoskeletal units in phagosome transport.
Previously, we have developed protocols to study cytoskeleton associated functions in macrophages, such as phagosome transport, mechanical cytoskeletal integrity and phagocytosis, using ferromagnetic microparticles, in vitro in cell cultures and in vivo after voluntary inhalation [14–17]. Magnetic twisting cytometry (MTC) has been used to investigate the role of the different cytoskeletal structures in macrophage function after application of selectively acting cytoskeletal drugs (Cytochalasin D, Nocodazole; ). Additionally it has been shown that MTC can monitor cytotoxicity of GaAs-particles in vivo in lung macrophages of animals [18, 19] and of ultrafine particles in vitro [20, 21].
The aim of this study was first, to investigate stochastic and directed phagosome motions in healthy subjects with respect to in vivo reactions of macrophages to a chronic cigarette smoke exposure, which was evident from in vitro studies [22–24]. The second objective was to verify whether reactions seen in smokers accumulate in patients with chronic obstructive bronchitis (COB), which is primarily the result of a long cigarette smoking history, and third, to correlate phagosome motions with interstitial lung diseases, like sarcoidosis (SAR) and idiopathic lung fibrosis (IPF), where the ethiology of the disease is not known. It was proposed that a chronic inflammation in the lungs of these patients might influence the phagosome transport and the cytoskeletal integrity.
Subjects and pulmonary function testing
Age, cumulative cigarette smoke consumption, and lung function data of all subjects of the study.
54 +/- 7
48 +/- 14
49 +/- 15
60 +/- 8
49 +/- 18
18 +/- 13
15 +/- 6
40 +/- 25
105 +/- 15
93 +/- 15 (*)
82 +/- 23 (*)
72 +/- 28 (**)
91 +/- 10
94 +/- 6 (ns)
94 +/- 15 (ns)
69 +/- 19 (**)
0.22 +/- 0.08
0.16 +/- 0.1 (ns)
0.22 +/- 0.14 (ns)
0.28 +/- 0.16 (ns)
RV % TLC
32 +/- 6
33 +/- 6 (ns)
37 +/- 12 (ns)
45 +/- 10 (**)
112 +/- 25
89 +/- 23 (*)
91 +/- 33 (ns)
119 +/- 34 (ns)
118 +/- 13
102 +/- 17 (**)
86 +/- 19 (**)
103 +/- 25 (ns)
107 +/- 35
92 +/- 17 (ns)
90 +/- 45 (ns)
52 +/- 37 (**)
82 +/- 27
75 +/- 24 (ns)
71 +/- 40 (ns)
32 +/- 25 (**)
62 +/- 27
48 +/- 22 (ns)
51 +/- 27 (ns)
22 +/- 18 (**)
107 +/- 33
98 +/- 14 (ns)
82 +/- 13 (**)
92 +/- 21 (ns)
Body plethysmography and spirometry were performed using a Jäger Masterlab (Erich Jäger, Würzburg, Germany). Relative values of conventional lung parameters were calculated by normalizing to the reference values proposed by the European Community for Steel and Coal . The transfer factor of the lung for carbon monoxide (TL,CO) was calculated as proposed by Cotes . A lung function test and the MPG measurement of the natural ferromagnetic contamination of the lungs of every subject were obtained before inhalation. MPG measurements were performed 30 min., two days, one week, one month, five months and nine months after particle inhalation.
Preparation of ferrimagnetic tracer-particles, inhalation and detection
The preparation, inhalation and detection of the magnetic particles is described in detail elsewhere . In brief spherical monodisperse ferrimagnetic iron-oxide particles (Fe3O4, 2.9 μm aerodynamic, 1.35 μm geometric diameter, σg < 1.1) were produced by a Spinning Top Aerosol Generator (STAG) , concentrated by using a virtual impactor, and directly inhaled by the participants under standard conditions (250 cm3/s flow rate, 1 L tidal volume). After inhalation, the subject lies on a bed with the lungs directly under the magnetizing coils. Magnetization is performed by discharging a capacitor battery into a 40 cm diameter copper coil. After the magnetizing current has decayed, the magnetized particles produce a weak remanent magnetic lung field (LF) of about 100 pT, which was detected by moving the subject under a superconducting magnetic field sensor (SQUID, superconducting quantum interference device). Particle twisting was performed by a weak magnetizing current in the 40 cm diameter copper coil, which was controlled for discrete time durations.
