Photo-acoustic tomography based on laser optical feedback imaging of surface displacements.

We present how a laser optical feedback imaging (LOFI) setup can be used for the optical detection of ultrasound in photo-acoustic tomography (PAT). A PAT image is reconstructed by an inversion algorithm using surface displacement measurements made at several locations with our LOFI setup and following the optical irradiation with a pulsed Nd:YAG laser of a sample with absorbing inclusions. The width of the reconstructed inclusions and the signal-to-noise ratio (SNR) of the reconstructed images are first studied on the numerical model of a sample with three absorbing inclusions (i.e., with three acoustic punctual sources). Finally, an experimental PAT image of a phantom composed of two polyamide tubes with an internal diameter of 800 µm filled with red ink and submerged at -3.5 mm depth in a tank filled with water is reconstructed. Experimentally, the water surface displacement measurements have been made with our LOFI vibrometer, which provides an amplitude sensitivity of 1 nm (for a single-shot measurement) in a detection bandwidth of roughly 1 MHz adapted to the detection of the polyamide tubes. Under our experimental conditions, the surface energy densities of the LOFI focalized beam for the detection and of the pulsed Nd:YAG laser used for the irradiation, are compatible with the maximum permissive exposure for future biomedical measurements. The SNR and the resolution of the reconstructed PAT images are in good agreement with the theoretical predictions.

Microscopic DTI accurately identifies early glioma cell migration: correlation with multimodal imaging in a new glioma stem cell model.

Monitoring glioma cell infiltration in the brain is critical for diagnosis and therapy. Using a new glioma Glio6 mouse model derived from human stem cells we show how diffusion tensor imaging (DTI) may predict glioma cell migration/invasion. In vivo multiparametric MRI was performed at one, two and three months of Glio6 glioma growth (Glio6 (n = 6), sham (n = 3)). This longitudinal study reveals the existence of a time window to study glioma cell/migration/invasion selectively. Indeed, at two months only Glio6 cell invasion was detected, while tumor mass formation, edema, blood-brain barrier leakage and tumor angiogenesis were detected later, at three months. To robustly confirm the potential of DTI for detecting glioma cell migration/invasion, a microscopic 3D-DTI (80 µm isotropic spatial resolution) technique was developed and applied to fixed mouse brains (Glio6 (n = 6), sham (n = 3)). DTI changes were predominant in the corpus callosum (CC), a known path of cell migration. Fractional anisotropy (FA) and perpendicular diffusivity (D⊥ ) changes derived from ex vivo microscopic 3D-DTI were significant at two months of tumor growth. In the caudate putamen an FA increase of +38% (p < 0.001) was observed, while in the CC a - 28% decrease in FA (p < 0.005) and a + 95% increase in D⊥ (p < 0.005) were observed. In the CC, DTI changes and fluorescent Glio6 cell density obtained by two-photon microscopy in the same brains were correlated (p < 0.001, r = 0.69), validating FA and D⊥ as early quantitative biomarkers to detect glioma cell migration/invasion. The origin of DTI changes was assessed by electron microscopy of the same tract, showing axon bundle disorganization. During the first two months, Glio6 cells display a migratory phenotype without being associated with the constitution of a brain tumor mass. This offers a unique opportunity to apply microscopic 3D-DTI and to validate DTI parameters FA and D⊥ as biomarkers for glioma cell invasion.

The brain tissue response to surgical injury and its possible contribution to glioma recurrence.

Surgery is the first line therapy for glioma. However, glioma recurs in 90 % of the patients in the resection margin. The impact of surgical brain injury (SBI) on glioma recurrence is largely overlooked. Herein, we review some of the mechanisms involved in tissue repair that may impact glioma recurrence at the resection margin. Many processes or molecules involved in tissue repair after brain injury are also critical for glioma growth. They include a wide array of secreted growth factors, cytokines and transcription factors including NFКB and STAT3 which in turn activate proliferative and anti-apoptotic genes and processes such as angiogenesis and inflammation. Because some residual glioma cells always remain in the tumor resection margin, there are now compelling arguments to suggest that some aspects of the brain tissue response to SBI can also participate to glioma recurrence at the resection margin. Brain tissue response to SBI recruits angiogenesis and inflammation that precede and then follow tumor recurrence at the resection margin. The healing response to SBI is double edged, as inflammation is involved in regeneration and healing, and has both pro- and anti-tumorigenic functions. A promising therapeutic approach is to normalize and re-educate the molecular and cellular responses at the resection margin to promote anti-tumorigenic processes involved in healing while inhibiting pro-tumorigenic activities. Manipulation of the inflammatory response to SBI to prevent local recurrence could also enhance the efficacy of other therapies such as immunotherapy. However, our current knowledge is far from sufficient to achieve this goal. Acknowledging, understanding and manipulating the double-edged role played by SBI in glioma recurrence is surely challenging, but it cannot be longer delayed.

