Invasion Assay Using 3D Matrices

python画屈服准则屈服准则通常用来描述材料在受力作用下发生塑性变形的现象。

在 Python 中，可以使用一些常见的科学计算库来绘制屈服准则的图表，比如 NumPy 和 Matplotlib。

首先，我们需要定义屈服准则的方程。

常见的屈服准则包括von Mises 屈服准则和 Tresca 屈服准则。

这两种屈服准则都可以用来描述材料在受力作用下的塑性变形。

然后，我们可以使用NumPy 来生成一系列应力和应变的数据点，然后利用 Matplotlib来绘制应力-应变曲线。

下面是一个简单的示例代码，用来绘制 von Mises 屈服准则的应力-应变曲线：python.import numpy as np.import matplotlib.pyplot as plt.# 定义 von Mises 屈服准则的方程。

def von_mises(sigma1, sigma2, sigma3):return np.sqrt(sigma12 + sigma22 + sigma32sigma1sigma2 sigma2sigma3 sigma3sigma1)。

# 生成一系列应力数据。

stress = np.linspace(0, 100, 100) # 生成 0 到 100 之间的 100 个数据点。

# 计算对应的 von Mises 应变。

strain = von_mises(stress, stress0.5, stress0.3)。

# 绘制应力-应变曲线。

plt.plot(strain, stress)。

plt.xlabel('Strain')。

plt.ylabel('Stress')。

plt.title('Stress-Strain Curve for von Mises Yield Criterion')。

plt.show()。

在这个示例中，我们首先定义了 von Mises 屈服准则的方程von_mises，然后生成了一系列应力数据点，并利用 von_mises 函数计算了对应的应变数据点。

