ATRIAL NATRIURETIC POLYPEPTIDE (AMP) INHIBITS VASOPRESSIN (VP)-INDUCED HYPERTENSION IN CONSCIOUS RATS : Atrial Natriuretic Polypeptide (I) : PROCEEDINGS OF THE 50th ANNUAL SCIENTIFIC MEETING OF THE JAPANESE CIRCULATION SOCIETY
スポンサーリンク
概要
- 論文の詳細を見る
- 社団法人日本循環器学会の論文
- 1986-08-20
著者
-
KIYOHARA Yutaka
Kyushu University
-
Sato Makito
The Second Department Of Internal Medicine Tohoku University School Of Medicine
-
Kurata Yasutaka
Department Of Cardiovascular Medicine Faculty Of Medicine Tottori University
-
Yasujima Minoru
東北大学 医系研究内部障害学分野
-
Abe Keishi
The Second Department Of Internal Medicine Tohoku University School Of Medicine
-
Yoshida K
Furukawa City Hospital
-
Yoshinaga Kaoru
The Second Department Of Internal Medicine Tohoku University School Of Medicine
-
Totsune Kazuhito
東北大学 医学部保健学科
-
Totsune Kazuhito
Second Department Of Internal Medicine Tohoku University School Of Medicine
-
Yasujima Minoru
Department Of Laboratory Medicine Hirosaki University School Of Medicine
-
KASAI YUTAKA
The Second Department of Internal Medicine, Tohoku University School of Medicine
-
OTA Kozo
Furukawa City Hospital
-
YASUJIMA MINORU
The Second Department of Internal Medicine, Tohoku University School of Medicine
-
KOHZUKI MASAHIRO
The Second Department of Internal Medicine, Tohoku University School of Medicine
-
OMATA KEN
The Second Department of Internal Medicine, Tohoku University School of Medicine
-
TANNO MASAYA
The Second Department of Internal Medicine, Tohoku University School of Medicine
-
KUDO Kei
The Second Department of Internal Medicine, Tohoku University School of Medicine
-
TAKEUCHI Kazuhisa
The Second Department of Internal Medicine, Tohoku University School of Medicine
-
Takeuchi Kazuhisa
Department Of Analytical Medical Technology Tohoku University School Of Health Sciences
-
Yasujima M
Division Of Cardiology Department Of Internal Medicine The Jikei University School Of Medicine
-
Abe Koji
The Department Of Cardiovascular Medicine Graduate School Of Medical Sciences Kumamoto University
-
Omata Ken
The Second Department Of Internal Medicine Tohoku University School Of Medicine
-
Tanno Masaya
The Second Department Of Internal Medicine Tohoku University School Of Medicine
-
Sato Ko
Tohoku Univ. Sendai Jpn
-
Abe Keishi
The Second Department Of Internal Medicine
-
Yasujima Minoru
Division Of Cardiology Department Of Internal Medicine The Jikei University School Of Medicine
-
Kiyohara Yutaka
The Research Committee For Primary Hyperlipidemia Research On Measures For Intractable Diseases By T
-
Saito K
The Second Department Of Internal Medicine Tohoku University School Of Medicine
-
Kasai Yutaka
Division Of Gastroenterological Surgery Department Of Surgery Kawasaki Medical School
-
Kusaka Takashi
Dept. Of Intern. Med Tohoku Univer. School Of Med
-
Kohzuki M
Department Of Internal Medicine And Rehabilitation Science Tohoku University Graduate School Of Medi
-
Omata K
Furukawa City Hospital
-
Omata K
Health Administration Center Miyagi University Of Education
-
Takeuchi Kazuhisa
Division Of Nephrology Endocrinology And Vascular Medicine Department Of Medicine Tohoku University
-
Kohzuki Masahiro
Department Of Internal Medicine And Rehabilitation Science Tohoku University Graduate School Of Medi
-
Kohzuki Masahiro
Department Of Internal Medicine And Rehabilitation Science Tohoku University Graduate School Of Medi
-
Kohzuki Masahiro
Department Of Internal Medicine And Rehabilitation Science Tohoku University Graduate School Of Medi
-
Yoshinaga Kaoru.
