الجامعة :جامعة المنصورة |
الكلية :كلية العلوم |
القسم :الفيزياء |
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| 1- بيانات المقرر :- |
| | الرمز الكودى: | Phys621 | | اسم المقرر: | الرياضيات الحيوية | | الفرقة: | درجة الماجستير فى العلوم / الفيزياء / الفيزياء النظرية | | عنوان البرنامج: | - جميع البرامج الاكاديمية
- الماجستير فى الفيزياء النظرية
| | التخصص: | رئيسياً | | عدد الساعات: | نظري: | 2 | فصل: | 1 | عملى: | |
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| 2- أهداف المقرر :- |
| - to introduce Mathematical Biology
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| 3- نواتج التعلم المستهدفة للمقرر :- |
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| 4- محتويات المقرر :- |
| | م | الموضوع | الأسبوع |
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| 1 | Multi-Species Waves and Practical Applications 1 1.1 Intuitive Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Waves of Pursuit and Evasion in Predator–Prey Systems . . . . . . . 5 1.3 Competition Model for the Spatial Spread of the Grey Squirrel in Britain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4 Spread of Genetically Engineered Organisms . . . . . . . . . . . . . 18 1.5 Travelling Fronts in the Belousov–Zhabotinskii Reaction . . . . . . . 35 1.6 Waves in Excitable Media . . . . . . . . . . . . . . . . . . . . . . . 41 1.7 Travelling Wave Trains in Reaction Diffusion Systems with Oscillatory Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 1.8 Spiral Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 1.9 Spiral Wave Solutions of λ–ω Reaction Diffusion Systems . . . . . . 61 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2. Spatial Pattern Formation with Reaction Diffusion Systems 71 2.1 Role of Pattern in Biology . . . . . . . . . . . . . . . . . . . . . . . 71 2.2 Reaction Diffusion (Turing) Mechanisms . . . . . . . . . . . . . . . 75 2.3 General Conditions for Diffusion-Driven Instability: Linear Stability Analysis and Evolution of Spatial Pattern . . . . . . . 82 2.4 Detailed Analysis of Pattern Initiation in a Reaction Diffusion Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 2.5 Dispersion Relation, Turing Space, Scale and Geometry Effects in Pattern Formation Models . . . . . . . . . . . . . . . . . . . . . . 103 2.6 Mode Selection and the Dispersion Relation . . . . . . . . . . . . . . 113 2.7 Pattern Generation with Single-Species Models: Spatial Heterogeneity with the Spruce Budworm Model . . . . . . . . . . . . 120 xvi Contents, Volume II 2.8 Spatial Patterns in Scalar Population Interaction Diffusion Equations with Convection: Ecological Control Strategies . . . . . . . 125 2.9 Nonexistence of Spatial Patterns in Reaction Diffusion Systems: General and Particular Results . . . . . . . . . . . . . . . . . . . . . 130 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 3. Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms 141 3.1 Mammalian Coat Patterns—‘How the Leopard Got Its Spots’ . . . . . 142 3.2 Teratologies: Examples of Animal Coat Pattern Abnormalities . . . . 156 3.3 A Pattern Formation Mechanism for Butterfly Wing Patterns . . . . . 161 3.4 Modelling Hair Patterns in a Whorl in Acetabularia . . . . . . . . . . 180 4. Pattern Formation on Growing Domains: Alligators and Snakes 192 4.1 Stripe Pattern Formation in the Alligator: Experiments . . . . . . . . 193 4.2 Modelling Concepts: Determining the Time of Stripe Formation . . . 196 4.3 Stripes and Shadow Stripes on the Alligator . . . . . . . . . . . . . . 200 4.4 Spatial Patterning of Teeth Primordia in the Alligator: Background and Relevance . . . . . . . . . . . . . . . . . . . . . . . 205 4.5 Biology of Tooth Initiation . . . . . . . . . . . . . . . . . . . . . . . 207 4.6 Modelling Tooth Primordium Initiation: Background . . . . . . . . . 213 4.7 Model Mechanism for Alligator Teeth Patterning . . . . . . . . . . . 215 4.8 Results and Comparison with Experimental Data . . . . . . . . . . . 224 4.9 Prediction Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 228 4.10 Concluding Remarks on Alligator Tooth Spatial Patterning . . . . . . 232 4.11 Pigmentation Pattern Formation on Snakes . . . . . . . . . . . . . . . 234 4.12 Cell-Chemotaxis Model Mechanism . . . . . . . . . . . . . . . . . . 238 4.13 Simple and Complex Snake Pattern Elements . . . . . . . . . . . . . 