Methods 37 (2005) 208–215/locate/ymeth1046-2023/$ - see front matter 2005 Elsevier Inc. All rights reserved.doi:10.1016/j.ymeth.2005.08.001Cell migration and invasion assaysAline Valster a,1, Nhan L. Tran d,1, Mitsutoshi Nakada d , Michael E. Berens d ,Amanda Y. Chan a , Marc Symons a,b,c,¤aFeinstein Institute for Medical Research at North Shore-LIJ, 350 Community Drive, Manhasset, NY 11030, USAbDepartment of Surgery, North Shore University Hospital, Manhasset, NY 11030, USAcDepartment of Anatomy and Structural Biology, Albert Einstein College of Medicine, Bronx, NY 10461, USAdNeurogenomics Division, The Translational Genomics Research Institute, Phoenix, AZ 85004, USAAccepted 24 May 2005AbstractThe processes of cell migration and invasion are integral to embryonic development and the functioning of adult organisms.Deregulation of these processes contributes to numerous diseases. Ras GTPases and in particular members of the Rho subfamily of GTPases play critical roles in cell migration and invasion. Here, we provide a collection of protocols to assay these functions. We describe two cell migration assays. The monolayer wound healing assay is very easy to implement, whereas the microliter-scale migration assay allows examination of cell behavior on de W ned extracellular matrices. We also describe two methods that allow the quanti W cation of tumor cell invasion, a versatile transwell Matrigel invasion assay and an organotypic assay that examines the inva-sion of glioma cells through a rat brain slice. 2005 Elsevier Inc. All rights reserved.Keywords:Migration; Invasion; siRNA; Rac; Glioma1. IntroductionCell migration is a process that is critical at many stages of embryonic development, and is essential for tis-sue repair and immune function [1]. Importantly, dereg-ulated motile behavior contributes to pathological processes including tumor angiogenesis and metastasis,atherosclerosis, and arthritis [2–4].Members of the Ras superfamily of GTPases, most notably the Rho proteins, play a prominent role in cell migration [5]. Thus, the Rac, Cdc42, and Rho GTPases are essential for growth factor- and cytokine-stimulated chemotaxis in W broblasts, macrophages and neutrophils [6–9]. In addition, Rac, Cdc42, and Rho are necessary for the invasive behavior of carcinoma cells and W bro-blasts [7,10–12]. The signaling pathways that are acti-vated by Rho proteins to regulate cell migration and invasion are under intense scrutiny [1,5,13].We will focus this review on glioma cells. The migra-tory and invasive properties of these tumor cells are important prerequisites for the in W ltrative and destructive growth patterns of malignant gliomas. In W ltrative growth prevents complete tumor resection and therefore, causes signi W cant neurological morbidity and mortality [14].To date, examination of the roles of Rho proteins in cell migration and invasion has heavily relied on the inhibitory e V ects of dominant negative mutants of these GTPases and on the stimulation of signaling pathways by constitutively active versions. Introduction of these mutants into cells has been achieved by microinjection of plasmids or recombinant proteins [8,15,16], transient transfection or the establishment of stable cell lines [7].Dominant negative GTPases act by competing with their endogenous counterparts for access to guanine*Corresponding author. Fax: +1 516 365 5090.E-mail address: msymons@ (M. Symons).1Both the authors contributed equally to this work.A. Valster et al. / Methods 37 (2005) 208–215209nucleotide exchange factors (GEF s) [17]. However, GEF s often catalyze nucleotide exchange on a number of di V erent Rho family members [18], thereby limiting the speci W city of dominant negative mutants. This is illustrated by the observation that expression of domi-nant negative mutant Rac1 interferes with the activation of RhoA by the Dbl GEF[19]. F or this reason, we recently have employed RNA interference (RNAi) [20,21] to speci W cally inhibit the expression of Rho GTP-ases. A protocol for transient transfection of short inter-fering RNA (siRNA) is described in Section 2.1.2. Monolayer wound healing assayMonolayer wound healing assays have been used very e V ectively for studying the roles of Rho GTPases in cell migration [16]. Recently, monolayer wounding has also been used to examine signaling events that are involved in the establishment of cell polarity during directed loco-motion [22,23].Most of our recent experiments have been carried out using the SNB19 and U87MG grade IV glioblastoma cell lines. The SNB19 cell line can be obtained from the Developmental Therapeutics Program (NCI/NIH) and the U87MG line from ATTC. Both cell lines are very migratory and invasive.2.1. siRNA-mediated protein knock down in glioblastoma cells2.1.1. Selection of siRNA oligonucleotide sequenceCareful consideration concerning the selection of oli-gonucleotide sequence should be given to achieve e Y cient protein knock down and to avoid nonspeci W c e V ects. In the past, we have designed our own oligos fol-lowing speci W cations as established by the Tuschl labo-ratory. Guidelines are detailed on the Tuschl website: /labheads/tuschl/sirna.html. This website is updated on a regular basis. Recently, we have started to use the services of Dharmacon (http:// ) to select our siRNA oligonucleo-tide sequences. F or known genes siGenome oligo sequences directed against the gene’s open reading frame are successfully used in our laboratory and oligos against speci W c regions such as 3ЈUTR regions can be designed using the siDesign center that uses Smart Selec-tion design algorithms developed by Dharmacon [24]. The advantage of region-speci W c oligonucleotides such as 3ЈUTR-speci W c oligos is the ability to perform recon-stitution studies, by speci W cally knocking down endoge-nous proteins, without a V ecting expressed recombinant versions of these proteins [25].O V-target interactions of siRNA have been described [26–28]. This problem can be circumvented by utilizing two independent targeting sequences, as the probability of generating similar o V-target e V ects by di V erent oligos is extremely low. We routinely have been using an oligo-nucleotide directed against GL2 luciferase as a negative control [29]. As a positive control, we have been using an oligonucleotide directed against dynamin 2 (see Section 2.4—1.). Kits with additional control oligos are also available from Dharmacon. An in X uential editorial regarding the use of controls for RNA interference experiments has been published in Nat. Cell Biol. [30].2.1.2. Transient siRNA oligonucleotide transfectionA lipid-based method is used to introduce siRNA oli-gonucleotides into SNB19 glioblastoma cells. We prefer to use Lipofectamine 2000 (Invitrogen) as the lipid car-rier over other reagents we have tested because of the high e Y ciency knock down of proteins at low oligonu-cleotide concentrations (20nM W nal concentration) we routinely observe using this method. As some variability exists between transfections, we plate and transfect mul-tiple wells per treatment.In preparation for Lipofectamine 2000-mediated trans-fections, SNB 19 cells are plated in a 24-well plate at a con X uency of 50–70% (»3–4£104 cells per well) in 500 l plating medium (DMEM medium supplemented with 10% FBS but without antibiotics). The con X uency of the cells is important because at lower cell counts toxicity of the transfection reagent becomes limiting and at higher cell counts lower transfection e Y ciency hampers e Y cient protein knock down. The optimum con X uency for trans-fection is cell-type dependent and should be determined for each cell line independently to optimize transfection e Y ciency. SNB19 cells are allowed to attach to the tissue culture dish for about 2h as it is important to transfect the cells while they are in the early stages of cell spreading.0.6 l siRNA oligonucleotide duplex (at 20 M) is added to 47–49 l DMEM medium (to make a total vol-ume of 50 l) without serum and in a separate tube 1 l Lipofectamine 2000 is added to 49 l DMEM. After a 5min incubation at room temperature, the diluted siRNA oligonucleotide and lipid are combined, gently mixed, and further incubated for 20min to allow the for-mation of the transfection complexes. The complexes are subsequently added to the cells and mixed with the plat-ing medium by gently swirling the tissue culture dish.After about 24h, the medium containing the transfec-tion complexes should be aspirated and replaced by reg-ular plating medium (DMEM with 10% F BS). By this time, the cells typically display an array of ‘vacuole-like’structures that do not seem to have any negative e V ect in subsequent culture and analysis of the cells. F or most proteins studied in our lab, in SNB19 cells, protein knock down reaches an optimum at around day 3 after transfection and typically lasts for another 2 or 3 days. Hence, cells are routinely assayed 3 days post transfec-tion. However, the timeline for optimum protein knock down is dependent on the protein and cell line of interest210 A. Valster et al. / Methods 37 (2005) 208–215and should be determined for each protein and cell line separately.2.2. Transient plasmid transfections in glioblastoma cellsWe also have established a protocol that allows e Y cient transient expression of proteins in SNB19 cells using the E V ectene transfection reagent (Qiagen). Using this method, transfection e Y ciencies of >80% are routinely obtained. It is important for e Y