For MPG measurements about 1 mg of iron oxide particles were deposited in the lung. This amount is low compared to occupational exposure at work places, such as welders [30, 31]. In a previous study a bronchoalveolar lavage was performed in one subject 7 days after particle inhalation . In this study only single particles could be found in the alveolar macrophages, confirming the rotational behavior of single particles in cells.
Correction for non-rotational particles (phagocytosis)
During inhalation, the particles are deposited on the epithelial surface of the lungs. Over the following 24 hours, they are phagocytized by alveolar macrophages. Directly after inhalation, particle twisting in a weak magnetic field reveals an alignment asymmetry, which reflects a certain fraction of non-rotatable particles . After the particles are pulse magnetized, they are aligned with the magnetizing field. Then they are twisted by a reverse magnetic field into the opposite direction. When again reversing the twisting field, the particles are rotated to the initial direction of pulse magnetization. Free particles stack on the epithelium, are unable to follow this rotation and induce an asymmetry in the particle alignment, which allows estimating the fraction of non-rotatable particles. Directly after inhalation (30 min.), about 50% of the particles are not rotatable. This fraction decreases in the following hours to 5 – 10%. We suggest that the non-rotatable particles are not phagocytized by macrophages and stick to the alveolar epithelium. In vitro studies with J774 macrophages have shown that all particles which are phagocytized by macrophages are rotatable in weak twisting fields. Microscopic investigations have shown that these particles are covered by surfactant, displacing them into the epithelial lineage . This tight contact to the epithelium hinders the particle rotation for a complete alignment. This in vivo measurement of non-rotatable particles measures the phagocytosis process in the human lungs. All relaxation and particle twisting data are corrected by the fraction of non-rotatable particles.
Macrophage motility (relaxation)
Macrophage motility (randomization energy)
where m is the magnetic dipole moment and BM is the external weak twisting field. This allows a direct measure of Er. The experiments were performed in a way that first, all particles were magnetized and aligned in a strong magnetic field, yielding the maximum lung field (Bmax). Relaxation was allowed over a period of 10 min., during which the lung field decayed below 50% of the initial value. Then a weak field of 1 mT strength was applied over 3 min. in order to realign the particles. The equilibrium lung field (Beq) is a measure of the achieved dipole alignment. Cellular energy Er was then estimated from B eq (B M ) = Bmax·L(α). This method of estimating cell motility is independent of the viscoelastic environment.
Cytoskeletal integrity: mechanical properties of the cytoskeleton of macrophages
Application of a weak magnetic field mediates an external particle twisting (Figure 1) and allows the investigation of mechanical properties of the cytoskeleton, like cytoplasmic rheology and mechanical integrity. Experiments for both discrete and continuous particle twisting were performed. Discrete particle twisting implies the force application for a short time period of 10 sec. This causes an angular shear of the particles and a measure of apparent viscosity. If the surrounding medium has elastic properties, we get elastic recoil which yields information about substructures of the cytoskeleton. During continuous particle rotation, the twisting field BM is applied for 3 min. until the dipole orientation reaches equilibrium.
Brownian rotational particle motion has an influence on particle twisting in a weak magnetic field, and, as was shown above, it prevents complete particle alignment. The influence is significant when the twisting force is small, as we have in small twisting fields, or when the magnetic dipole aligns with the twisting field, which is the case at continuous particle twisting during the equilibrium phase. For the estimation of viscous and elastic parameters, the influence of Brownian motion was neglected.
Continuous particle twisting
where dθ/dt is the shear rate, σ is the applied shear stress. The viscosity η is the constant of proportionality. The complete course of particle twisting under certain boundary conditions is described in detail in the Appendix.
The curve NV in Figure 4a shows particle twisting in a Newtonian viscosity (ηm), and the time constant was adapted to the initial measurements. Increasing duration of stress application reveals a retarded particle rotation in the cells, which implies stiffening and non-Newtonian behavior of the cytoskeleton. The non-Newtonian apparent viscosity is characterized by the shear rate dependence according to Eq. A6 and is shown in Figure 4b. Apparent viscosity increases with decreasing shear rate sr according to a power law: η ~ sr-α, where the power α is near unity. This behavior is called pseudoplastic  and is characteristic for particle twisting in alveolar macrophages and in J774 macrophages . Simulations have shown that this behavior originates in part by elastic properties . The previous analyses show that the first measure of apparent viscosity after 5 sec. stress duration (ηm) is a reliable estimation of the viscosity of a more complex viscoelastic system.