Multiscale investigation of USPIO nanoparticles in atherosclerotic plaques and their catabolism and storage in vivo.

The storage and catabolism of Ultrasmall SuperParamagnetic Iron Oxide (USPIO) nanoparticles were analyzed through a multiscale approach combining Two Photon Laser Scanning Microscopy (TPLSM) and High-Resolution Transmission Electron Microscopy (HRTEM) at different times after intravenous injection in an atherosclerotic ApoE(-/-) mouse model. The atherosclerotic plaque features and the USPIO heterogeneous biodistribution were revealed down from organ's scale to subcellular level. The biotransformation of the nanoparticle iron oxide (maghemite) core into ferritin, the non-toxic form of iron storage, was demonstrated for the first time ex vivo in atherosclerotic plaques as well as in spleen, the iron storage organ. These results rely on an innovative spatial and structural investigation of USPIO's catabolism in cellular phagolysosomes. This study showed that these nanoparticles were stored as non-toxic iron compounds: maghemite oxide or ferritin, which is promising for MRI detection of atherosclerotic plaques in clinics using these USPIOs. From the Clinical Editor: Advance in nanotechnology has brought new contrast agents for clinical imaging. In this article, the authors investigated the use and biotransformation of Ultrasmall Super-paramagnetic Iron Oxide (USPIO) nanoparticles for analysis of atherosclerotic plagues in Two Photon Laser Scanning Microscopy (TPLSM) and High-Resolution Transmission Electron Microscopy (HRTEM). The biophysical data generated from this study could enable the possible use of these nanoparticles for the benefits of clinical patients.

Rapid-Steady-State-T1 signal modeling during contrast agent extravasation: toward tumor blood volume quantification without requiring the arterial input function.

PURPOSE: This study demonstrates how to quantify the tumor blood volume fraction (BVf) using the dynamic Rapid-Steady-State-T1 (RSST1 )-MRI method despite contrast agent (CA) leakage and without arterial input function (AIF) determination. METHODS: For vasculature impermeable to CAs, the BVf is directly quantified from the RSST1 signal amplitude. In case of CA extravasation, we propose a two-compartment model to describe the dynamic RSST1 signal increase. We applied the mathematical model in a pilot-study on a RG2-glioma model to compare extravasation of two Gd-based CAs. The BVf quantification using the mathematical model in a C6-glioma model (n = 8) with the clinical CA Gd-DOTA was validated using a ΔR2 *-steady-state MRI method with an USPIO and by immunohistochemical staining of perfused vessels labeled with Hoechst-33342 dye in the same rats. RESULTS: BVf in tumor and in healthy brain tissues (0.034 ± 0.005 and 0.026 ± 0.004, respectively) derived from the dynamic RSST1 signal were confirmed by ΔR2 *-steady-state MRI (0.036 ± 0.003 and 0.027 ± 0.002, respectively, correlation coefficient rS = 0.74) and by histology (0.036 ± 0.003 and 0.025 ± 0.004 respectively, rS = 0.87). CONCLUSION: Straightforward tumor BVf quantification without AIF determination is demonstrated in presence of CA leakage. The method will facilitate angiogenesis assessment in longitudinal neuro-oncologic studies in particular when monitoring the response to antiangiogenic therapies.

Gelatine-collagen photo-crosslinkable 3D matrixes for skin regeneration.

