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Functional Fokker-Planck Equation Approach for a Gompertzian Model of Tumour Cell Growth

机译：肿瘤细胞生长金刚氏模型的功能Fokker-Planck方程方法

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摘要

In this communication, based upon the deterministic Gompertz law of cell growth, a stochastic model in tumour growth is proposed. This model takes account of both cell fission and mortality too. The corresponding density function of the size of the tumour cells obeys a functional Fokker-Planck equation which can be solved analytically. It is found that the density function exhibits an interesting "multi-peak" structure generated by cell fission as time evolves.

机译：在这种通信中，基于细胞生长的确定性Gompertz定律，提出了一种肿瘤生长的随机模型。该模型也考虑了细胞裂变和死亡率。肿瘤细胞尺寸的相应密度函数遵守功能性Fokker-Planck等式，其可以分析解决。发现密度函数随着时间的推移而表现出通过细胞裂变产生的有趣的“多峰”结构。

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《World Congress on Engineering》|2007年||共5页
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作者
C. F. Lo;
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中图分类 T-53;
关键词
Tumor cell growth; Gompertz law; Fokker-Planck equation;

机译：肿瘤细胞生长;Gompertz Law;Fokker-Planck方程;

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专利

1. Exact solution of the functional Fokker-Planck equation for cell growth with asymmetric cell division [J] . Lo C. F. Physica, A. Statistical mechanics and its applications . 2019,第期

机译：用非对称细胞分裂函数Fokker-Planck方程的精确解
2. DISTRIBUTED APPROXIMATING FUNCTIONAL APPROACH TO THE FOKKER-PLANCK EQUATION - EIGENFUNCTION EXPANSION [J] . Zhang DS., Kouri DJ., Hoffman DK., The Journal of Chemical Physics . 1997,第12期

机译：福克-普朗克方程的分布式近似函数方法-本征函数展开
3. DISTRIBUTED APPROXIMATING FUNCTIONAL APPROACH TO THE FOKKER-PLANCK EQUATION - TIME PROPAGATION [J] . Wei GW., Kouri DJ., Hoffman DK., The Journal of Chemical Physics . 1997,第8期

机译：福克-普朗克方程的分布逼近函数方法-时间传播。
4. Functional Fokker-Planck Equation Approach for a Gompertzian Model of Tumour Cell Growth [C] . C. F. Lo World Congress on Engineering . 2007

机译：肿瘤细胞生长金刚氏模型的功能Fokker-Planck方程方法
5. Integration of an irregular cellular automata approach and geographic information systems for high-resolution modelling of urban growth. [D] . Stevens, Daniel. 2005

机译：集成了不规则细胞自动机方法和地理信息系统，可对城市发展进行高分辨率建模。
6. AN EVOLUTIONARY MODEL OF TUMOR CELL KINETICS AND THE EMERGENCE OF MOLECULAR HETEROGENEITY DRIVING GOMPERTZIAN GROWTH [O] . JEFFREY WEST, ZAKI HASNAIN, PAUL MACKLIN, -1