cient transfection to use freshly plated cells (less than 24h after plating the cells).The details of the transfection protocol for SNB19 cells are as follows. Cells are plated at »70% con X uency (»4£104 cells/well in 24-well plate) in 500 l plating medium (DMEM with 10% FBS) without antibiotics. A mixture of the following is made using the E V ectene transfection kit components provided by Qiagen: 120 l bu V er EC; 0.4 g plasmid DNA, and 6.4 l Enhancer. This mixture is incubated for 3min at room temperature, after which 8 l E V ectene is added. After an additional 7min incubation during which transfection complexes are formed, 700 l DMEM with 10% FBS is added and this mixture is applied to the cells. We typically assay cells 24h after transfection.2.3. Monolayer wound healing assaySNB19 cells are treated according to experimental design. F or siRNA transfections two wells in a 24-well plate are transfected using Lipofectamine 2000 transfec-tion reagent as described above. The next day, the cells are combined in one well of a six-well culture dish. Before plating into this dish, two parallel lines are drawn at the underside of the well with a Sharpie marker. These lines will serve as W ducial marks for the wound areas to be analyzed. At the day of analysis, the monolayer should be absolutely con X uent. In preparation for mak-ing the wound, the growth medium is aspirated and replaced by calcium-free PBS to prevent killing of cells at the edge of the wound by exposure to high calcium concentrations. Two (or more) parallel scratch wounds of approximately 400 m width are made perpendicular to the marker lines with a blue P1000 pipet tip (Fisher). This procedure makes it possible to image the entire width of the wound using a 10£ objective.The wounds are observed using phase contrast microscopy on an inverted microscope. Images are taken at regular intervals over the course of 12–24h of both areas X anking the intersections of the wound and the marker lines (D8 images per treatment).The width of the wound should be as consistent as possible, since narrow wounds tend to close faster than wider wounds. If more than two scratches are made, wounds with similar widths can be chosen for analysis. Images are analyzed by digitally drawing lines (using Adobe Photoshop) averaging the position of the migrat-ing cells at the wound edges. The cell migration distance is determined by measuring the width of the wound divided by two and by subtracting this value from the initial half-width of the wound (Fig.1).2.4. Notes1.A positive control that is useful for the implementa-tion of siRNA methodologies is siRNA directed against dynamin 2 [31]. This protein is ubiquitously expressed at high levels and is readily detected by immuno X uorescence. In contrast to lamin A/C, which also has been used as positive control [29], dynamin 2 tends to be expressed in a very uniform fashion throughout the cell population, making it easier to evaluate the transfection e Y ciency.2.Transient transfection of adherent cells that arerefractory to the described protocols can be improved point and condition.Rac1 si RNAcontrolA. Valster et al. / Methods 37 (2005) 208–215211by either transiently trypsinizing the cells [32] or by detaching the cells and transfecting in suspension [33].3.F or the determination of chemotaxis (migrationdirected upward a concentration gradient of chemo-attractant), a number of assays have been described.These include the use of the Boyden-chamber [7,34] and the Dunn-chamber assays [8].3. Microliter-scale migration assayThe microliter-scale migration assay that we discuss allows examination of the migratory responses of cells to speci W c extracellular matrix (ECM) components. The assay is conducted in a small volume of medium, which is favorable for testing expensive or rare reagents for their e V ect on cell migration, such as pharmacological agents, antisense oligonucleotides, siRNA, and antibod-ies. This protocol allows for assaying adherent or nonad-herent cells that have been activated to adhere. In addition, subsequent immunostaining of the migrating cells can be performed to examine reorganization of the actin cytoskeleton, localization of proteins involved in cytoskeletal organization, matrix remodeling, adhesion complexes, and signaling events. F inally, multiple phe-notypic endpoints can be measured to study the e V ect of molecular and biochemical determinants on cell motility, proliferation, apoptosis, gene expression, and signal transduction [35–37].3.1. Assembly of the migration assayTen-well Te X on-printed microscope slides that have been designed for this assay can be obtained commer-cially (CSM, Phoenix, AZ). F irst, place the 10-well slide(s) into a petri dish and add two drops of water under each end of the slide. The drops will disperse by capillary action and keep the slide in place. Coat the 10-well slides with the ECM component of interest by add-ing 20 l to each well, followed by 1h incubation at 37°C. After coating, rinse the wells three times with PBS and block the nonspeci W c binding sites with 0.1% BSA in PBS for 30min at 37°C. Rinse the slides twice with PBS, add 50 l PBS to each well and store at 4°C in PBS until ready to use.Next, aspirate the PBS from the wells and replace by 50 l medium. Carefully place the pre-chilled (4°C) Cell Sedimentation Manifold (CSM; CSM, Phoenix, AZ) onto the slide. The CSM is designed to W t over the 10-well Te X on-slides and allow cells to settle and attach within a 1mm circumference in the center of each well. Carefully remove any air bubbles that reside in the channels. This is important to ensure that cells will properly fall through the channel onto the slide. Finally, harvest cells by trypsin-ization, adjust cell concentration to approximately 2000 cells/ l (2£106 cells/ml), and keep the cell suspension on ice. Carefully place 1 l of the cell suspension into each well. If the cells are injected too quickly, the cells will tend to disperse out of the bottom of the well. Injection of air bubbles can be avoided by over W lling the pipet with cells (1.3 l) and expulsing only to the W rst stop on the pipet. Place a 35-mm petri dish W lled with sterile water in the chamber with the slide to ensure 100% humidity. To allow cell attachment, incubate the slides with the CSM over-night at 37°C, 5% CO2 atmosphere and constant humid-ity. Cell attachment can be veri W ed with the manifold still mounted. Subsequently, gently remove the manifold and refeed each well.3.2. Quantitation of cell migrationCell migration is measured using an inverted micro-scope. A glass microscope slide is suspended over the 10-well Te X on slide (1mm above cell surface) using a manu-factured silicone suspension pad (CSM). This prevents drying of the wells and facilitates imaging by eliminating the aberration e V ects caused by the meniscus of the medium. The glass microscope slide can subsequently be removed without disrupting the cell monolayer for drug treatment or medium exchange.The area occupied by the cells is visualized by inverted microscopy using a 2.5£ objective (Fig.2). Images are captured most e Y ciently using digital imag-ing. A digital video of cell migration is hosted on the TGen W le server at /supplemen-tal_glioma/glioma_migration.mpg. The radius of the migrating cell population can be measured at the appro-priate intervals using a macro that can be downloaded from the CSM, website at . The average migration rate of W ve to ten replicates is cal-culated as the increasing radius of the entire cell popula-tion over time.3.3. Notesponents of the cell sedimentation system can besterilized. Package the Cell Sedimentation Manifold Fig.2. Bright W eld micrographs of glioma migration on human lami-nin substrate. Micrographs were taken 16h after plating (t D0) and after allowing cells to migrate out for 24h (t D24). The circle circum-scribing the cells is used to calculate the migration rate. Bar D2mm.212 A. Valster et al. / Methods 37 (2005) 208–215and Te X on-masked and plain slides in separate auto-clave bags. Steam autoclave the bags. The manifold can be stored at 4°C until ready to use. The slides can be stored at room temperature.2.At the end of the appropriate migration period, the cells can be W xed and processed for microscopic eval-uation by a number of techniques, including immuno-cytochemistry and in situ hybridization [36,37].4. Transwell invasion assaySNB19 cells are experimentally treated as described in Section 2.1. Two days after transfection, Matrigel Inva-sion Chambers (Becton Dickinson) are hydrated for at least 2h in the tissue culture incubator with 500 l serum free DMEM in the bottom of the well and 500 l in the top of the chamber. After hydration of the Matrigel, the DMEM in the bottom of the well is replaced with DMEM containing 10% F BS. 4£104 SNB19 cells are plated in 500 l DMEM supplemented with 10% FBS in the top of the chamber.The invasion assay is carried out for 24h in the tissue culture incubator. The cells are W xed by replacing the culture medium in the bottom and top of the chamber with 4% formaldehyde dissolved in PBS. After W xing for 15min at room temperature, the chambers are rinsed in PBS and stained with 0.2% crystal violet for 10min.After washing the chambers 5 times by dipping thechambers in a large beaker W lled with dH 2O the cells (now blue in color) at the top of the Matrigel membrane are removed with several Q-tips. It is safe to assume that all cells are removed when no