The 2nd Department Of Internal Medicine Tohoku University School Of Med
-
Kohzuki Masahiro
Department Of Internal Medicine And Rehabilitation Science Tohoku University Graduate School Of Medi
-
Ota Kozo
Division Of Nephrology Endocrinology And Vascular Medicine Tohoku University School Of Medicine
関連論文
- PE-404 Improvement of γ-glutamyl Transferase Activity by CPAP may Reduce Cardiovascular Risk in Patients with Obstructive Sleep Apnea(PE068,Obesity/SAS 2 (H),Poster Session (English),The 73rd Annual Scientific Meeting of the Japanese Circulation Society)
- The Japanese Society of Hypertension Committee for Guidelines for the Management of Hypertension
- PJ-005 Localization of von Willebrand Factor-cleaving Protease (ADAMTS-13) in Coronary Thrombi from Patients with Acute Myocardial Infarction(Acute myocardial infarction, clinical (pathophysiology)-3 (IHD) PJ1,Poster Session (Japanese),The 70th Anniversar
- Association of SLC6A9 Gene Variants with Human Essential Hypertension
- PE-463 Similarities and Differences between Coronary Spasm and Atherosclerosis : a Coronary Angiographic Study(PE078,Angina Pectoris (Clinical) (IHD),Poster Session (English),The 73rd Annual Scientific Meeting of the Japanese Circulation Society)
- A Simple Risk Score to Predict In-Hospital Death of Elderly Patients With Acute Decompensated Heart Failure : Hypoalbuminemia as an Additional Prognostic Factor
- PJ-584 Contributing Factors for the Incidence of Paroxysmal Atrial Fibrillation in Patients with Obstructive Sleep Apnea(PJ098,Obesity/SAS (H),Poster Session (Japanese),The 73rd Annual Scientific Meeting of The Japanese Circulation Society)
- PJ-513 Hyponatremia is an Important Predictor for In-hospital Mortality in Heart Failure Patients with Preserved Ejection Fraction(PJ086,Heart Failure (Treatment) 2 (M),Poster Session (Japanese),The 73rd Annual Scientific Meeting of The Japanese Circulati
- PE-037 A Q312X Mutation in the Hemojuvelin Gene is Associated with Cardiomyopathy due to Juvenile Hemochromatosis(Cardiomyopathy, basic/clinical(03)(M),Poster Session(English),The 72nd Annual Scientific Meeting of the Japanese Circulation Society)
- PJ-704 Delays of Hospital Admission from the Onset of Acute Myocardial infarction Induce Poor Prognosis in Women in Kumamoto Prefecture(Preventive medicine/Epidemiology/Education-5, The 71st Annual Scientific Meeting of the Japanese Circulation Society)
- PJ-188 Changes in Plasma Von Willebrand Factor-cleaving Protease (ADAMTS13) Levels in Patients with Unstable Angina(Angina pectoris, basic/clinical-4, The 71st Annual Scientific Meeting of the Japanese Circulation Society)
- PE-179 Changes in Von Willebrand Factor-cleaving Protease (ADAMTS13) and Prognosis after Acute Myocardial Infarction(Thromboembolism/Antithrombotic therapy/Thrombolysis-3, The 71st Annual Scientific Meeting of the Japanese Circulation Society)
- OE-052 Targeted Deletion of Class A Macrophage Scavenger Receptor (CD204) Increases the Risk of Cardiac Rupture after Experimental Myocardial Infarction(Acute myocardial infarction, basic-1, The 71st Annual Scientific Meeting of the Japanese Circulation S
- OJ-179 Aldosterone Production Level is Strongly Predicted by Absolute Value of Difference of Subcutaneous and Visceral Fat Area in Essential Hypertension(OJ30,Hypertension, Clinical (H),Oral Presentation (Japanese),The 73rd Annual Scientific Meeting of Th
- OJ-134 Aldosterone, but Not Angiotensin II, Reduces Angiotensin Converting Enzyme 2 Gene Expression Levels in Cultured Neonatal Rat Cardiomyocytes(OJ23,Hypertension, Basic (H),Oral Presentation (Japanese),The 73rd Annual Scientific Meeting of The Japanese