机译：肿瘤细胞动力学的进化模型和驱动非均质性的哥氏增长的出现
7. Poster session 2Morphogenetic mechanisms290MiR-133 regulates retinoic acid pathway during early cardiac chamber specification291Bmp2 regulates atrial differentiation through miR-130 during early heart looping formationDevelopmental genetics294Association of deletion allele of insertion/deletion polymorphism in alpha 2B adrenoceptor gene and hypertension with or without type 2 diabetes mellitus295Association of G1359A polymorphism of the endocannabinoid type 1 receptor (CNR1) with coronary artery disease (CAD) with type 2 diabetes mellitusCell growth, differentiation and stem cells - Vascular298Gamma-secretase inhibitor prevents proliferation and migration of ductus arteriosus smooth muscle cells: a role of Notch signaling in postnatal closure of ductus arteriosus299Mesenchymal stromal-like cells (MLCs) derived from induced pluripotent stem (iPS) cells: a promising therapeutic option to promote neovascularization300Sonic Hedgehog promotes mesenchymal stem cell differentiation to vascular smooth muscle cells in cardiovacsular disease301Proinflammatory cytokine secretion and epigenetic modification in endothelial cells treated LPS-GinfivalisCell death and apoptosis - Vascular304Mitophagy acts as a safeguard mechanism against human vascular smooth muscle cell apoptosis induced by atherogenic lipidsTranscriptional control and RNA species - Vascular307MicroRNA-34a role in vascular calcification308Local delivery of a miR-146a inhibitor utilizing a clinically applicable approach attenuates neointima formation after vascular injury309Long noncoding RNA landscape of hypoxic endothelial cells310Specific circulating microRNAs levels associate with hypertension, hyperglycemia and dysfunctional HDL in acute coronary syndrome patientsCytokines and cellular inflammation - Vascular313Phosphodiesterase5A up-regulation in vascular endothelium under pro-inflammatory conditions: a newly disclosed anti-inflammatory activity for the omega-3polyunsaturated aatty acid docosahexaenoic acid314Cardiovascular risk modifying with extra-low dose anticytokine drugs in rhematoid arthritis315Conversion of human M-CSF macrophages into foam cells reduces their proinflammatory responses to classical M1-polarizing activation316Lymphocytic myocarditis coincides with increased plaque inflammation and plaque hemorrhage in coronary arteries, facilitating myocardial infarction317Serum osteoprotegerin level predictsdeclined numerous of circulating endothelial- derived and mononuclear-derived progenitor cells in patients with metabolic syndromeGrowth factors and neurohormones - Vascular320Effect of gastrin-releasing peptide (GRP) on vascular inflammationSignal transduction - Heart323A new synthetic peptide regulates hypertrophy in vitro through means of the inhibition of nfkb324Inducible fibroblast-specific knockout of p38 alpha map kinase is cardioprotective in a mouse model of isoproterenol-induced cardiac hypertrophy325Regulation of beta-adrenoceptor-evoked inotropic responses by inhibitory G protein, adenylyl cyclase isoforms 5 and 6 and phosphodiesterases326Binding to RGS3 and stimulation of M2 muscarinic acetylcholine receptors modulates the substrate specificity of p190RhoGAP in cardiac myocytes327Cardiac regulation of post-translational modifications, parylation and deacetylation in LMNA dilated cardiomyopathy mouse model328Beta-adrenergic regulation of the b56delta/pp2a holoenzyme in cardiac myocytes through b56delta phosphorylation at serine 573Nitric oxide and reactive oxygen species - Vascular331Oxidative stress-induced miR-200c disrupts the regulatory loop among SIRT1, FOXO1 and eNOS332Antioxidant therapy prevents oxidative stress-induced endothelial dysfunction and Enhances Wound Healing333Morphological and biochemical characterization of red blood cell in coronary artery diseaseCytoskeleton and mechanotransduction - Heart336Novel myosin activator, JSH compounds, increased myocardial contractility without chronotropic effect in ratsExtracellular matrix and fibrosis - Vascular339Ablation of Toll-like receptor 9 causes cardiac rupture after myocardial infarction by attenuating proliferation and differentiation of cardiac fibroblasts340Altered vascular remodeling in the mouse hind limb ischemia model in Factor VII activating protease (FSAP) deficiencyVasculogenesis, angiogenesis and arteriogenesis343Pro-angiogenic effects of proly-hydroxylase inhibitors and their potential for use in a novel strategy of therapeutic angiogenesis for coronary total occlusion344Nrf2 drives angiogenesis in transcription-independent manner: new function of the master regulator of oxidative stress response345Angiogenic gene therapy, despite efficient vascular growth, is not able to improve muscle function