more blue dye can be removed with the Q-tips. Now all cells that remain are the ones that have invaded and made it to the bottom side of the membrane (Fig.3). These cells are counted using an inverted microscope equipped with either a 4£or a 10£ objective and plotted as the percentage of invading cells of the total number of plated cells.Note. The invasive behavior of most cell lines is enhanced by passaging the cells the day before starting the invasion assay.5. Brain slice invasion assayCellular behavior and signaling in general is strikingly di V erent when evaluated on a two-dimensional substrate in contrast to a three-dimensional environment [38,39].Although studies of both melanoma and glioma cells have shown that there is a strong correlation between increased migration on two-dimensional substrates in vitro and increased invasiveness in vivo [40,41],in vitro migration assays performed on de W ned matrix components do not adequately incorporate the complex interplay between tumor cells and stroma required for cell invasion in situ [42]. Thus, the establishment of ex vivo rat brain slice models presents a unique system for the evaluation of the invasive properties of glioma cells in more physiologically relevant conditions [37,43,44].5.1. Establishment of GFP-expressing cell linesF or the establishment of GF P-expressing cell lines,we utilize the Retro-X system (Becton Dickinson).Brie X y, PLAT-E packaging cells are transfected with the retroviral expression vector using E V ectene, using the protocol provided by the manufacturer (Qiagen). The culture supernatant of the PLAT-E cells is removed 48h after transfection, W ltered through a 0.45 M cellulose-acetate W lter, and added to subcon X uent cultures of cells.For the rapid selection of cells that stably and uniformly express GFP, we use a two-tiered selection process. First,two days after transfection, cells are sorted by F ACS and subsequently selected in DMEM containing G418(200 g/ml).5.2. Brain slice invasion assay5.2.1. Preparation of rat brain slicesThe brain slice model system of rat whole cerebrum is modi W ed from the organotypic culture methods previ-ously reported [37,43,44]. Brain tissue is prepared from 4-week-old male Wister rats (Crl: (WI)BR; Charles100120Control Rac1 RNAiA. Valster et al. / Methods 37 (2005) 208–215213River Lab, Wilmington, MA). After halothane anesthe-sia, the whole brains are quickly removed and placed in cold Hanks’ Balanced Salt Solution (GIBCO), which contains 100units/ml penicillin and 100 g/ml strepto-mycin. The brain is cut vertically to the base with a scal-pel, 1mm inward from both rostral and caudal ends of the cerebrum. The cerebrum is attached to the stage of a vibratome (1000 Plus; The Vibratome, St. Louis, MO) using glue (Krazy Glue, Elmer’s Products, Columbus, OH)). The attached cerebrum is further supported by small cubes of 3% agarose gel, which are also attached to the stage by glue. The cerebrum is then cut vertically to the base in 400- m-thick sections. Six slices can be obtained from one rat.The brain slices are transferred to the upper chamber of a transwell insert (six-well plate) and placed on top of the 0.4- m micropore polycarbonate W lter (Becton Dick-inson). Next, 500 l of medium is added to the upper chamber and 1.5ml to the lower chamber. The slice cul-ture medium consists of DMEM with 10% FBS, 100units/ ml penicillin and 100 g/ml streptomycin. The brain slice culture is incubated at 37°C under standard conditions of 100% humidity, 95% air, and 5% CO2. The slices are kept in the incubator until use. The organotypic cytoarchitec-ture of these cultured brain slices and neuronal viability can be preserved for over two weeks [43].5.2.2. Implanting the GFP-expressing cells on brain sliceThree days after transfection with siRNA (Section 2.1), the GF P-expressing cells are trypsinized, collected in DMEM with FBS and spun down. After resuspension in DMEM without FBS, the cells are counted and fur-ther diluted in serum-free DMEM to 2£108 cells/ml. Before the cells are placed on the brain slice, the medium in the upper chamber is aspirated. The surface of brain slice should be semi-dry. This step is critical to avoid cell dispersion over the slice. 105 cells are gently placed on the putamen (0.5 l transfer volume). Subsequently, 500 l of serum-free medium is added onto the upper chamber to avoid drying of brain slice, but still allowing the surface of the slice to remain well exposed to the air. This is critical for the long-term survival of the neuronal cells in the slices. Both right and left sides of the brain slice are used. Typically, we perform three transfections for three brain slices each.Lateral migration of the cells on the upper side of the brain slice can be examined by X uorescent stereomicro-scopic imaging using a Macro-Fluorescent Imaging Sys-tem at 10£ magni W cation (SZX12-RF L3; Olympus) equipped with a GF P barrier W lter (DP50; Olympus). Half of the medium is replaced with fresh medium every 2 days. Depending on the cell line, observations are car-ried out over one to several days.5.2.3. Quantitation of glioma cell invasion into the ex vivo brain sliceTo quantitate glioma cell invasion into the brain slice, the brain slice is W xed overnight on the membrane in 4% paraformaldehyde at 4°C. Subsequently, the polycarbon-ate membrane is cut out using a scalpel and the W lter with the brain slice are transferred onto a microscope slide for observation using an inverted laser confocal microscope (LSM 5; Zeiss). Serial sections are obtained every 7.5 m downward from the top surface to the bottom of the slice (Fig.4A). Scion image software is used to calculate total area of GFP-stained cells. The area is plotted as a function of the distance from the top surface of the brain slice and the distribution curve is constructed. The extent of gliomaFig.4. (A) Confocal X uorescence micrographs showing invasion of U251 glioma cells 5 days after transfer to brain slices. Serial sections wereobtained every 7.5 m downward from the brain slice surface (0 m) to a deeper site (82.5 m). Six representative sections are shown. Bar D100 m.(B) Fluorescence distribution curve calculated from the data in (A).214 A. Valster et al. / Methods 37 (2005) 208–215cell invasion in the slice is de W ned as the depth ( m) that shows half of the maximum area of invasive cells (Fig.4B). Data showing that siRNA-mediated depletion of Rac1 inhibits the invasive behavior of glioma cells in this system are shown in Fig.5.5.3. NoteA common problem with brain slice invasion assay is bacterial contamination. To avoid this,1.Disinfect all instruments before starting this assay using 70% ethanol.e gloves that are sterilized.e medium that contains antibiotics.e sterile hood when the brain slices are handled.6. Concluding remarksWith the exception of the brain slice invasion model,the methods described in this review are applicable toother cells types in addition to glioma. On the other hand,although logistically and technically much more involved,the brain slice invasion model described here is unique in that it allows examination of tumor cell invasion in an organotypic fashion. An alternative approach that permits the detailed study of the invasive behavior of other tumor cells in a physiological setting is intravital imaging, either in whole animals [45] or in isolated organs [46].AcknowledgmentsThis work was supported by National Institutes of Health Grant CA87567 to M.S. and NS042262 and NS043446 to M.E.B.References[1]A.J. Ridley, M.A. Schwartz, K. Burridge, R.A. Firtel, M.H. Gins-berg, G. Borisy, J.T. Parsons, A.R. Horwitz, Science 302 (2003)1704–1709.[2]J.D. Hood, D.A. Cheresh, Nat. Rev. Cancer 2 (2002) 91–100.[3]C.H. Heldin, B. Westermark, Physiol. Rev. 79 (1999) 1283–1316.[4]M.E. DeVries, L. Ran, D.J. Kelvin, Semin. Immunol. 11 (1999) 95–104.[5]K. Burridge, K. Wennerberg, Cell 116 (2004) 167–179.[6]B. Anand-Apte, B.R. Zetter, A. Viswanathan, R.G. Qiu, J. Chen,R. Ruggieri, M. Symons, J. Biol. Chem. 272 (1997) 30688–30692.[7]J. Banyard, B. Anand-Apte, M. Symons, B.R. Zetter, Oncogene 19(2000) 580–591.[8]W.E. Allen, D. Zicha, A.J. Ridley, G.E. Jones, J. 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Hannon, Trends Biochem. Sci. 28 (2003) 196–201.[21]D.M. Dykxhoorn, C.D. Novina, P.A. Sharp, Nat. Rev. Mol. CellBiol. 4 (2003) 457–467.[22]S. Etienne-Manneville, A. Hall, Nature 421 (2003) 753–756.[23]S. Etienne-Manneville, A. Hall, Cell 106 (2001) 489–498.[24]A. Reynolds, D. Leake, Q. Boese, S. Scaringe, W.S. Marshall, A.Khvorova, Nat. Biotechnol. 22 (2004) 326–330.[25]P. Lassus, J. Rodriguez, Y. Lazebnik, Sci STKE (2002) http:///cgi/content/full/sigtrans;2002/147/pl13.[26]A.L. Jackson, S.R. Bartz, J. Schelter, S.V. Kobayashi, J. Burchard,M. Mao, B. Li, G. Cavet, P.S. Linsley, Nat. Biotechnol. 21 (2003)635–637.Fig.5. Rac1-directed siRNA inhibits invasion of glioblastoma cells in rat brain slices. (A) Confocal X uorescence micrographs of SNB19 gli-oma cells stably expressing green X uorescent protein. Cells were trans-fected with siRNAs directed against luciferase (control) or Rac1, two days prior to transfer to the bilateral putamen of rat brain slices and observed at the indicated time. Bar D 500 m. (B) Invasion rates of SNB19 and U87MG cells treated with the indicated siRNA constructs were calculated from Z axis images collected by confocal laser scan-ning microscopy. The mean values of the invasion rates were obtained from six independent experiments.。