241 4.14 Propagating Pattern Generation with the Cell-Chemotaxis System . . 248 5. Bacterial Patterns and Chemotaxis 253 5.1 Background and Experimental Results . . . . . . . . . . . . . . . . . 253 5.2 Model Mechanism for E. coli in the Semi-Solid Experiments . . . . . 260 5.3 Liquid Phase Model: Intuitive Analysis of Pattern Formation . . . . . 267 5.4 Interpretation of the Analytical Results and Numerical Solutions . . . 274 5.5 Semi-Solid Phase Model Mechanism for S. typhimurium . . . . . . . 279 5.6 Linear Analysis of the Basic Semi-Solid Model . . . . . . . . . . . . 281 5.7 Brief Outline and Results of the Nonlinear Analysis . . . . . . . . . . 287 5.8 Simulation Results, Parameter Spaces and Basic Patterns . . . . . . . 292 5.9 Numerical Results with Initial Conditions from the Experiments . . . 297 5.10 Swarm Ring Patterns with the Semi-Solid Phase Model Mechanism . 299 5.11 Branching Patterns in Bacillus subtilis . . . . . . . . . . . . . . . . . 306 6. Mechanical Theory for Generating Pattern and Form in Development 311 6.1 Introduction, Motivation and Background Biology . . . . . . . . . . . 311 Contents, Volume II xvii 6.2 Mechanical Model for Mesenchymal Morphogenesis . . . . . . . . . 319 6.3 Linear Analysis, Dispersion Relation and Pattern Formation Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 6.4 Simple Mechanical Models Which Generate Spatial Patterns with Complex Dispersion Relations . . . . . . . . . . . . . . . . . . . . . 334 6.5 Periodic Patterns of Feather Germs . . . . . . . . . . . . . . . . . . . 345 6.6 Cartilage Condensations in Limb Morphogenesis and Morphogenetic Rules . . . . . . . . . . . . . . . . . . . . . . . . 350 6.7 Embryonic Fingerprint Formation . . . . . . . . . . . . . . . . . . . 358 6.8 Mechanochemical Model for the Epidermis . . . . . . . . . . . . . . 367 6.9 Formation of Microvilli . . . . . . . . . . . . . . . . . . . . . . . . . 374 6.10 Complex Pattern Formation and Tissue Interaction Models . . . . . . 381 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 7. Evolution, Morphogenetic Laws, Developmental Constraints and Teratologies 396 7.1 Evolution and Morphogenesis . . . . . . . . . . . . . . . . . . . . . 396 7.2 Evolution and Morphogenetic Rules in Cartilage Formation in the Vertebrate Limb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 7.3 Teratologies (Monsters) . . . . . . . . . . . . . . . . . . . . . . . . . 407 7.4 Developmental Constraints, Morphogenetic Rules and the Consequences for Evolution . . . . . . . . . . . . . . . . . . . . 411 8. A Mechanical Theory of Vascular Network Formation 416 8.1 Biological Background and Motivation . . . . . . . . . . . . . . . . . 416 8.2 Cell–Extracellular Matrix Interactions for Vasculogenesis . . . . . . . 417 8.3 Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 8.4 Analysis of the Model Equations . . . . . . . . . . . . . . . . . . . . 427 8.5 Network Patterns: Numerical Simulations and Conclusions . . . . . . 433 9. Epidermal Wound Healing 441 9.1 Brief History of Wound Healing . . . . . . . . . . . . . . . . . . . . 441 9.2 Biological Background: Epidermal Wounds . . . . . . . . . . . . . . 444 9.3 Model for Epidermal Wound Healing . . . . . . . . . . . . . . . . . 447 9.4 Nondimensional Form, Linear Stability and Parameter Values . . . . . 450 9.5 Numerical Solution for the Epidermal Wound Repair Model . . . . . 451 9.6 Travelling Wave Solutions for the Epidermal Model . . . . . . . . . . 454 9.7 Clinical Implications of the Epidermal Wound Model . . . . . . . . . 461 9.8 Mechanisms of Epidermal Repair in Embryos . . . . . . . . . . . . . 468 9.9 Actin Alignment in Embryonic Wounds: A Mechanical Model . . . . 471 9.10 Mechanical Model with Stress Alignment of the Actin Filaments in Two Dimensions . . . . . . . . . . . . . . . . . . . . . 482 10. Dermal Wound Healing 491 10.1 Background and Motivation—G | 1-12 |
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| 5- أساليب التعليم والتعلم :- |
| | م | الاسلوب |
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| Teaching and Learning Methods 5.1 - Lectures using board. 5.2 - Discussion sessions 5.3 - Problem classes 5.4 - class activity |
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| 6- أساليب التعليم والتعلم للطلاب ذوى القدرات المحدودة :- |