in normoxic or chronically ischemic rabbit hindlimbs -role of capillary arterialization and shunting346Effect of PAR-1 inhibition on collateral vessel growth in the murine hind limb model347Quaking is a key regulator of endothelial cell differentiation, neovascularization and angiogenesis348"Emerging angiogenesis" in the chick chorioallantoic membrane (CAM). An in vivo study349Exosomes from cardiomyocyte progenitor cells and mesenchymal stem cells stimulate angiogenesis in vitro and in vivo via EMMPRINEndothelium352Reciprocal regulation of GRK2 and bradykinin receptor stimulation modulate Ca2+ intracellular level in endothelial cells353The roles of bone morphogenetic proteins 9 and 10 in endothelial inflammation and atherosclerosis354The contribution of GPR55 to the L-alpha-lysophosphatidylinositol-induced vasorelaxation in isolated human pulmonary arteries355The endothelial protective ACE inhibitor Zofenoprilat exerts anti-inflammatory activities through H2S production356A new class of glycomimetic drugs to prevent free fatty acid-induced endothelial dysfunction357Endothelial progenitor cells to apoptotic endothelial cell-derived microparticles ration differentiatesas preserved from reduced ejection fractionheart failure358Proosteogenic genes are activated in endothelial cells of patients with thoracic aortic aneurysm359Endothelin ETB receptors mediate relaxing responses to insulin in pericardial resistance arteries from patients with cardiovascular disease (CVD)Smooth muscle and pericytes362CX3CR1 positive myeloid cells regulate vascular smooth muscle tone by inducing calcium oscillations via activation of IP3 receptors363A novel function of PI3Kg on cAMP regulation, role in arterial wall hyperplasia through modulation of smooth muscle cells proliferation364NRP1 and NRP2 play important roles in the development of neointimal hyperplasia in vivo365Azithromycin induces autophagy in aortic smooth muscle cellsCoagulation, thrombosis and platelets368The real time in vivo evaluation of platelet-dependent aldosterone prothrombotic action in mice369Development of a method for in vivo detection of active thrombi in mice370The antiplatelet effects of structural analogs of the taurine chloramine371The influence of heparin anticoagulant drugs on functional state of human platelets372Regulation of platelet aggregation and adenosine diphosphate release by d dimer in acute coronary syndrome (in vitro study)Oxygen sensing, ischaemia and reperfusion375Sirtuin 5 mediates brain injury in a mouse model of cerebral ischemia-reperfusion376Abscisic acid: a new player in cardiomyocyte protection from ischaemia?377Protective effects of ultramicronized palmitoylethanolamide (PEA-um) in myocardial ischaemia and reperfusion injury in vivo378Identification of stem cell-derived cardiomyocytes using cardiac specific markers and additional testing of these cells in simulated ischemia/reperfusion system379Single-dose intravenous metformin treatment could afford significant protection of the injured rat kidney in an experimental model of ischemia-reperfusion380Cardiotoxicity of long acting muscarinic receptor antagonists used for chronic obstructive pulmonary disease381Dependence antioxidant potential on the concentration of amino acids382The impact of ischemia-reperfusion on physiological parameters,apoptosis and ultrastructure of rabbit myocardium with experimental aterosclerosisMitochondria and energetics385MicroRNA-1 dependent regulation of mitochondrial calcium uniporter (MCU) in normal and hypertrophied hearts386Mitochondrial homeostasis and cardioprotection: common targets for desmin and aB-crystallin387Overexpression of mitofusin-2 (Mfn2) and associated mitochondrial dysfunction in the diabetic heart388NO-dependent prevention of permeability transition pore (MPTP) opening by H2S and its regulation of Ca2+ accumulation in rat heart mitochondria389G protein coupled receptor kinase 2 (GRK2) is fundamental in recovering mitochondrial morphology and function after exposure to ionizing radiation (IR)Gender issues392Sex differences in pulmonary vascular control; focus on the nitric oxide pathwayAging395Heart failure with preserved ejection fraction develops when feeding western diet to senescence-accelerated mice396Cardiovascular markers as predictors of cognitive decline in elderly hypertensive patients397Changes in connexin43 in old rats with volume overload chronic heart failureGenetics and epigenetics400Calcium content in the aortic valve is associated with 1G>2G matrix metalloproteinase 1 polymorphism401Neuropeptide receptor gene s (NPSR1) polymorphism and sleep disturbances402Endothelin-1 gene Lys198Asn polymorphism in men with essential hypertension complicated and uncomplicated with chronic heart