$$Feb.2021Vo . 42$No. 12021年 2月 第 42 卷$ 第 1 期首都医科大学学报Journal of Capital Medical Universi/[doi ： 10. 3969/j. issp. 1006-7795. 2021. 01. 022]・临床研究*3D MEDIC 和3D SPACE 磁共振神经成像在腰骶丛神经根的一 致性对比研究孙峥1!2孔超3鲁世保3陈海％笪宇威％张苗1>2卢洁心（1.首都医科大学宣武医院放射科，北京100053； 2.磁共振成像脑信息学北京市重点实验室，北京100053； 3.首都医科大学宣武医院骨科，北京100053； 4.首都医科大学宣武医院神经内科，北京100053）$摘要】 目的 验证三维多回波数据联合成像(three dimensional multi-echo data imagine combination with selective water excitation , 3D MEDIC WE)和三维快速自旋回波成像(three dimensional sampling peSection with application optimized contrasts byusing d/ferent Uip angle evelu/on , 3D SPACE STIR )序列在腰骶丛神经根成像中的可行性和重复性。

方法 将55例受试者分为腰椎无异常表现的正常对照组(20例)、单纯性腰椎间盘突出症(lumbar d/c hernm/on , LDH )组(20例)和慢性炎性脱髓鞘性多发性神经根神经病症(ch/nw inUamma"/ demyelinating polyradwuloneuropathy , CIBP )组(15例)，分别应用两种腰骶丛神经根成 像，评价图像质量参数信噪比(signal " noise ratio , SNR )、对比噪声比(contrast " noise ratio , CNR )和对比度(contrast ratio , CR )，并验证正常对照组、CBP 组和LDH 组测量神经根直径的一致性。