Discrete particle twisting (viscoelastic recoil)
Continuous particle twisting experiments demonstrate non-Newtonian viscous properties, but do not allow a direct measure of cytoskeletal elasticity. A visualization of cytoskeletal elasticity was achieved by applying the twisting field for a short time period of 10 sec. According to Hoke's law the applied shear stress is proportional to the strain (rotation angle θ), and the constant of proportionality is the rigidity ν.
σ = ν·θ (3)
Cell stiffness was estimated as the ratio between mean stress to strain after a constant twisting duration of 10 sec.:
This analysis of stiffness does not view for specific viscous or elastic properties. Therefore this parameter provides an integral description of the cytoskeletal mechanical properties.
Results of the measurement of relaxation and of randomization energy, Er
0.76 +/- 0.04
0.79 +/- 0.03 (**)
0.79 +/- 0.07 (ns)
0.75 +/- 0.06 (ns)
20.6 +/- 7.0
14.5 +/- 3.8 (**)
14.2 +/- 5.6 (**)
16.9 +/- 5.4 (ns)
259 +/- 61
257 +/- 39 (ns)
221 +/- 47 (ns)
239 +/- 57 (ns)
66.1 +/- 16.3
57.5 +/- 9.1 (ns)
50.2 +/- 12.5 (**)
55.7 +/- 14.5 (*)
0.61 +/- 0.05
0.63 +/- 0.02 (ns)
0.60 +/- 0.04 (ns)
0.59 +/- 0.07 (ns)
0.23 +/- 0.07
0.24 +/- 0.04 (ns)
0.20 +/- 0.06 (ns)
0.21 +/- 0.07 (ns)
Er, 10-18 J
6.0 +/- 2.1
4.6 +/- 1.5 (*)
5.2 +/- 2.6 (ns)
5.4 +/- 3.1 (ns)
Lung function data
Lung function data of the study groups are given in Table 1. Healthy smokers had normal lung function data (FEV1 = 108 +/- 13 % predicted). The study groups did not differ significantly from healthy subjects in their airway resistance (Raw). The severity of airflow limitation based on values of FEV1 (% predicted) was mild or moderate in the group of patients with COB, SAR and IPF. Patients with chronic obstructive bronchitis (COB) had a significantly lower FEV1/VC ratio and MEF75-25 than that of healthy subjects. In patients with SAR and IPF, vital capacity was significantly lower than that of healthy subjects. As for TL,CO, only patients with IPF differed significantly from healthy subjects.
Macrophage motility (relaxation) in healthy and diseased subjects
Table 2 and Figure 2 show the results of relaxation in all investigated groups. In healthy subjects and in patients none of the relaxation parameters was significantly influenced by cigarette smoking. Therefore, in every group, the data of NS and S were matched together, allowing the direct relation of all relaxation data of the patient groups to the healthy subjects. Figure 2 gives a plot of the mean relaxation curve in every group. This curve is a function of two exponential terms (Eq. A2) and was calculated by the mean relaxation time constants of every group. The solid line describes the behavior in healthy subjects (Healthy) together with the relative decay after 1 min. and after 5 min., b1 and b5, and the corresponding standard deviation (SD). The mean relaxation behavior in patients (COB, SAR and IPF) is in the range of relaxation in healthy subjects. We can estimate in tendency a faster relaxation in patients with COB and with IPF.
More structural information can be obtained from the analysis of the two exponential- term relaxation model. In SAR, the fraction of slow relaxation (Ar_s) is significantly increased (p = 0.01). In SAR and in IPF, there is an initially faster decay (smaller Tr_f) compared to healthy (p < 0.01). In IPF, the slow relaxation is faster (smaller Tr_s) in tendency (p = 0.07).
Randomization energy Er
Cellular randomization energy estimated by the Langevin model is Er ≈ 10-18 J. This value is much higher than thermal energy (kT = 4.2·10-21 J at 37°C) and shows that thermal energy can be neglected in the analysis of intracellular phagosome motions. In vitro investigations have shown that Er is correlated with the energy (ATP) status of the macrophages . The hydroxylation of one ATP molecule yields an energy of ≈ 10-19 J. Cellular energy Er represents the motor of relaxation and phagosome transport in the hydrodynamic relaxation model. In healthy subjects, the cell energy Er is not influenced by cigarette smoking, allowing the matching of NS, S and XS data. The data of all investigated groups are shown in Table 2. Compared to healthy subjects, Er is lower in SAR (p < 0.05). In IPF and COB, Er is lower in tendency.
