Math

Analysis of Biological Measurements and Calculations

Creatinine and Renal Function Tests

  • Urine Creatinine Clearance (mg/dL):

    • Formula:
      \frac{\text{Hematocytometer cell count} \times \text{Urine volume (mL)}}{\text{ squares counted} \times \text{dilution}} = \text{cells/}\mu L
    • Correction factor:
      \text{corrected count} = \text{cells in squares} \times 0.1
    • Body Surface Area (BSA):
      BSA = \text{Body surface area (m}^2\text{)}
    • Mean Cell Volume (MCV):
      \text{MCV} = \frac{\text{Hematocrit} \times 10}{\text{RBC count (cells/}\mu L)}
    • Mean Corpuscular Hemoglobin (MCH):
      \text{MCH} = \frac{\text{Hgb} \times 10}{\text{RBC count (cells/}\mu L)}
    • Mean Corpuscular Hemoglobin Concentration (MCHC):
      \text{MCHC} = \frac{\text{Hgb} \times 100}{\text{Volume of blood (g/dL)}}
    • Hematocrit (Hct): Measurement of the proportion of blood volume that is occupied by red blood cells.
    • Red Cell Distribution Width (RDW): Represents the variation in size among red blood cells.

  • Cerebrospinal Fluid (CSF) Analysis:

    • CSF to Albumin Index:
      \text{CSF Albumin (mg/dL)} \text{ mean} \div \text{ serum albumin (g/dL)}
    • Reticulocyte Count:
      \text{Reticulocyte %} = \frac{\text{total reticulocytes in the field}}{\text{total RBCs in field}} \times 100
    • IgG Index:
      \text{IgG Index} = \frac{\text{CSF IgG} \times \text{serum albumin}}{\text{CSF albumin}}
    • pH Count Estimate:
      \text{pHs in fields} \times \text{number of fields counted}

Fecal Analysis

  • Fecal Osmolality:

    • Formula:
      2 \times (\text{fecal Na} + \text{fecal K})
    • Analysis of osmotic diarrhea: A significant osmotic gap indicates osmotic diarrhea, with a threshold typically greater than 50 mOsm/kg.

  • Fecal Fat Quantification:

    • Dietary Fat Calculation:
      \frac{\text{dietary fat} - \text{fecal fat}}{\text{dietary fat}} \times 100
    • Steatorrhea Calculation:
      \text{Steatorrhea}= \text{grams of fat per day}
    • Steatocrit:
      \frac{\text{Fatty layer (cm)}}{\text{Solid layer (cm)}} \times 100
    • Normal ranges:
    • Child: <10%
    • Adult: <31%

Electrical and Chemical Principles

  • Ohm's Law:

    • Formula:
      V = IR
    • Where V = voltage, I = current, R = resistance.

  • Temperature and Conversion:

    • Fahrenheit to Celsius Conversion:
      F = \frac{9}{5}C + 32

Hematological Measurements

  • Anion Gap Calculation: \text{Anion Gap} = (\text{Na} + \text{K}) - (\text{Cl} + \text{HCO}_3)
    • Normal gap: >20 suggests metabolic acidosis.

Henderson-Hasselbalch Equation

  • Equation: \text{pH} = pKa + \log \left(\frac{\text{HCO}3^{-}}{\text{CO}_2} \right)
    • This equation is used to estimate the pH of a buffer solution.

Biostatistical Analysis

  • Coefficient of Variation (CV):
    • Formula:
      \text{CV \%} = \frac{\text{SD}}{\text{mean}} \times 100
    • Used to assess the precision of lab measurements.

Free PSA and Predictive Values in Diagnostics

  • Free PSA Calculation:

    • Formula:
      \text{Free PSA \%} = \frac{\text{Free PSA}}{\text{Total PSA}} \times 100
    • Used in the diagnosis of prostate cancer.

  • Positive Predictive Value (PPV):

    • Formula:
      \text{PPV} = \frac{\text{True Positives}}{\text{True Positives + False Positives}} \times 100

  • Negative Predictive Value (NPV):

    • Formula:
      \text{NPV} = \frac{\text{True Negatives}}{\text{True Negatives + False Negatives}} \times 100

Beer’s Law in Spectrophotometry

  • Beer’s Law:
    • Formula:
      A = abc
    • Where A = absorbance, a = proportionality constant, b = path length, c = concentration.
  • Transmittance Relation: A = -2 \log(T)
    • Where T = transmittance.