- 2 The Effects of Statin for Coronary Artery Spasm(Recent Progress in the Management of Vasospastic Angina,Meet the Expert 6 (ME-6) (IHD),The 73rd Annual Scientific Meeting of The Japanese Circulation Society)
- Aldosterone, but Not Angiotensin II, Reduces Angiotensin Converting Enzyme 2 Gene Expression Levels in Cultured Neonatal Rat Cardiomyocytes
- PJ-321 Clinical Factors Affecting Serum Potassium Concentration(Heart failure, clinical(16)(M),Poster Session(Japanese),The 72nd Annual Scientific Meeting of the Japanese Circulation Society)
- PE-343 Effects of the Infusion of A-type Natriuretic Hormone (ANP) on the Activity of Hypothalamic-Pitultary-Adrenal Axis in Patients With Heart Failure(Heart failure, clinical(10)(M),Poster Session(English),The 72nd Annual Scientific Meeting of the Japan
- PE-239 The Effects of Statins on Coronary Artery Spasm (S-CAST Study)(Acute coronary syndrome, basic/clinical(04)(IHD),Poster Session(English),The 72nd Annual Scientific Meeting of the Japanese Circulation Society)
- PE-003 Coronary spasm is frequently induced after stent implantation in patients with acute coronary syndrome(Angina pectoris, basic/clinical(03)(IHD),Poster Session(English),The 72nd Annual Scientific Meeting of the Japanese Circulation Society)
- OJ-229 A Significant Decrease of Circulating Blood Dendritic Cells in Patients with Coronary Artery Disease(Atherosclerosis, clinical(04)(IHD),Oral Presentation (Japanese),The 72nd Annual Scientific Meeting of the Japanese Circulation Society)
- OE-083 Coronary Spasm Preferentially Occurs at the Branching Site : possible role of impaired endothelial NO activity due to low shear tress(Angina pectoris, basic/clinical(01)(IHD),Oral Presentation(English),The 72nd Annual Scientific Meeting of the Japa
- FRS-005 Aldosterone Excretion Rate is Associated with Abdominal Subcutaneous Fat Area and with Diastolic Blood Pressure in Patients with Essential Hypertension(New Clinical Aspects for Hypertension(H),Featured Research Session,The 72nd Annual Scientific M
- 2 Spastic Angina Genetic (SAGE) Study(Plenary Session 7 (PL-7) (M) Genomic Approaches to Cardiovascular Diseases : Present and Future,Special Program,The 72nd Annual Scientific Meeting of the Japanese Circulation Society)
- Osteopontin Expression of Circulating T Cells and Plasma Osteopontin Levels are Increased in Relation to Severity of Heart Failure
- Coronary Spasm and hs-CRP(Letter to the Editor)
- Hypoadiponectinemia is Associated With Impaired Glucose Tolerance and Coronary Artery Disease in Non-Diabetic Men
- Coronary Spasm is Associated With Chronic Low-Grade Inflammation
- PJ-249 Impaired Waveform Index of Ophthalmic Artery Predicts the Severity of Systemic Atherosclerosis(Echo/Doppler-16, The 71st Annual Scientific Meeting of the Japanese Circulation Society)
- PE-372 Smoking Cessation is Associated with Increased Plasma Levels of Adiponectin in Men with Stable Effort Angina(Smoking, The 71st Annual Scientific Meeting of the Japanese Circulation Society)
- OE-145 Hypoadiponectinemia is Associated with Coronary Endothelial Dysfunction in Patients with Coronary Spastic Angina(Coronary circulation, basic/clinical-1, The 71st Annual Scientific Meeting of the Japanese Circulation Society)
- OE-187 Clinical Outcomes of Sirolimus-Eluting Stent in Coronary Intervention Kumamoto Study(Coronary revascularization, PCI-1 (IHD) OE32,Oral Presentation (English),The 70th Anniversary Annual Scientific Meeting of the Japanese Circulation Society)
- Proposed Guidelines for Hypertriglyceridemia in Japan with Non-HDL Cholesterol as the Second Target