| - 1. Giving them more chance through the office hours to raise their competencies 2. class activity
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| 7- تقويم الطلاب :- |
| أ- التوقيت |
| | م | الطريقة | الأسبوع |
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| 1 | final exam | 12 | | 2 | med term exam | 6 | | 3 | oral exam | 12 | | 4 | report | 11 |
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| ب- توزيع الدرجات |
| | م | الطريقة | الدرجة |
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| 1 | final exam | 70 | | 2 | med term exam | 10 | | 3 | oral exam | 10 | | 4 | oral exam | 10 | | المجموع | 100% |
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| 8- قائمة الكتب الدراسية والمراجع |
| | م | العنصر | النوع |
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| 1 | mathematical biology | كتب ملزمة |
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| 9- مصفوفة المعارف والمهارات المستهدفة من المقرر الدراسي |
| | م | المحتوى | أسبوع الدراسة |
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| Multi-Species Waves and Practical Applications 1 1.1 Intuitive Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Waves of Pursuit and Evasion in Predator–Prey Systems . . . . . . . 5 1.3 Competition Model for the Spatial Spread of the Grey Squirrel in Britain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4 Spread of Genetically Engineered Organisms . . . . . . . . . . . . . 18 1.5 Travelling Fronts in the Belousov–Zhabotinskii Reaction . . . . . . . 35 1.6 Waves in Excitable Media . . . . . . . . . . . . . . . . . . . . . . . 41 1.7 Travelling Wave Trains in Reaction Diffusion Systems with Oscillatory Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 1.8 Spiral Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 1.9 Spiral Wave Solutions of λ–ω Reaction Diffusion Systems . . . . . . 61 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2. Spatial Pattern Formation with Reaction Diffusion Systems 71 2.1 Role of Pattern in Biology . . . . . . . . . . . . . . . . . . . . . . . 71 2.2 Reaction Diffusion (Turing) Mechanisms . . . . . . . . . . . . . . . 75 2.3 General Conditions for Diffusion-Driven Instability: Linear Stability Analysis and Evolution of Spatial Pattern . . . . . . . 82 2.4 Detailed Analysis of Pattern Initiation in a Reaction Diffusion Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 2.5 Dispersion Relation, Turing Space, Scale and Geometry Effects in Pattern Formation Models . . . . . . . . . . . . . . . . . . . . . . 103 2.6 Mode Selection and the Dispersion Relation . . . . . . . . . . . . . . 113 2.7 Pattern Generation with Single-Species Models: Spatial Heterogeneity with the Spruce Budworm Model . . . . . . . . . . . . 120 xvi Contents, Volume II 2.8 Spatial Patterns in Scalar Population Interaction Diffusion Equations with Convection: Ecological Control Strategies . . . . . . . 125 2.9 Nonexistence of Spatial Patterns in Reaction Diffusion Systems: General and Particular Results . . . . . . . . . . . . . . . . . . . . . 130 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 3. Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms 141 3.1 Mammalian Coat Patterns—‘How the Leopard Got Its Spots’ . . . . . 142 3.2 Teratologies: Examples of Animal Coat Pattern Abnormalities . . . . 156 3.3 A Pattern Formation Mechanism for Butterfly Wing Patterns . . . . . 161 3.4 Modelling Hair Patterns in a Whorl in Acetabularia . . . . . . . . . . 180 4. Pattern Formation on Growing Domains: Alligators and Snakes 192 4.1 Stripe Pattern Formation in the Alligator: Experiments . . . . . . . . 193 4.2 Modelling Concepts: Determining the Time of Stripe Formation . . . 196 4.3 Stripes and Shadow Stripes on the Alligator . . . . . . . . . . . . . . 200 4.4 Spatial Patterning of Teeth Primordia in the Alligator: Background and Relevance . . . . . . . . . . . . . . . . . . . . . . . 205 4.5 Biology of Tooth Initiation . . . . . . . . . . . . . . . . . . . . . . . 207 4.6 Modelling Tooth Primordium Initiation: Background . . . . . . . . . 213 4.7 Model Mechanism for Alligator Teeth Patterning . . . . . . . . . . . 215 4.8 Results and Comparison with Experimental Data . . . . . . . . . . . 224 4.9 Prediction Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 228 4.10 Concluding Remarks on Alligator Tooth Spatial Patterning . . . . . . 