Continuous particle twisting
The increase of apparent viscosity η with decreasing shear rate sr according to the power law η ~ sr-α(Figure 4) could be verified in all measurements. The power was α = 0.98 ± 0.02, implying a linear increase of apparent viscosity with decreasing shear rate. The power α was not influenced by cigarette smoking or by disease. Using the power law behavior, the normalized viscosity η5 at a shear rate of 0.05 rad/s was estimated for all subjects and is shown in Figure 6b. The principal behavior of η5 in healthy subjects and in patients is not different to ηm (Figure 6a), but the data have a smaller variation.
Discrete particle twisting
Cell stiffness is not different in patients with COB compared to healthy, as shown in Figure 7. The pure viscous shear reveals results comparable to healthy subjects, but the viscoelastic compartment shows a faster elastic recoil (Terc = 17 ± 6 s, p < 0.01), which may originate from a significantly lowered viscosity in this compartment (η2 = 107 ± 42 Pa·s, p < 0.01). Finally, the elasticity modulus ν remains unchanged compared to healthy.
Patients with SAR show no modifications in the integrating parameter cell stiffness. The shear strain in the pure viscous compartments yields a viscosity comparable to healthy subjects. The viscoelastic compartments has a faster elastic recoil (Terc = 20 ± 7 s, p = 0.01), which is not correlated with a (compared to healthy subjects) modified viscosity in this compartment, but the elasticity modulus is increased in tendency.
In patients with IPF, cytoskeletal stiffness is significantly reduced (4.2 ± 1.2 Pa, p < 0.02), as shown in Figure 7. This reduced stiffness primarily results from a decreased viscosity of the pure viscous compartment (η1 = 61 ± 15 Pa·s, p = 0.02). The viscoelastic compartment (including elastic recoil time constant) is not altered in patients with IPF compared to healthy. This is in agreement with continuous particle twisting where apparent viscosity was lowered.
Effect of cigarette smoking in healthy subjects
Relaxation shows no differences between healthy NS and S, although there seems to be in tendency a slower decay with a reduced motility in healthy smokers. This result is surprising because we expected a strong influence of cigarette smoking on AM motility and on relaxation. Two in vitro studies on relaxation in smokers and non-smokers have been done [22–24]. In both studies, alveolar macrophages were harvested by bronchoalveolar lavage (BAL) from the human lungs and then incubated together with magnetic micro particles for 24 hours. Relaxation was measured in a cytomagnetometric system. In Valberg's study, relaxation was faster in smokers compared to non-smokers. In this study, the cigarette smoke consumption was not clearly reported, but the subjects seem to be younger (20 – 30 years of age). In the second study by Gehr and Im Hof, relaxation did not show differences between NS and S. The subjects in this study had a mean cumulative cigarette smoke consumption of 8 PY, suggesting that they are younger. In agreement to Gehr's and Imhof's study our data suggest that even with a high cigarette smoke consumption of 45 PY cell organelle motions are not affected. We have to keep in mind that our data do not report the response of an acute cigarette smoking. In smokers there seems to be an adaptation and the primary response of the lung to the permanent cigarette smoke exposure is the increase in the number of macrophages in the lungs. The differences found in one of the in vitro studies are probably influenced by the BAL procedure and by the incubation method.
In agreement to the relaxation behavior in relation to cigarette smoking is the result for the driving energy of relaxation. Cellular energy Er was not influenced by cigarette smoking. The significantly lower Er in SAR and in tendency in IPF and in COB may account for effects on the energy status and metabolism of macrophages.
Additionally, cigarette smoking did not influence any of the mechanical properties estimated by continuous or by discrete particle twisting. The results suggest that cigarette smoking does not influence intracellular phagosome transport processes, (relaxation), which reflects macrophage motility, nor directed phagosome motion (magnetic twisting), which reflects the cytoskeletal integrity. The biochemical and immunological response of the lungs to chronic cigarette smoking has no correlation to the cell motility and mechanical integrity of the cytoskeleton of macrophages.
