Med School Atlas

    Block 2 Equations Cheat Sheet

    Pharmacodynamics

    Equilibrium dissociation constant (Kd)

    Kd=[D]×[R][DR]K_d = \frac{[D] \times [R]}{[DR]}

    [D] = drug concentration
    [R] = receptor concentration
    [DR] = bound drug/receptor complex

    Fractional Occupancy (FR)

    FR=[DR][R]+[DR]=[D]Kd+[D]FR = \frac{[DR]}{[R] + [DR]} = \frac{[D]}{K_d + [D]}

    [D] = drug concentration
    [R] = receptor concentration
    [DR] = bound drug/receptor complex
    Kd = Equilibrium dissociation constant

    FR=eEmaxFR = \frac{e}{E_{max}}

    e = observed effect size
    Emax = maximum response

    Pharmacokinetics

    Molecule protonation

    unprotonatedprotonated=10pH−pKa\frac{\text{unprotonated}}{\text{protonated}} = 10^{pH - pKa}

    log(unprotonatedprotonated)=pH−pKalog(\frac{\text{unprotonated}}{\text{protonated}}) = pH - pKa

    pKa = the point at which half the molecules are protonated
    pKa = -log(Ka)

    Half-life

    t12=0.69Ket_{\frac{1}{2}} = \frac{0.69}{K_e}

    Ke = rate constant of elimination

    Drug concentration

    C=e−ket(C0)C = e^{-k_et}(C_0)

    C = concentration at time t
    e = 2.7 (constant)
    Ke = rate constant of elimination
    C0 = initial concentration

    ln(C)=−kt+ln(C0)ln(C) = -kt + ln(C_0)

    k = rate constant of elimination
    t = time
    C0 = initial concentration

    Volume of distribution

    Vd=DCoV_d = \frac{D}{C_o}

    D = dosage (drug quantity)
    C0 = initial concentration

    Dosage

    D=C0×VdD = C_0 \times V_d

    Vd = compartment volume
    C0 = initial concentration

    Clearance rate

    CR=Ke×VdCR = K_e \times V_d

    Ke = rate constant of elimination
    Vd = compartment volume

    90% clearance < 4×t124 \times t_{\frac{1}{2}}

    t1/2 = half-life

    Bioavailability

    F=quantity in circulationquantity administeredF = \frac{\text{quantity in circulation}}{\text{quantity administered}}

    Steady-state concentration

    CSS=F×doseCR×timeC_{SS} = \frac{F \times \text{dose}}{CR \times \text{time}}

    F = bioavailability
    dose (mg) = quantity administered
    CR (mg/time) = clearance rate

    Dosing rate

    DR=CR×CSSFDR = \frac{CR \times C_{SS}}{F}

    F = bioavailability
    dose (mg) = quantity administered
    CR (mg/time) = clearance rate

    Heart Circulation

    Mean Arterial Pressure

    MAP=CO∗TPRMAP = CO * TPR

    CO (Cardiac Output) = stroke volume (SV) * heart rate (HR)
    TPR (Total Peripheral Resistance) = The resistance of the entire circulatory system

    MAP=DBP+(SBP−DBP)3MAP = \frac{DBP + (SBP - DBP)}{3}

    SBP = The contracting pressure, which correlates with the cardiac output (CO). Normally between 90-120 mmHg.
    DBP = The arterial pressure when the heart is relaxes, which correlates with total peripheral resistance (TPR). Normally between 60-80 mmHg.

    Pulse Pressure

    PP = SBP - DBP

    SBP = The contracting pressure, which correlates with the cardiac output (CO). Normally between 90-120 mmHg.
    DBP = The arterial pressure when the heart is relaxes, which correlates with total peripheral resistance (TPR). Normally between 60-80 mmHg.

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