Immediate care of skin wounds and burns is essential to repair this mechanical and chemical barrier to infections. Hydrogels have become one of the standard methods for wound care. Here, gelatine-collagen photo-crosslinkable matrixes or hydrogels were manufactured by two-photon polymerization (TPP) or one-photon UV exposure using a Digital Light Processing (DLP) setup. Both techniques are able to construct matrixes from computer-aided design models, which is important for future clinical applications in which wound dressings should be customized. Although TPP can mimic the 3D dermo-epidermal junction with a high spatial resolution (i.e., ∼6 µm3), the manufacturing time was too slow to produce large wound dressings. Therefore, a DLP setup was explored in this study to fabricate large 2D matrixes of several cm2 using the same photo-resist as for TPP, except for the photoinitiator. The fibroblast viability, adherence, and proliferation were analysed in time on both 3D and 2D matrixes in vitro using two-photon microscopy. For both types of matrixes, the adherence and proliferation of fibroblasts (3T3-NIH) were optimal for stiff structures with a Young's modulus of 191 ± 35 kPa compared to softer matrixes of 37 ± 12 kPa. Fibroblast showed complete confluence on Day 14 after seeding on these matrixes, which may create the granulation tissue composed of fibronectin, collagen, and various proteoglycans in the future dermis before repair of the epidermis and disintegrating of their host matrix. For the monitoring of this repair, gelatine-collagen matrixes can easily incorporate bio-optical sensors for the simultaneous monitoring of inflammation processes and wound healing in time.

Matrix design for optimal pancreatic ß cells transplantation.

New therapeutic approaches to treat type 1 diabetes mellitus relies on pancreatic islet transplantation. Here, developing immuno-isolation strategies is essential to eliminate the need for systemic immunosuppression after pancreatic islet grafts. A solution is the macro-encapsulation of grafts in semipermeable matrixes with a double function: separating islets from host immune cells and facilitating the diffusion of insulin, glucose, and other metabolites. This study aims to synthesize and characterize different types of gelatin-collagen matrixes to prepare a macro-encapsulation device for pancreatic islets that fulfill these functions. While natural polymers exhibit superior biocompatibility compared to synthetic ones, their mechanical properties are challenging to reproduce. To address this issue, we conducted a comparative analysis between photo-crosslinked gelatin matrixes and chemically crosslinked collagen matrixes. We show that the different crosslinkers and polymerization methods influence the survival and glucose-stimulated insulin production of pancreatic ß cells (INS1) in vitro, as well as the in vitro and in vivo stability of the matrix and the immuno-isolation in vivo. Among the matrixes, the stiff multilayer GelMA matrixes (8.5 kPa), fabricated by digital light processing, were the best suited for pancreatic ß cells macro-encapsulation regarding these parameters. Within the alveoli of this matrix, pancreatic ß cells spontaneously formed aggregates.

Synergistic effect of cisplatin and synchrotron irradiation on F98 gliomas growing in nude mice.

Among brain tumors, glioblastoma multiforme appears as one of the most aggressive forms of cancer with poor prognosis and no curative treatment available. Recently, a new kind of radio-chemotherapy has been developed using synchrotron irradiation for the photoactivation of molecules with high-Z elements such as cisplatin (PAT-Plat). This protocol showed a cure of 33% of rats bearing the F98 glioma but the efficiency of the treatment was only measured in terms of overall survival. Here, characterization of the effects of the PAT-Plat on tumor volume and tumor blood perfusion are proposed. Changes in these parameters may predict the overall survival. Firstly, changes in tumor growth of the F98 glioma implanted in the hindlimb of nude mice after the PAT-Plat treatment and its different modalities have been characterized. Secondly, the effects of the treatment on tumor blood perfusion have been observed by intravital two-photon microscopy. Cisplatin alone had no detectable effect on the tumor volume. A reduction of tumor growth was measured after a 15 Gy synchrotron irradiation, but the whole therapy (15 Gy irradiation + cisplatin) showed the largest decrease in tumor growth, indicating a synergistic effect of both synchrotron irradiation and cisplatin treatment. A high number of unperfused vessels (52%) were observed in the peritumoral area in comparison with untreated controls. In the PAT-Plat protocol the transient tumor growth reduction may be due to synergistic interactions of tumor-cell-killing effects and reduction of the tumor blood perfusion.

Hypoxia-induced expression of VE-cadherin and filamin B in glioma cell cultures and pseudopalisade structures.