- Prevalence of chronic kidney disease (CKD) in the Japanese general population predicted by the MDRD equation modified by a Japanese coefficient
- Estimation of glomerular filtration rate by the MDRD study equation modified for Japanese patients with chronic kidney disease
- Guidelines for Diagnosis and Treatment of Patients With Vasospastic Angina (Coronary Spastic Angina) (JCS 2008) : Digest Version
- PJ-513 Hyponatremia is an Important Predictor for In-hospital Mortality in Heart Failure Patients with Preserved Ejection Fraction(PJ086,Heart Failure (Treatment) 2 (M),Poster Session (Japanese),The 73rd Annual Scientific Meeting of The Japanese Circulati
- OE-081 A Simple Risk Score to Stratify Risk of In-hospital Mortality in Elderly Patients with Acute Decompensated Heart Failure(OE14,Heart Failure (Biomarker) (M),Oral Presentation (English),The 73rd Annual Scientific Meeting of The Japanese Circulation S
- PJ-113 Nkx2.5(+) But Not Flk1(+) Cardiac Progenitor Cells are Fated to Pacemaker Cells Expressing I_f Predominantly Encoded by HCN4 Gene(Heart failure, basic(05)(M),Poster Session(Japanese),The 72nd Annual Scientific Meeting of the Japanese Circulation So
- PJ-781 Continuous Positive Airway Pressure Therapy Reduces Serum Amyloid A/LDL Complex in Patients with Obstructive Sleep Apnea(Diabetes/Obesity/Metabolic syndrome-13, The 71st Annual Scientific Meeting of the Japanese Circulation Society)
- PJ-104 Delayed Onset of Beating and Decreased Expression of T-type Ca^ Channel in Mouse ES Cell-Derived Cardiocytes Carrying Human Chromosome 21(Excitation-contraction coupling/Ion channel, The 71st Annual Scientific Meeting of the Japanese Circulatio
- PE-526 Nasal Continuous Positive Airway Pressure and Serum Uric Acid Levels in Patients with Obstructive Sleep Apnea(Kidney/Renal circulation-3, The 71st Annual Scientific Meeting of the Japanese Circulation Society)
- Inhibition of Inward Rectifier K^+ Currents by Angiotensin II in Rat Atrial Myocytes : Lack of Effects in Cells from Spontaneously Hypertensive Rats
- Effects of Angiotensin II on the Action Potential Durations of Atrial Myocytes in Hypertensive Rats
- Developmental Changes of Ni^ Sensitivity and Automaticity in Nkx2.5-Positive Cardiac Precursor Cells From Murine Embryonic Stem Cell
- State-Dependent Blocking Actions of Azimilide Dihydrochloride (NE-10064) on Human Cardiac Na^+ Channels
- L-Cysteine Prevents Oxidation-Induced Block of the Cardiac Na^+ Channel Via Interaction With Heart-Specific Cysteinyl Residues in the P-Loop Region
- OJ-219 Hypoadiponectinemia Enhances the Formation of Large Fibro-fatty-rich Coronary Plaques while Hypercholesterolemia Promotes the Development of Necrotic Core-rich Coronary Plaques(Intravascular endoscopy/Intravascular ultrasound-2, The 71st Annual Sci
- FRS-007 Coronary Plaque Characterization of Culprit Lesions Assessed by Intracoronary Ultrasonography Radiofrequency Data can Predict Angiographic No-reflow/Slow-flow Phenomenon during Coronary Intervention(Coronary Revascularization (clinical) 1, The 71s
- Coronary artery spasm-Clinical features, diagnosis, pathogenesis, and treatment
- PJ-113 Nkx2.5(+) But Not Flk1(+) Cardiac Progenitor Cells are Fated to Pacemaker Cells Expressing I_f Predominantly Encoded by HCN4 Gene(Heart failure, basic(05)(M),Poster Session(Japanese),The 72nd Annual Scientific Meeting of the Japanese Circulation So
- INSIG2 gene rs7566605 polymorphism is associated with severe obesity in Japanese
- Variations in the FTO gene are associated with severe obesity in the Japanese