failure403Association of common polymorphisms of the lipoprotein lipase and pon1 genes with the metabolic syndrome in a sample of community participantsGenomics, proteomics, metabolomics, lipidomics and glycomics405Gene expression quantification using multiplexed color-coded probe pairs to determine RNA content in sporadic cardiac myxoma406Large-scale phosphorylation study of the type 2 diabetic heart subjected to ischemia / reperfusion injury407Transcriptome-based identification of new anti-inflammatory properties of the olive oil hydroxytyrosol in vascular endothelial cell under basal and proinflammatory conditions408Gene polymorphisms combinations and risk of myocardial infarctionComputer modelling, bioinformatics and big data411Comparison of the repolarization reserve in three state-of-the-art models of the human ventricular action potentialMetabolism, diabetes mellitus and obesity414Endothelial monocyte-activating polypeptide-II improves heart function in type -I Diabetes mellitus415Admission glucose level is independent predictor of impaired left ventricular function in patients with acute myocardial infarction: a two dimensional speckle-tracking echocardiography study416Association between biochemical markers of lipid profile and inflammatory reaction and stiffness of the vascular wall in hypertensive patients with abdominal obesity417Multiple common co-morbidities produce left ventricular diastolic dysfunction associated with coronary microvascular dysfunction, oxidative stress and myocardial stiffening418Investigating the cardiovascular effects of antiretroviral drugs in a lean and high fat/sucrose diet rat model of obesity419Statins in the treatment of non-alcoholic steatohepatitis (NASH). Our experience from a 2-year prospective study in Constanta County, Romania420Epicardial adipose tissue as a predictor of cardiovascular outcome in patients with ACS undergoing PCI?Arterial and pulmonary hypertension423Dependence between heart rhythm disorers and ID polymorphism of ACE gene in hypertensive patients424Molecular mechanisms underlying the beneficial effects of Urocortin 2 in pulmonary arterial hypertension425Inhibition of TGf-b axis and action of renin-angiotensin system in human ascending aorta aneurysms426Early signs of microcirculation and macrocirculation abnormalities in prehypertension427Vascular smooth muscle cell-expressed Tie-2 controls vascular tone428Cardiac and vascular remodelling in the development of chronic thrombo-embolic pulmonary hypertension in a novel swine modelBiomarkers431Arrhythmogenic cardiomyopathy: a new, non invasive biomarker432Can circulating microRNAs distinguish type 1 and type 2 myocardial infarction?433Design of a high-throughput multiplex proteomics assay to identify left ventricular diastolic dysfunction in diabetes434Monocyte-derived and P-selectin-carrying microparticles are differently modified by a low fat diet in patients with cardiovascular risk factors who will and who will not develop a cardiovascular event435Red blood cell distribution width assessment by polychromatic interference microscopy of thin films in chronic heart failure436Invasive and noninvasive evaluation of quality of radiofrequency-induced cardiac denervation in patients with atrial fibrillation437The effect of therapeutic hypothermia on the level of brain derived neurotrophic factor (BDNF) in sera following cardiopulmonary resustitation438Novel biomarkers to predict outcome in patients with heart failure and severe aortic stenosis439Biological factors linking depression and anxiety to cardiovascular disease440Troponins and myoglobin dynamic at coronary arteries graftingInvasive, non-invasive and molecular imaging443Diet composition effects on the genetic typing of the mouse ob mutation: a micro-ultrasound characterization of cardiac function, macro and micro circulation and liver steatosis444Characterization of pig coronary and rabbit aortic lesions using IV-OCT quantitative analysis: correlations with histologyGene therapy and cell therapy447Enhancing the survival and angiogenic potential of mouse atrial mesenchymal cells448VCAM-1 expression in experimental myocardial infarction and its relation to bone marrow-derived mononuclear cell retentionTissue engineering451Advanced multi layered scaffold that increases the maturity of stem cell-derived human cardiomyocytes452Response of engineered heart tissue to simulated ischemia/reperfusion in the presence of acute hyperglycemic conditions453Serum albumin hydrogels prevent de-differentiation of neonatal cardiomyocytes454A novel paintbrush technique for transfer of low viscosity ultraviolet light curable cyan methacrylate on saline immersed in-vitro sheep heart [O] . V Garcia-Martinez, C Lopez Sanchez, W Hamed, 2016