一种多点拟合的恒定立体角纤维重建模型
李浩东;王远军
【期刊名称】《小型微型计算机系统》
【年(卷),期】2024(45)5
【摘要】基于弥散磁共振成像DTI的纤维追踪技术是非侵入性活体脑神经研究的关键技术.恒定立体角重建模型CSA是基于DTI发展而来的一种纤维重建模型,能够根据采样球壳上的数据对弥散方向分布函数进行线性径向投影计算,从而进行纤维重建.目前,恒定立体角纤维重建模型存在鲁棒性较差,重建纤维过于杂乱以及弥散方向分布偏差的问题.针对上述问题,本文提出MCSA(Multipoint Constant Solid Angle)模型,首先引入可以使弥散方向分布函数更加准确的最小二乘法,接着通过自适应高斯函数引入多点拟合弥散信息提高模型鲁棒性和抗噪性.最后,本文分别使用Fibercup、ISMRM2015年模拟数据以及Stanford HARDI真实影像数据对传统CSA模型以及本文提出MCSA模型进行对比分析,结果表明,利用本文提出MCSA 模型重建的纤维更加符合客观规律,并且在一定程度上减少了假阳性纤维的生成.【总页数】6页(P1116-1121)
【作者】李浩东;王远军
【作者单位】上海理工大学医学影像工程研究所
【正文语种】中文
【中图分类】TP391
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JOVE SE(Science Education)科学教育专辑内容介绍JOVE出版社是生命科学领域出版视频最多的出版社，总部位于美国马萨诸塞州剑桥市，紧邻哈佛大学、麻省理工学院、塔夫斯大学、波士顿大学等多所知名学府。