Phagosome motion and twisting in lung diseases
Although it is known from biochemical and immunological investigations that macrophages are activated in SAR, and specifically during exacerbations, such as enhanced proliferation activity ; enhanced release of tumor necrosis factor alpha (TNF α) and interleukin-1 (IL-1) , the course of relaxation (b5) does not differ significantly from healthy subjects, only the initial decay was accelerated. In addition Er, the driving energy of relaxation, was lower in SAR, which is opposite to expectations from a faster initial relaxation, suggesting an increase in Er. But the faster initial relaxation in SAR correlates with the faster elastic recoil after discrete particle twisting, which may reveal altered elastic properties of the cytoskeleton. The data show that the rheological properties of the cytoskeleton have significant impact on phagosome motion and on relaxation. We have previously shown that cytoskeletal elasticity is primarily related to the actin cytoskeleton , suggesting that the SAR may influence the microfilamentous structure of the macrophages. The limited effects of the disease SAR on the cytoskeletal dynamics may result in part from the stable status of the disease during the investigation period and the use of specific drugs.
In COB, a faster initial relaxation was recorded, which correlates with the faster elastic recoil in discrete particle twisting. The compartmental analysis showed that reason for this faster recoil is a lowered viscosity in the viscoelastic compartment (η2).
The faster relaxation in IPF correlates with significant alterations in the mechanical integrity of the cytoskeleton of the macrophages. This is verified both in continuous and in discrete phagosome twisting, where all viscosities and the stiffness of the cytoskeleton are lowered. We conclude that IPF coincides with a structural damage of the cytoskeletal integrity, resulting in multiple cytoskeletal dysfunctions. In vitro, such damage can be induced by cytoskeletal drugs, such as Cytochalasin D, which disrupts microfilaments, Nocodazole, which disrupts microtubuli, or Acrylamide, which disrupts intermediate filaments [16, 42]. Destruction of cytoskeletal filaments of macrophages can cause several dysfunctions, such as retarded migration and phagocytosis, together with a retarded cytotoxicity against bacteria or viruses, besides other immunological and biochemical dysfunctions. Comparable inhibition of cytoskeletal functions was shown after incubation of macrophages with toxic particles , or with different types of ultrafine environmental particles, resulting in a impairment of relaxation, and a stiffening of the cytoskeleton , and it could be shown that the calcium metabolism plays an important role in this dysfunctions . The significant damage in cytoskeletal structure and function may explain the impaired phagocytosis  and impaired alveolar clearance  in IPF patients.
Analysis of correlation
Estimation of the relaxation parameters, cellular energy, cumulative, and discrete particle twisting are separate measurements. A correlation analysis of all data provides information about the interconnection of parameters and can be used to test the proposed rheological models. The Voigt-Maxwell system used in this study is the simplest configuration giving characteristic features.
The randomization energy Er is the motor of relaxation. Therefore, a strong correlation between the relaxation time constants and Er was expected, which can not be verified by the data. Er shows a strong correlation with the viscosity parameters, both estimated from discrete as well as from continuous particle twisting, where the pure viscous compartment η1 is the relevant parameter (coefficient of correlation, cc = 0.64, p < 0.001). This suggests that the viscosity estimations are influenced by the intracellular phagosome transport mechanisms.
Continuous particle twisting
Discrete particle twisting
Since the viscous shear is dominant in discrete particle twisting and the slow decay is the main relaxation behavior, we suggest that both phenomena result from the same hydrodynamic and cytoskeletal unit, the viscosity η1. But in the correlation analysis, the two parameters Tr_s and η1 appear to be independent. None of the relaxation parameters correlate with any of the twisting parameters. These results suggest that relaxation (cellular phagosome motion) and magnetic particle twisting (directed external phagosome motion) may reflect two independent mechanisms within the cell dynamics. Relaxation measures the transport of phagosomes along cytoskeletal units, while magnetic particle twisting measures the mechanical integrity (viscoelasticity) of the cytoskeletal units via the application of external forces.
There are several indications that vesicles and phagosomes are primarily coupled to the microtubules . Our data are in agreement with these studies and suggest that the pure viscous compartment of discrete particle twisting reflects the mechanical behavior of microtubules. Because microfilaments appear highly viscoelastic [48, 49], the viscoelastic compartment may be associated with the microfilaments.
Although the role of the different cytoskeletal substructures during a defense reaction in the lung is not understood, we can conclude that the method delivers information about basic physiological processes in macrophages. Microfilaments mediate phagocytosis and the formation of phagosomes, and the microtubuli provide the structure for phagosome trafficking and phagosome – lysosome fusion. Therefore MPG investigations deliver in vivo information about the function of macrophages and might help to interpret pathophysiological reactions in macrophages in the lungs.
