biosim2 - Last Time Two Models For Bacteria Growth Linear...

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ast Time Last Time wo Models For Bacteria Growth Two Models For Bacteria Growth – Linear, Homogeneous onlinear Homogeneous – Nonlinear, Homogeneous Today homogeneous Linear Models and Systems of Inhomogeneous Linear Models and Systems of Linear Equations – Breathing – Programmed cell death and tumor growth
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Two Models Examined So Far • Model 1 (linear): Geometric Growth +1 = x + kx x n+1 x n kx n x n+1 = rx n , where r = 1+k odel 2 (nonlinear): Logistic Growth • Model 2 (nonlinear): Logistic Growth x n+1 = x n + k(N - x n ) x n x n+1 = rx n (1-x n /K), where r = 1+kN and K = r/k
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Model 1: Geometric Growth • The Model: x n+1 = rx n • The Solution: x n = x 0 r n 0 < r < 1 >1 r >1 x n r < -1 n -1 < r < 0
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Discrete Model of Breathing A Discrete Model of Breathing Lecture 2
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The Process of Breathing Pulmonary ventilation or breathing is the first step to y gp bringing O 2 and removing CO 2 from the cells of the body. • Contracting the muscles of the diaphragm results in an flow of fresh air or spiration hile relaxation of these inflow of fresh air or inspiration , while relaxation of these muscles or contraction of the abdominals causes expiration of air with the waste product CO 2 .
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Respiration Facts • During normal respiration , the lungs exchange about 500 ml (tidal volume) of air 12 times a minute. young adult males there is an spiratory • In young adult males, there is an inspiratory reserve volume of about 3000 ml that can be inspired above the tidal volume, while the expiratory reserve volume is about 1100 ml, which can be forcefully expired. he ital capacity cludes all of the above • The vital capacity includes all of the above yielding about 4600 ml. 30-40% higher for athletes 20-25% less for women
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Respiration Facts • The lungs contain surfactants, which prevent them from totally collapsing (expelling all air) as it requires too much energy to re-inflate em from the collapsed state them from the collapsed state. • The residual volume represents the amount of air that cannot be expelled even by forceful expiration and averages about 1200 ml. • The functional reserve capacity is the amount of air that remains behind during normal breathing, which amounts to 2300 ml.
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Lung Volumes/Capacities During Breathing
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portance of Vital Capacity Importance of Vital Capacity • The vital capacity is a parameter that helps py pp physiologists determine the health of the pulmonary system. • This quantity captures the ability of an individual to transport oxygen through the ngs to the rest of the body lungs to the rest of the body. • Serious respiratory diseases can decrease the vital capacity to as low as 500 ml, barely enough to maintain life. – The vital capacity is easily measured by taking a eep breath and expiring into a pirometer deep breath and expiring into a spirometer.
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Importance of Tidal Volume and Functional Reserve Capacity When the ratio of the quantities becomes too low, there is insufficient exchange of air to maintain adequate supplies of oxygen to the body.
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The Experiment
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biosim2 - Last Time Two Models For Bacteria Growth Linear...

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