- A Circadian Variation in the Excretion of Urinary Kinin, Kallikrein and Prostaglandin E in Normal Volunteers : THE 10th CONFERENCE ON THE PATHOGENESIS OF HYPERTENSION
- Implication of Endogenous Prostaglandin System in the Antihypertensive Effect of Captopril,SQ14225, in Low Renin Hypertension : IX Conference on the Pathogenesis of Hypertension
- THE ROLE OF RENAL PROSTAGLANDIN E AND KALLIKREIN IN PATHOGENESIS OF ESSENTIAL HYPERTENSION
- INHIBITION OF ANGIOTENSIN CONVERTING ENZYME BY SQ 14,225 IN RENOVASCULAR HYPERTENSION : Cardiac Surgery II, Hemodialysis, Hypertension II : IInd Auditorium : Proceedings of the 43rd Annual Meeting of the Japanese Circulation Society, Tokyo, 1979
- Implication of Renal Prostaglandin E in Urinary Sodium Excretion : VII CONFERENCE ON THE PATHOGENESIS OF HYPERTENSION
- -127-THE ROLE OF RENIN-ANGIOTENSIN-ALDOSTERONE SYSTEM,RENAL DEPRESSOR SUBSTANCE AND BODY FLUID IN THE PATHOGENESIS OF RENAL HYPERTENSION : Hypertension,Catecholamine : PROCEEDINGS OF THE 42nd ANNUAL MEETING OF THE JAPANESE CIRCULATION SOCIETY
- Studies on Renomedullary Prostaglandin and Renal Kallikrein-Kinin System in Hypertension
- RENAL KALLIKREIN-KININ SYSTEM IN ESSENTIAL HYPERTENSION : IInd Auditorium
- Renoprotective Effect of Angiotensin-Converting Enzyme Inhibitor Combined with α_1-Adrenergic Antagonist in Spontaneously Hypertensive Rats with Renal Ablation
- Glucocorticoidal Regulation of Pituitary Vasopressin Content in Rats
- Cardiac Angiotensin Converting Enzyme and Endothelin Receptor in Rats With Chronic Myocardial Infarction
- -P103-THE AUGMENTED BLOOD PRESSURE RESPONSE TO CHRONIC ANGIOTENSIN II (ANG II) INFUSION IN PARTIALLY NEPHRECTOMIZED RATS : Hypertension : FREE COMMUNICATIONS(III) : PROCEEDINGS OF THE 53th ANNUAL SCIENTIFIC MEETING OF THE JAPANESE CIRCULATION SOCIETY
- Effects of Chronically Administered Atrial Natriuretic Factor in Aldosterone-Infused Hypertensive Rats : SYMPOSIUM ON ATRIAL NATRIURETIC POLYPEPTIDE (ANP): Basic and Clinical Research : 51th Annual Scientific Session of the Japanese Circulation Society
- RENAL VEIN PLASMA RENIN ACTIVITY IN PATIENTS WITH UNILATERAL RENOVASCULAR HYPERTENSION
- Antihypertensive Effect of Synthetic Atrial Natriuretic Factor in Vasopressin-Infused Rats : THE 15th CONFERENCE ON THE PATHOGENESIS OF HYPERTENSION
- CHANGES IN PLASMA α-HUMAN ATRIAL NATRIURETIC POLYPEPTIDE, AND URINARY PROSTAGLANDIN E AND KALLIKREIN-KININ DURING ACUTE SALINE VOLUME EXPANSION IN MAN : Atrial Natriuretic Polypeptide (I) : PROCEEDINGS OF THE 50th ANNUAL SCIENTIFIC MEETING OF THE JAPANESE
- ATRIAL NATRIURETIC POLYPEPTIDE (AMP) INHIBITS VASOPRESSIN (VP)-INDUCED HYPERTENSION IN CONSCIOUS RATS : Atrial Natriuretic Polypeptide (I) : PROCEEDINGS OF THE 50th ANNUAL SCIENTIFIC MEETING OF THE JAPANESE CIRCULATION SOCIETY
- EFFECTS OF KALLIKREIN AND KININ ON THE SYNTHESIS OF PROSTAGLANDIN E_2 (PGE_2) IN THE MICRODISSECTED RABBIT NEPHRONS : Hypertension (I) : FREE COMMUNICATIONS (I) : PROCEEDINGS OF THE 49th ANNUAL SCIENTIFIC MEETING OF THE JAPANESE CIRCULATION SOCIETY
- PLASMA PROSTAGLANDIN E_1 LEVELS IN VARIOUS TYPES OF HYPERTENSION
- PE-418 Adipocyte Type-1 Plasminogen Activator Inhibitor and Adiponectin Production are Affected by Metabolic Syndrome Factors : Triglycerides and Insulin(Diabetes/Obesity/Metabolic syndrome-06, The 71st Annual Scientific Meeting of the Japanese Circulatio
- PJ-377 Postprandial Platelet Activation in Obesity : Role of an Adipocytes-derived ob-gene Product Leptin(Diabetes/Obesity/Metabolic syndrome-9 (H) PJ64,Poster Session (Japanese),The 70th Anniversary Annual Scientific Meeting of the Japanese Circulation S