Most of our knowledge regarding glioma cell biology comes from cell culture experiments. For many years the standards for glioma cell culture were the use of cell lines cultured in the presence of serum and 20 % O2. However, in vivo, normoxia in many brain areas is in close to 3 % O2. Hence, in cell culture, the experimental value referred as the norm is hyperoxic compared to any brain physiological value. Likewise, cells in vivo are not usually exposed to serum, and low-passaged glioma neurosphere cultures maintained in serum-free medium is emerging as a new standard. A consequence of changing the experimental normoxic standard from 20 % O2 to the more brain physiological value of 3 % O2, is that a 3 % O2 normoxic reference point enabled a more rigorous characterization of the level of regulation of genes by hypoxia. Among the glioma hypoxia-regulated genes characterized using this approach we found VE-cadherin that is required for blood vessel formation, and filamin B a gene involved in endothelial cell motility. Both VE-cadherin and filamin B were found expressed in pseudopalisades, a glioblastoma pathognomonic structure made of hypoxic migrating cancer cells. These results provide additional clues on the role played by hypoxia in the acquisition of endothelial traits by glioma cells and on the functional links existing between pseudopalisades, hypoxia, and tumor progression.

Translation of the ecological trap concept to glioma therapy: the cancer cell trap concept.

Viewing tumors as ecosystems offers the opportunity to consider how ecological concepts can be translated to novel therapeutic perspectives. The ecological trap concept emerged approximately half a century ago when it was observed that animals can prefer an environment of low quality for survival over other available environments of higher quality. The presence of such a trap can drive a local population to extinction. The cancer cell trap concept is the translation of the ecological trap into glioma therapy. It exploits and diverts the invasive potential of glioma cells by guiding their migration towards specific locations where a local therapy can be delivered efficiently. This illustrates how an ecological concept can change therapeutic obstacles into therapeutic tools.

On the importance of the submicrovascular network in a computational model of tumour growth.

A computational model is potentially a powerful tool to apprehend complex phenomena like solid tumour growth and to predict the outcome of therapies. To that end, the confrontation of the model with experiments is essential to validate this tool. In this study, we develop a computational model specifically dedicated to the interpretation of tumour growth as observed in a mouse model with a dorsal skinfold chamber. Observation of the skin vasculature at the dorsal window scale shows a sparse network of a few main vessels of several hundreds micrometers in diameter. However observation at a smaller scale reveals the presence of a dense and regular interconnected network of capillaries about ten times smaller. We conveniently designate this structure as the submicrovascular network (SMVN).(1) The question that we wish to answer concerns the necessity of explicitly taking into account the SMVN in the computational model to describe the tumour evolution observed in the dorsal chamber. For that, simulations of tumour growth realised with and without the SMVN are compared and lead to two distinct scenarios. Parameters that are known to strongly influence the tumour evolution are then tested in the two cases to determine to which extent those parameters can be used to compensate the observed differences between these scenarios. Explicit modelling of the smallest vessels appears mandatory although not necessarily under the form of a regular grid. A compromise between the two investigated cases can thus be reached.

The role of fluctuations and stress on the effective viscosity of cell aggregates.

Cell aggregates are a tool for in vitro studies of morphogenesis, cancer invasion, and tissue engineering. They respond to mechanical forces as a complex rather than simple liquid. To change an aggregate's shape, cells have to overcome energy barriers. If cell shape fluctuations are active enough, the aggregate spontaneously relaxes stresses ("fluctuation-induced flow"). If not, changing the aggregate's shape requires a sufficiently large applied stress ("stress-induced flow"). To capture this distinction, we develop a mechanical model of aggregates based on their cellular structure. At stress lower than a characteristic stress tau*, the aggregate as a whole flows with an apparent viscosity eta*, and at higher stress it is a shear-thinning fluid. An increasing cell-cell tension results in a higher eta* (and thus a slower stress relaxation time t(c)). Our constitutive equation fits experiments of aggregate shape relaxation after compression or decompression in which irreversibility can be measured; we find t(c) of the order of 5 h for F9 cell lines. Predictions also match numerical simulations of cell geometry and fluctuations. We discuss the deviations from liquid behavior, the possible overestimation of surface tension in parallel-plate compression measurements, and the role of measurement duration.

3D two-photon polymerization of smart cell gelatin - collagen matrixes with incorporated ruthenium complexes for the monitoring of local oxygen tensions.