232 4.11 Pigmentation Pattern Formation on Snakes . . . . . . . . . . . . . . . 234 4.12 Cell-Chemotaxis Model Mechanism . . . . . . . . . . . . . . . . . . 238 4.13 Simple and Complex Snake Pattern Elements . . . . . . . . . . . . . 241 4.14 Propagating Pattern Generation with the Cell-Chemotaxis System . . 248 5. Bacterial Patterns and Chemotaxis 253 5.1 Background and Experimental Results . . . . . . . . . . . . . . . . . 253 5.2 Model Mechanism for E. coli in the Semi-Solid Experiments . . . . . 260 5.3 Liquid Phase Model: Intuitive Analysis of Pattern Formation . . . . . 267 5.4 Interpretation of the Analytical Results and Numerical Solutions . . . 274 5.5 Semi-Solid Phase Model Mechanism for S. typhimurium . . . . . . . 279 5.6 Linear Analysis of the Basic Semi-Solid Model . . . . . . . . . . . . 281 5.7 Brief Outline and Results of the Nonlinear Analysis . . . . . . . . . . 287 5.8 Simulation Results, Parameter Spaces and Basic Patterns . . . . . . . 292 5.9 Numerical Results with Initial Conditions from the Experiments . . . 297 5.10 Swarm Ring Patterns with the Semi-Solid Phase Model Mechanism . 299 5.11 Branching Patterns in Bacillus subtilis . . . . . . . . . . . . . . . . . 306 6. Mechanical Theory for Generating Pattern and Form in Development 311 6.1 Introduction, Motivation and Background Biology . . . . . . . . . . . 311 Contents, Volume II xvii 6.2 Mechanical Model for Mesenchymal Morphogenesis . . . . . . . . . 319 6.3 Linear Analysis, Dispersion Relation and Pattern Formation Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 6.4 Simple Mechanical Models Which Generate Spatial Patterns with Complex Dispersion Relations . . . . . . . . . . . . . . . . . . . . . 334 6.5 Periodic Patterns of Feather Germs . . . . . . . . . . . . . . . . . . . 345 6.6 Cartilage Condensations in Limb Morphogenesis and Morphogenetic Rules . . . . . . . . . . . . . . . . . . . . . . . . 350 6.7 Embryonic Fingerprint Formation . . . . . . . . . . . . . . . . . . . 358 6.8 Mechanochemical Model for the Epidermis . . . . . . . . . . . . . . 367 6.9 Formation of Microvilli . . . . . . . . . . . . . . . . . . . . . . . . . 374 6.10 Complex Pattern Formation and Tissue Interaction Models . . . . . . 381 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 7. Evolution, Morphogenetic Laws, Developmental Constraints and Teratologies 396 7.1 Evolution and Morphogenesis . . . . . . . . . . . . . . . . . . . . . 396 7.2 Evolution and Morphogenetic Rules in Cartilage Formation in the Vertebrate Limb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 7.3 Teratologies (Monsters) . . . . . . . . . . . . . . . . . . . . . . . . . 407 7.4 Developmental Constraints, Morphogenetic Rules and the Consequences for Evolution . . . . . . . . . . . . . . . . . . . . 411 8. A Mechanical Theory of Vascular Network Formation 416 8.1 Biological Background and Motivation . . . . . . . . . . . . . . . . . 416 8.2 Cell–Extracellular Matrix Interactions for Vasculogenesis . . . . . . . 417 8.3 Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 8.4 Analysis of the Model Equations . . . . . . . . . . . . . . . . . . . . 427 8.5 Network Patterns: Numerical Simulations and Conclusions . . . . . . 433 9. Epidermal Wound Healing 441 9.1 Brief History of Wound Healing . . . . . . . . . . . . . . . . . . . . 441 9.2 Biological Background: Epidermal Wounds . . . . . . . . . . . . . . 444 9.3 Model for Epidermal Wound Healing . . . . . . . . . . . . . . . . . 447 9.4 Nondimensional Form, Linear Stability and Parameter Values . . . . . 450 9.5 Numerical Solution for the Epidermal Wound Repair Model . . . . . 451 9.6 Travelling Wave Solutions for the Epidermal Model . . . . . . . . . . 454 9.7 Clinical Implications of the Epidermal Wound Model . . . . . . . . . 461 9.8 Mechanisms of Epidermal Repair in Embryos . . . . . . . . . . . . . 468 9.9 Actin Alignment in Embryonic Wounds: A Mechanical Model . . . . 471 9.10 Mechanical Model with Stress Alignment of the Actin Filaments in Two Dimensions . . . . . . . . . . . . . . . . . . . . . 482 10. Dermal Wound Healing 491 10.1 Background and Motivation—G | 1-12 |
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| اساتذة المادة: - |
| - السيد عبد العاطى حسن الوكيل
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| رئيس مجلس القسم العلمى: - |
| عادل محمد صادق عجور |