JOVE出版社于2006年创办JOVE实验视频期刊，致力于以视频方式展现生物学、医学、化学、物理学等学科领域的研究过程与成果。

SE科学教育专辑专门为教学设计，旨在通过简单易懂的视频展现实验基础教学。

目前共有9个子集，其中5个子集已有中文配音以及人工翻译，方便学生学习以及课堂教学。

SE每个子集有90个视频（15个教学视频，75个应用实验视频）。

每年会更新1-2个新子集，现有子集视频数量无更新。

1)General Laboratory Techniques基础实验技术2)Basic Methods in Cellular and Molecular Biology细胞与分子生物学基本方法3)Essentials of Biology1: Yeast, Drosophila and C.Elegans生物学精要I: 酵母，果蝇，线虫4)Essentials of Biology 2: Mouse, Zebrafish, and Chick生物学精要II:鼠，斑马鱼，鸡5)Essentials of Neuroscience神经科学精要6)Essentials of Developmental Biology发育生物学精要7)Essentials of Behavioral Science行为科学精要8)Essentials of Genetics基因学精要9)Essentials of Cell Biology 细胞生物学精要1）General Laboratory Techniques基础实验技术该子集展示了如何使用在许多实验中都至关重要的一些标准实验室仪器，以及如何进行实验室基本操作。