Another feature of MPG might be an in vivo monitor of the action of toxic pollutants and of drugs on macrophages in the lungs.
Hydrodynamic model of relaxation
A first step to model relaxation is to describe the stochastic particle twisting as rotational Brownian motion. In this model, thermal energy kT induces random rotational pulses on the particles that cause a stochastic twisting of the magnetic dipole particles. These rotational movements happen within a viscous environment (viscosity η). We apply this model to the intracellular rotation of particle containing phagosomes in macrophages, where kT is replaced by some unknown cellular energy Er. When using spherical particles, the decay of the lung field (LF) follows an exponential function according to :
where V is the volume of the particles, η is the viscosity of the cytoplasm, and κ is the rotational shape factor (κ = 6 for spheres). An exponential relaxation could be verified using monodisperse spherical magnetic particles, which were suspended in a Newtonian viscosity .
In vivo and in vitro investigations of relaxation with spherical particles in macrophages yield deviations from a single exponential decay. An initially fast decaying phase (over the first 30 s) was followed by a slower exponential phase lasting up to 20 min. Therefore, the decay was fitted by a double exponential function:
where Tr_f and Tr_s are the time constants for the fast and the slow relaxation phases, respectively; Ar_s describes the fraction of relaxation following the slow phase. About 20% of the LF followed the fast decay with a half-time of 20 sec., while 80% of the LF followed the slowly decay with half-times near 200 sec. Further studies have shown that both the fast and the slow decaying fraction depend on the particle size .
Particle twisting in a magnetic field (secondary magnetization)
Secondary magnetization describes the twist of the dipole particles in a weak magnetic field BM. A magnetic torque Nmag = m BM sinθ acts on a remanent dipole m in an external magnetic field BM that twists the particle until the dipole is aligned with the magnetizing field: θ is the angle between BM and m. The viscosity η of the surrounding fluid resists this twist, resulting a hydrodynamic retarding torque Nhyd = -κVη·dθ/dt; dθ/dt is the angular velocity of rotation (shear rate), V is the volume and κ is the shape factor of the particle (κ = 6 for spheres). The balance of both torques describes the dipole particle rotation:
with the solution:
MT = m/V is the remanent magnetization of the particles, θ0 is the initial orientation of the dipole m. Only the component of magnetic moment parallel to the magnetizing field, m·cosθ(θ0,t), is detected. From Eq. A4, cosθ(θ0,t) can be expressed as:
The time constant τ (Eq. A4) shows that particle twisting is independent of particle size. This method of viscosity measurement was calibrated with magnetite spheres suspended in a highly viscous Newtonian fluid .
Equations A3 – A5 only hold for Newtonian viscosities, where the viscosity is independent of the shear rate. Including elastic properties makes the system non-Newtonian. Nevertheless, secondary magnetization measurements can be analyzed with Eq. A3, yielding a shear rate dependent apparent viscosity. Since the relative LF is a measure of cosθ(t), the orientation angle θ(t) = arccos(B(t)/Bmax) and the shear rate Δθ/Δt can be predicted. Then Eq. A3 is used to estimate the apparent viscosity as:
The relaxation and particle twisting measurements have shown that the viscosity of the cytoskeleton behaves non-Newtonian and has elastic properties. The simplest viscoelastic body is a Voigt-body, where the viscosity η is in parallel with an elastic element with rigidity ν. The differential equation for this simple viscoelastic system is:
θ0 is the orientation before particle twist. During particle rotation in a viscoelastic Voigt-body, elastic energy is stored. After removing the magnetic torque (BM = 0), elastic recoil happens. Eq. A7 predicts elastic recoil behavior (σ = 0) as:
Terc is the time constant of elastic recoil. Knowing the viscosity η, the rigidity modulus ν can be estimated from the time path of the elastic recoil process. In a Voigt-body, elastic recoil returns the dipoles to their orientation before stress application, independent of applied stress.
The experimental results show this behavior only for weak twisting fields . Particle twisting with higher stress does not yield complete recoil; some non-recoverable strain remains. Non-recoverable strain might indicate permanent deformations in the cytoplasm. For a rheological description, the Voigt-body was extended by an additional viscous element. The whole system is called a Voigt-Maxwell body.
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