机译：早期心脏腔室specification291Bmp2期间海报会议2Morphogenetic mechanisms290MiR-133调控对视黄酸途径在早期心脏具有或不具有2型糖尿病mellitus295Association循环的α2B肾上腺素受体基因插入/缺失多态性的缺失等位基因和高血压的formationDevelopmental genetics294Association通过的miR-130调节心房分化陷波的作用：Vascular298Gamma分泌酶抑制剂阻止增殖和动脉导管未闭的迁移平滑肌细胞 - 内源性大麻素1型受体（CNR1）与冠状动脉疾病（CAD）的2型糖尿病mellitusCell生长，分化和干细胞的G1359A多态性的在出生后的闭合信令导管arteriosus299Mesenchymal基质状从诱导的多能干细胞（iPS）衍生的单元（MLC）细胞：有希望的治疗选项，以促进neovascularization300Sonic刺猬促进间充质干细胞分化为vascula ř平滑肌细胞cardiovacsular disease301Proinflammatory细胞因子分泌和在内皮细胞中表观遗传学修饰处理的LPS-GinfivalisCell死亡和细胞凋亡 - Vascular304Mitophagy充当针对人血管平滑肌细胞中的保障机制凋亡诱导动脉粥样硬化lipidsTranscriptional控制和RNA种类 - 在Vascular307MicroRNA-34a的作用利用后缺氧内皮cells310Specific循环微RNA水平的血管injury309Long非编码RNA景观临床适用的方法衰减新内膜形成与miR-146a的抑制剂的血管calcification308Local递送关联与高血压，高血糖和功能失调的HDL在急性冠状动脉综合征patientsCytokines和细胞炎症 - Vascular313Phosphodiesterase5A向上调控血管内皮促炎性条件下进行：为ω-3polyunsaturated aatty酸二十二碳六acid31一个新公开的抗炎活性4Cardiovascular风险修改与超低剂量抗细胞因子药物在人M-CSF的巨噬细胞的类风湿arthritis315Conversion成泡沫细胞降低了其经典M1偏振activation316Lymphocytic心肌炎具有增加斑块炎症和在冠状动脉中的斑块出血一致时，促进心肌infarction317Serum骨保护素水平的促炎性应答通过抑制手段Heart323A新的合成肽对肥大体外 - predictsdeclined众多患者的代谢syndromeGrowth因子和神经激素循环内皮 - 衍生的细胞和单核衍生的祖细胞 - 胃泌素释放肽（GRP）对血管inflammationSignal转导的Vascular320Effect p38的α图激酶nfkb324Inducible成纤维细胞特异性敲除是在异丙基肾上腺素诱导的心脏hypertrophy325Regulation的小鼠模型中的心脏保护β-肾上腺素受体诱发由抑制性肌力响应ORY G蛋白，腺苷酸环化酶同种型5,6和phosphodiesterases326Binding到RGS3和M2毒蕈碱性乙酰胆碱受体调制的刺激p190RhoGAP的翻译后修饰，parylation和脱乙酰化中LMNA的心脏myocytes327Cardiac调节底物特异性扩张的心肌病小鼠model328Beta肾上腺素能调节所述b56delta / PP2A全酶在心肌细胞通过b56delta磷酸化丝氨酸573Nitric氧化物和活性氧 - Vascular331Oxidative应激诱导的miR-200c的破坏SIRT1，FOXO1和eNOS332Antioxidant疗法防止氧化应激诱导内皮功能障碍和提高之间的调节环路伤口Healing333Morphological和在冠状动脉diseaseCytoskeleton红细胞和机械传导的生化特征 - Heart336Novel肌球蛋白的活化剂，JSH化合物，ratsExtracellular矩阵增加心肌收缩力没有变时作用和纤维化 - 的Vascular339Ablation Toll样受体9通过衰减增殖和心脏fibroblasts340Altered血管在因子VII小鼠后肢缺血模型重塑活化蛋白酶（FSAP）deficiencyVasculogenesis，血管生成和proly的arteriogenesis343Pro血管生成作用的分化导致心肌梗死后心脏破裂羟化酶抑制剂及其在用于冠状动脉总occlusion344Nrf2驱动治疗性血管生成的新颖的策略的使用潜在的血管生成转录非依赖性方式：氧化应激response345Angiogenic基因治疗的主调节器的新功能，尽管高效血管生长，不能改善上在鼠后肢侧支血管生长PAR-1抑制的毛细动脉和shunting346Effect在含氧量正常或慢性缺血性后肢的兔肌肉功能-Role model347Quaking是内皮细胞分化的关键调节剂，新血管形成和angiogenesis348在鸡胚绒毛尿囊膜（CAM）“新兴血管生成”。