一、概述机械臂是一种常见的自动化设备，广泛应用于工业制造、医疗和军事领域等。

在机械臂控制中，雅可比矩阵是一个重要的数学工具，用于描述机械臂的运动学特性和动力学特性。

Python作为一种强大的编程语言，可以用来求解机械臂的雅可比矩阵，为机械臂的控制和优化提供有力支持。

二、机械臂的雅可比矩阵1. 机械臂的运动学描述机械臂的运动学描述了机械臂的空间位置和姿态。

其中，雅可比矩阵是描述机械臂末端速度与关节速度之间的关系的重要工具。

通过雅可比矩阵，可以将末端速度转换为关节速度，进而控制机械臂的运动。

2. 雅可比矩阵的求解雅可比矩阵的求解可以使用数值方法或符号方法。

数值方法通过数值计算得到雅可比矩阵的近似值，而符号方法则通过符号计算得到雅可比矩阵的精确表达式。

在实际应用中，符号方法通常更加准确和高效。

三、Python求解机械臂的雅可比矩阵1. Python在机械臂控制中的应用Python是一种开源的、优雅的、易学易用的编程语言，广泛应用于科学计算、数据分析、人工智能和机器学习等领域。

在机械臂控制中，Python可以用来实现机械臂的建模、运动学分析、动力学仿真和控制算法等。

2. 使用Python求解机械臂的雅可比矩阵在Python中，可以使用符号计算库SymPy来求解机械臂的雅可比矩阵。

SymPy是Python的一个符号计算库，提供了符号计算的功能，可以精确地求解雅可比矩阵。

通过SymPy，可以轻松地建立机械臂的运动学模型，并求解雅可比矩阵。

四、案例分析1. 案例背景假设有一个3自由度的平面机械臂，需要求解其雅可比矩阵。

2. 案例实现利用SymPy建立机械臂的运动学模型，并定义关节变量、末端位置和末端速度。

利用SymPy的求导功能，求解雅可比矩阵。

通过Python的可视化库matplotlib，可视化机械臂的雅可比矩阵。

五、总结与展望1. 总结Python作为一种强大的编程语言，在机械臂控制中具有重要的应用前景。

Chinese Journal of Tissue Engineering Research ｜Vol 25｜No.34｜December 2021｜54453D 生物打印负载转化生长因子β3的软骨复合支架杨 振1，2，李 浩1，2，付力伟1，2，高仓健1，2，姜双鹏2，王福鑫2，苑志国2，孙志强1，2，查康康1，2，1，22222文题释义：3D 生物打印：通过精准控制生物材料、种子细胞、生长因子在整体3D 结构中的位置、组合与互相作用，使之具有生物活性，并能实现与目标组织或生物器官接近相同，甚至更优越的功能。

转化生长因子β3：作为关节软骨组织形成的重要调节因子，可以促进干细胞迁移和成软骨分化，增强软骨损伤的修复，是一种理想的干细胞招募和促分化因子。

摘要背景：通过募集内源性干细胞原位再生软骨损伤的治疗策略，是未来软骨组织工程研究的新方向。

目的：构建既能募集干细胞又能促进其黏附和增殖，且有利于新生组织成熟的组织工程软骨复合支架。

方法：将脱细胞软骨细胞外基质(extracellular matrix ，ECM)与甲基丙烯酸酯化明胶(methacrylated gelatin ，GelMA)混合配制光敏性生物墨水，利用3D 生物打印技术分别制备单纯聚己内酯[poly(Ɛ-caprolactone)，PCL]支架、PCL/GelMA/ECM 支架。

将转化生长因子β3(transforming growth factor β3，TGF-β3)负载于生物墨水中制备PCL/GelMA/ECM/TGF-β3支架，检测其缓释性能。

从形态学、组织学、生物化学、生物力学等角度评价PCL/GelMA/ECM 支架的物理化学性质。

利用CCK-8法检测PCL/GelMA/ECM 支架的细胞毒性。

将脂肪间充质干细胞接种于PCL/GelMA/ECM 支架上，1，4，7 d 后，共聚焦显微镜下观察细胞活性，扫描电镜观察细胞黏附。

专利名称：一种抗干扰的三维虚拟切片的制作方法专利类型：发明专利
发明人：陈斌,贾守礼,何裕财,吴丹媛,陈进
申请号：CN200710009842.3
申请日：20071115
公开号：CN101436313A
公开日：
20090520
专利内容由知识产权出版社提供
摘要：一种抗干扰的三维虚拟切片的制作方法，包括：用计算机建模的方法得到整个切片的表面数学模型，利用此数学模型估计出每个视场图像z轴的大致位置；采用显微镜的自动聚焦算法精确得到每个视场图像的最佳聚焦位置，以此最佳聚焦位置作为三维平面的参考面；其余各z轴视场图像根据参考面依次排列得到三维聚焦平面图像序列，制作出最终的三维虚拟切片。

本发明可有效抵抗切片本身不平整和切片上的组织高低不平、全自动显微镜机械精度、环境扰动等干扰因素，从而形成连续平滑、清晰的虚拟切片图像。

申请人：麦克奥迪实业集团有限公司
地址：361006 福建省厦门市火炬高科技区麦克奥迪大厦
国籍：CN
代理机构：厦门市首创君合专利事务所有限公司
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