- PJ-119 Synergistic Interaction of Plasma BNP and Glucose Levels for Enhanced Risk for Cardiovascular Re-attacks in Patients with Heart Failure(Heart failure, clinical(13)(M),Poster Session(Japanese),The 72nd Annual Scientific Meeting of the Japanese Circu
- Dementia and Physical Disability as Competing Risks for Mortality in a Community-Based Sample of the Elderly Japanese
- PJ-589 Serial Changes in von Willebrand Factor-cleaving Protease, ADAMTS-13 in Patients with Acute Myocardial Infarction(Acute myocardial infarction, clinical (pathophysiology)-4 (IHD) PJ99,Poster Session (Japanese),The 70th Anniversary Annual Scientific
- A randomized open-label comparative study of conventional therapy versus mizoribine onlay therapy in patients with steroid-resistant nephrotic syndrome (postmarketing survey)
- Slower Decline of Glomerular Filtration Rate in the Japanese General Population : A Longitudinal 10-Year Follow-Up Study
- Clinical guidelines of IgA nephropathy
- FRS-116 Circulating Class A Macrophage Scavenger Receptor Positive Circulating Mononuclear Cells Were Specifically Increased in Patients with Acute Coronary Syndrome(Novel Aspects for Acute Coronary Syndrome(IHD),Featured Research Session,The 72nd Annual
- Predominant Effect of A-Type Natriuretic Peptide on Reduction of Oxidative Stress During the Treatment of Patients With Heart Failure
- PJ-799 A Predominant Effect on A-type Natriuretic Peptide on Reduction of Oxidative Stress during the Treatment of Patients with Heart Failure(Heart failure, clinical-18, The 71st Annual Scientific Meeting of the Japanese Circulation Society)
- PJ-616 A Novel Genetic Marker for Coronary Spasm in Women from a Genome-Wide Analysis(Genetics/Genetically engineered models/Gene therapy-4, The 71st Annual Scientific Meeting of the Japanese Circulation Society)
- -P30-MECHANISMS FOR INTRACELLULAR CALCIUM OSCILLATION RELATED TO CALCIUM OVERLOAD IN CARDIAC CELL : Electrophysiology : FREE COMMUNICATIONS(III) : PROCEEDINGS OF THE 53th ANNUAL SCIENTIFIC MEETING OF THE JAPANESE CIRCULATION SOCIETY
- BLOOD PRESSURE REGULATION IN CHRONIC HYPOTENSIVE AND HYPERTENSIVE PATIENTS WITH CHRONIC RENAL FAILURE
- Prevalence of chronic kidney disease in the Japanese general population
- Head-Down Tilt Posture Attenuates Anaphylactic Hypotension in Mice and Rats
- 7.Inhibitory effect of anaphylaxis on oxygen consumption of isolated perfused rat liver
- Effects of Norepinephrine and Histamine on Vascular Resistance in Isolated Perfused Mouse Liver
- Effect of Sodium Chloride on Prostaglandin E_2 Synthesis in Rat Renal Papillary Collecting Tubule Cells in Culture : THE 14th CONFERENCE ON THE PATHOGENESIS OF HYPERTENSION
- Bartter′s Syndrome with Normal Urinary Excretion of Prostaglandin E:Therapeutic Effects of Propranolol,Spironolactone,Indomethacin and Potassium Chloride
- Portacaval shunting attenuates portal hypertension and systemic hypotension in rat anaphylactic shock
- Japan Renal Biopsy Registry : the first nationwide, web-based, and prospective registry system of renal biopsies in Japan
- Guidelines for Smoking Cessation (JCS 2010) : Digest Version
- Reciprocal Control of hERG Stability by Hsp70 and Hsc70 with Implication for Restoration of LQT2 Mutant Stability
- Electrophysiological Properties of Prion-Positive Cardiac Progenitors Derived From Murine Embryonic Stem Cells
- Exaggerated response of renin secretion to captopril (SQ 14225) in renovascular hypertension.
- Roles of Na/Ca Exchanger and Sarcoplasmic Reticulum Ca Clock in SinoAtrial Node Pacemaking: Insights from Bifurcation Analysis of a Mathematical Model