The extra cellular matrix plays a major role in the biomechanical properties of tissues that impact cell behavior and fate. It is therefore crucial to mimic these complex cell-matrix interactions in 3D cell cultures. Here, two-photon polymerization is applied to produce gelatin methacryloyl (GelMA) - collagen matrixes that further enable local pO2matrix measurement, when ruthenium complexes are used as photo-activators. The fluorescence intensity of these complexes has a direct and inverse relationship with the local pO2matrix. The 3D structures reached their maximum size in cell culture conditions after 3H with a swelling factor of ~1.5. Their shape and the ruthenium fluorescence intensity of the alveoli walls stayed constant for at least 2 weeks in the absence of cells. They were used in time series to monitor the local pO2matrix adjacent to cancer cells during their division, migration and the formation of a tumor tissue mass. At the presence of these cell activities that consume O2, a significant ~3-fold increase of the ruthenium fluorescence intensity in the alveoli walls was observed. This study demonstrates that online monitoring of the local pO2matrix is possible. The ruthenium complexes provide the bio-optical sensors that are useful for further analysis of cancer and healthy cell energy metabolism in a 3D matrix that better mimics in vivo conditions and migration paths. Unraveling the cancer cell metabolic adaptations in a changing micro-environment will help the development of new therapeutic opportunities. STATEMENT OF SIGNIFICANCE: In 3D cell cultures, monitoring pericellular pO2 is as critical as controlling pH. This facility is currently missing. Here, we take advantage of the direct and inverse relationship between pO2 and the fluorescence intensity of ruthenium complexes to generate stable gelatin-collagen matrixes able to continuously monitoring the pO2 at the pericellular level. The ruthenium complexes, which are photo-activators in the two-photon polymerization of these matrixes, became covalently bind to the collagen fibers. Indeed, local O2 consumption by cancer cells during migration, mitosis and tumor mass formation caused a 3-fold increase of the ruthenium fluorescence. In the future, incorporating ruthenium complexes with other bio-optical sensors will create new drug screening platforms that monitor cell culture parameters at the pericellular level.

Optimizing stem cell culture.

Stem cells always balance between self-renewal and differentiation. Hence, stem cell culture parameters are critical and need to be continuously refined according to progress in our stem cell biology understanding and the latest technological developments. In the past few years, major efforts have been made to define more precisely the medium composition in which stem cells grow or differentiate. This led to the progressive replacement of ill-defined additives such as serum or feeder cell layers by recombinant cytokines or growth factors. Another example is the control of the oxygen pressure. For many years cell cultures have been done under atmospheric oxygen pressure which is much higher than the one experienced by stem cells in vivo. A consequence of cell metabolism is that cell culture conditions are constantly changing. Therefore, the development of high sensitive monitoring processes and control algorithms is required for ensuring cell culture medium homeostasis. Stem cells also sense the physical constraints of their microenvironment. Rigidity, stiffness, and geometry of the culture substrate influence stem cell fate. Hence, nanotopography is probably as important as medium formulation in the optimization of stem cell culture conditions. Recent advances include the development of synthetic bioinformative substrates designed at the micro- and nanoscale level. On going research in many different fields including stem cell biology, nanotechnology, and bioengineering suggest that our current way to culture cells in Petri dish or flasks will soon be outdated as flying across the Atlantic Ocean in the Lindbergh's plane.

Vascular bifurcation mapping with photoacoustic microscopy.

The early detection of microvascular changes in cancer diagnosis is needed in the clinic. A change in the vascular bifurcation density is a biomarker for the sprouting activity. Here, Optical-Resolution PhotoAcoustic Microscopy is used for quantitative vascular bifurcation mapping in 2D after the creation of Virtual Tubes out of Bifurcations. In stacks of OR-PAM images of the hemoglobin distribution, bifurcations become tubes and are selected by the 3D tubeness filter. These fast analyses will be compared to a classical approach and are easier to implement for functional analysis of the vascular bifurcation density in healthy and diseased tissues.

Short-term effects of synchrotron irradiation on vasculature and tissue in healthy mouse brain.