一种不同于心肌祖细胞体内study349Exosomes和间充质干细胞刺激血管生成的体外和GRK2的体内经由EMMPRINEndothelium352Reciprocal调节和血管舒缓激肽受体刺激调制的Ca 2+的细胞内骨的内皮cells353The角色形态发生蛋白9和10在内皮炎症和atherosclerosis354The贡献水平GPR55在分离的人将L-α-溶血磷脂酰肌醇诱导的血管舒张肺arteries355The内皮保护ACE抑制剂Zofenoprilat通过H2S production356A类新的糖模拟药物发挥抗炎活性，以防止游离脂肪酸诱导的内皮dysfunction357Endothelial祖细胞凋亡的内皮细胞从降低喷射fractionheart failure358Proosteogenic基因保留衍生微粒配给differentiatesas在患者的胸主动脉aneurysm359Endothelin ETB REC内皮细胞活化通过经由PI3Kg的对cAMP调节，在动脉的作用IP3 receptors363A新颖功能的激活诱导的钙振荡eptors调解放松来自患有心血管疾病（CVD）的平滑肌和pericytes362CX3CR1阳性髓样细胞在心包阻力动脉到胰岛素应答调节血管平滑肌紧张壁增生，通过平滑肌细胞proliferation364NRP1和NRP2的调制内膜增生的发展vivo365Azithromycin诱导自噬在主动脉平滑肌cellsCoagulation，血栓形成和platelets368The实时血小板依赖性醛固酮促血栓形成作用的体内评价mice369Development玩的方法的重要作用用于体内在mice370The活性血栓的检测抗血小板的血小板聚集和腺苷的人类platelets372Regulation的功能状态肝素抗凝药物的牛磺酸chloramine371The影响结构类似物的效果二磷酸酯的释放通过d二聚体在急性冠状动脉综合征（体外研究）氧传感，局部缺血和脑缺血reperfusion376Abscisic酸的小鼠模型reperfusion375Sirtuin 5介导的脑损伤：在从局部缺血心肌保护的新播放ultramicronized十六酰胺乙醇的377Protective效果（？ PEA-UM）在干细胞衍生的心肌细胞的vivo378Identification心肌缺血再灌注损伤的使用心脏特异性标志物，并在这些细胞中的额外的测试模拟缺血/再灌注system379Single剂量静脉二甲双胍治疗能买得起在受伤大鼠肾脏的显著保护的长效用于慢性阻塞性肺disease381Dependence抗氧化潜力上的缺血 - 再灌注的生理参数，细胞凋亡和超微结构氨基acids382The冲击浓度毒蕈碱性受体拮抗剂缺血reperfusion380Cardiotoxicity的实验模型兔心肌实验aterosclerosisMitochondria和energetics385MicroRNA-1在正常线粒体钙单向转运体（MCU）的依赖性调节和肥大hearts386Mitochondrial稳态和心脏保护：在糖尿病heart388NO结蛋白和线粒体融合蛋白-2 AB-crystallin387Overexpression（Mfn2的）和相关的线粒体功能障碍共同目标依赖性预防通透性转换孔（MPTP）的开口由H 2 S和其在大鼠心脏mitochondria389G蛋白偶联受体的Ca 2+积累的调节激酶2（GRK2）是在回收曝光后线粒体形态和功能于电离辐射（IR）性别issues392Sex差异基本在肺血管的控制;注重与射血分数一氧化氮pathwayAging395Heart失败开发当馈送西方饮食到衰老加速mice396Cardiovascular标志物的中老年大鼠与体积连接蛋白43在老年高血压patients397Changes认知衰退的预测过载慢性心脏failureGenetics和epigenetics400Calcium内容在主动脉瓣与1G相关联> 