Numerical Problems/Calculations - Shortcut Methods:

1. Cardiac Output (CO):

   • For a healthy adult at rest: Stroke Volume (SV) ≈ body weight in kg × 70 mL Cardiac Output (CO) ≈ HR × SV

     Example: HR = 72 bpm, SV = 70 mL CO ≈ 72 bpm × 70 mL = 5,040 mL/min or 5.04 L/min

   • To find the stroke volume (SV): SV ≈ CO/HR

     Example: CO = 5 L/min, HR = 75 bpm SV ≈ 5 L/min / 75 bpm = 66.7 mL

2. Blood Pressure:

   • Mean Arterial Pressure (MAP): MAP ≈ (systolic BP + 2 × diastolic BP) / 3

     Example: Systolic BP = 120 mmHg, Diastolic BP = 80 mmHg MAP ≈ (120 mmHg + 2 × 80 mmHg) / 3 = 93.3 mmHg

   • Conversion to kilopascals (kPa): 1 mmHg ≈ 0.133 kPa

     Example: Blood Pressure = 140/90 mmHg Conversion to kPa: (140 mmHg × 0.133 kPa) / (90 mmHg × 0.133 kPa) ≈ 18.7/12 kPa = 18.7/12.0 mmHg

3. Heart Rate and Pulse:

   • Heart rate (HR) and Pulse: HR = 1 / (time interval between heartbeats) Pulse = Heart rate measured at a peripheral artery

     Example: Time interval between heartbeats (R-R interval) = 0.8 seconds HR = 1 / 0.8 seconds ≈ 1.25 Hz or 75 bpm

   • Corresponding time interval between heartbeats: Time interval = 1 / HR

     Example: Pulse rate = 60 bpm Time interval = 1 / 60 bpm ≈ 1 second

4. Blood Volume:

   • Blood Volume Estimation: Blood Volume ≈ Body weight in kg × 7%

     Example: Body weight = 70 kg Blood Volume ≈ 70 kg × 7% ≈ 4.9 L or 4,900 mL

   • Blood Volume Conversion: 1 L ≈ 1000 cc or 1000 mL

     Example: Blood volume ≈ 5 liters Conversion to cc or mL: 5 L × 1000 cc / L = 5000 cc or 5000 mL

5. Blood pH:

   • Hydrogen Ion (H+) concentration: [H+] = 10-pH

     Example: pH = 7.45 [H+] = 10-7.45 ≈ 35.5 nano-moles per liter (nM)

   • Determining pH: pH = - log [H+]

     Example: [H+] concentration = 40 nM pH ≈ - log (40 × 10-9) ≈ 7.4

6. Cardiac Cycle:

   • Duration of systole and diastole: Duration of Cardiac Cycle = Duration of systole + Duration of diastole

     Example: Cardiac cycle duration = 0.8 seconds, duration of systole = 0.3 seconds Duration of diastole = Cardiac cycle duration - Duration of systole ≈ 0.8 seconds - 0.3 seconds = 0.5 seconds

Remember to practice and solve variations of these numericals to strengthen your understanding and problem-solving skills. Always verify the units and dimensions in your calculations to ensure accurate results.