The purpose of this study is to measure the effects of a tomographic synchrotron irradiation on healthy mouse brain. The cerebral cortexes of healthy nude mice were irradiated with a monochromatic synchrotron beam of 79 keV at a dose of 15 Gy in accordance with a protocol of photoactivation of cisplatin previously tested in our laboratory. Forty-eight hours, one week and one month after irradiation, the blood brain barrier (BBB) permeability was measured in the irradiated area with intravital multiphoton microscopy using fluorescent dyes with molecular weights of 4 and 70 kDa. Vascular parameters and gliosis were also assessed using quantitative immunohistochemistry. No extravasation of the fluorescent dyes was observed in the irradiated area at any measurement time (48 h, 1 week, 1 month). It appears that the BBB remains impermeable to molecules with a molecular weight of 4 kDa and above. The vascular density and vascular surface were unaffected by irradiation and no gliosis was induced. These findings suggest that a 15 Gy/79 keV synchrotron irradiation does not induce important damage on brain vasculature and tissue on the short term following irradiation.

Fluorescent Pluronic nanodots for in vivo two-photon imaging.

We report the synthesis of new nanosized fluorescent probes based on bio-compatible polyethylene-polypropylene glycol (Pluronic) materials. In aqueous solution, mini-emulsification of Pluronic with a high fluorescent di-stryl benzene-modified derivative, exhibiting a two-photon absorption cross section as high as 2500 Goeppert-Mayer units at 800 nm, leads to nanoparticles exhibiting a hydrodynamic radius below 100 nm. We have demonstrated that these new probes with luminescence located in the spectral region of interest for bio-imaging (the yellow part of the visible spectrum) allow deep (500 microm) bio-imaging of the mice brain vasculature. The dose injected during our experiments is ten times lower when compared to the classical commercial rhodamine-B isothicyanate-Dextran system but gives similar results to homogeneous blood plasma staining. The mean fluorescent signal intensity stayed constant during more than 1 h.

Multi-wavelength photo-acoustic microscopy in the frequency domain for simultaneous excitation and detection of dyes.

An optical-resolution photoacoustic microscope with modulated CW laser diodes allowing multi-channel imaging is presented that can be used for both imaging biological tissues and for targeted photo-dynamic therapy (PDT) varying the optical power and exposure time. The effects of this therapy are immediately monitored in order to optimize the time of irradiation. After the description of the experimental setup, in vitro and in vivo applications are presented on a synthetic sample and on the mouse ear using hemoglobin as endogenous and methylene blue as exogenous dye for imaging and PDT, respectively.

In vivo staining of neocortical astrocytes via the cerebral microcirculation using sulforhodamine B.

Staining and imaging glial cells in vivo while observing the microvasculature could help understand brain physiology, namely neuronal-glial-vascular communication. Two-photon excitation microscopy provides a means to monitor these interactions at the cellular level in living animals, but the cells of interest must be fluorescent. Injecting dyes intravenously is a rapid and quasi noninvasive method to stain cells in the brain. It necessitates that the dye is soluble in the blood plasma and crosses the blood brain barrier (BBB). We demonstrate here, using two-photon imaging, that sulforhodamine B (SRB) crosses the BBB and stains in vivo, specifically mouse astrocytes. This is confirmed by experiments on primary neurons and astrocytes cultures showing the preferential SRB staining of the latter. SRB is rapidly eliminated from the blood, which allows repeated injections in longitudinal studies.

Subtraction method for intravital two-photon microscopy: intraparenchymal imaging and quantification of extravasation in mouse brain cortex.

Brain pathologies, including stroke and tumors, are associated with a variable degree of breakdown of the blood-brain barrier (BBB), which can usefully be studied in animal models. We describe a new optical technique for quantifying extravasation in the cortex of the living mouse and for imaging intraparenchymal tissue. Leakiness of the BBB was induced by microbeam x-irradiation. Two fluorescent dyes were simultaneously infused intravenously, one of high molecular weight (fluorescein-labeled dextran, 70 kDa, green fluorescence) and one of low molecular weight (sulforhodamine B, 559 Da, red fluorescence). A two-photon microscope, directed through a cranial window, obtained separate images of the two dyes in the cortex. The gains of the two channels were adjusted so that the signals coming from within the vessels were equal. Subtraction of the image of the fluorescein-dextran from that of the sulforhodamine B gave images in which the vasculature was invisible and the sulforhodamine B in the parenchyma could be imaged with high resolution. Algorithms are presented for rapidly quantifying the extravasation without the need for shape recognition and for calculating the permeability of the BBB. Sulforhodamine B labeled certain intraparenchymal cells; these cells, and other details, were best observed using the subtraction method.