2G矩阵男性高血压并发和不复杂的与脂蛋白脂肪酶的常见多态性与PON1基因的慢性心脏failure403Association与代谢综合征金属蛋白酶1个polymorphism401Neuropeptide受体基因S（NPSR1）多态性与睡眠disturbances402Endothelin-1基因Lys198Asn多态性社区participantsGenomics，蛋白质组学，代谢组样品中使用复用颜色编码的探针对脂质组学和glycomics405Gene表达定量，以确定在经受的橄榄油的新抗炎性质基于injury407Transcriptome-缺血/再灌注鉴定2型糖尿病心脏的零星心脏myxoma406Large规模磷酸化研究RNA含量羟基酪醇在血管内皮细胞在人类心室动作potentialMetabolism，糖尿病三个国家的最先进的车型在基础和促炎conditions408Gene多态性组合和心肌infarctionComputer建模，生物信息学和复极储备的大data411Comparison的风险细胞和单核细胞obesity414Endothelial激活多肽-II型糖尿病-I mellitus415Admission葡萄糖水平改善心脏功能的左心室功能受损患者急性心肌梗死的独立预测因子：二维斑点追踪超声心动图脂质谱和炎症反应，在高血压患者腹部obesity417Multiple常见共病血管壁的刚度的生化标志物之间ýstudy416Association产生左心室冠状动脉微血管功能障碍，氧化应激和心肌stiffening418Investigating的抗逆转录病毒药物的心血管作用有关的舒张功能障碍贫和高脂肪/非酒精性脂肪性肝炎（NASH）的治疗obesity419Statins的蔗糖饮食大鼠模型。我们在康斯坦察县2年的前瞻性研究经验，Romania420Epicardial脂肪组织心血管结果的ACS患者接受PCI？动脉及肺动脉hypertension423Dependence心脏节律disorers和ACE基因ID多态性与高血压patients424Molecular机制背后的有益预测在TGF-β轴和在人类升主动脉中prehypertension427Vascular微循环和大循环异常aneurysms426Early迹象肾素 - 血管紧张素系统的动作的肺动脉hypertension425Inhibition尿皮质素2的影响平滑肌细胞表达的血管tone428Cardiac铁2控制和血管重塑在开发在一个新颖的猪modelBiomarkers431Arrhythmogenic心肌病慢性血栓栓塞性肺动脉高压：一个新的，非侵入性的biomarker432Can循环微RNA区分类型1和类型2心肌梗塞433Design的高通量含多处？前蛋白质组学测定，以确定左室舒张功能障碍diabetes434Monocyte衍生和P-选择携带微粒不同由低脂肪饮食的患者心血管危险因素谁将会和谁不会被开发宽度评估心血管event435Red血细胞分布修改在慢性心脏failure436Invasive和患者的治疗低温对脑的水平心房fibrillation437The效果射频诱导的心脏去神经支配的质量的非侵入性评价薄膜的多色干涉显微镜中的血清衍生的神经营养因子（BDNF）以下心肺resustitation438Novel生物标志物来预测结果患者心脏衰竭和冠状动脉graftingInvasive，非侵入性和分子imaging443Diet组成的影响Ø链接抑郁和焦虑心血管disease440Troponins和肌红蛋白动态重度主动脉瓣stenosis439Biological因素n中的鼠ob突变的基因分型，：心脏功能，宏观和微观循环和使用IV-OCT定量分析猪冠状动脉和兔子主动脉的病变的肝steatosis444Characterization的微超声表征：与histologyGene疗法和细胞相关性therapy447Enhancing存活和小鼠心房间充质cells448VCAM-1在实验性心肌梗塞表达及其与骨髓来源的单核细胞retentionTissue engineering451Advanced多层支架增加干细胞衍生的工程改造的心脏组织的人类cardiomyocytes452Response的成熟到模拟缺血/再灌注的血管生成潜力急性高血糖conditions453Serum白蛋白水凝胶的存在防止新生儿cardiomyocytes454A新颖画笔技术的去分化为低粘度的转印紫外光可固化青色甲基丙烯酸酯上的盐水浸没在体外羊心脏
8. Abstract Delay-Differential Equation Modeling Size Dependent Cell Growth and Division [R] . Gyllenberg, M., Heijmans, H. J. A. M. 1985

机译：抽象延迟微分方程模型尺度依赖细胞生长与分裂

Functional Fokker-Planck Equation Approach for a Gompertzian Model of Tumour Cell Growth

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