Routes of Drug Administration• Objectives– Gas laws – Inhalation– Surface area– Pressure units – Pressure:

gauge vs absolute

1

Oral, rectal

Topical

IntramuscularSubCutaneous…

Intravenous

Inhalation

Drug Blood

Lung

Skin

Membranes

Stomach, Intestines, GI

Cells

Medical Gases

Intranasal Mucous membranes

Inhalables: Gases and Aerosols• Pure gases, mixtures and

aerosols. Volatile?• Some drugs have inhalable

formulations from solutions• Nebulizers or special inhalers

make aerosols– cystic fibrosis, asthma, COPD,

others– Use O2, or compressed air to

make droplets• Gas itself (pure or gas mixtures)

can be used as therapeutics

2https://en.wikipedia.org/wiki/List_of_medical_inhalants

(Chronic Obstructive Pulmonary Disease)

- Medical air- O2 - N2- CO2- Nitrous Oxide (NNO)An aerosol is a suspension of fine solid particles

or liquid droplets, in air or another gas

Covid-19

3

Oxygen piping and regulator with flow meter

Anesthesia gas delivery and mixing

4

Moving Molecules, Gas LawGaseous Pharmaceutical and Toxic Agents

Degrees of Freedom in Gas of molecules (N atoms, needed to estimate Heat Capacity)

Monatomic Linear Non-linear ½ RT modesTranslation (x, y, and z) 3 3 3 1 (kinetic)Rotation (x, y, and z) 0 2 3 1 (kinetic)Vibrations 0 ≤3N − 5 ≤3N − 6 2 (vibrational)Total 3 ≤3N ≤3N

• N2, O2, CO2 Air, Diving, Pressure, High Altitudes• Free radical nitric oxide ·N=O physiology• Anesthetics, Xe, Nitrous Oxide (laughing gas, N2O)• Aerosols, pressured canisters• Acute lung injury and respiratory distress syndrome• CO poisoning (0.01%-headache to 1% unconsciousness)• Nerve gases, chemical weapons

PV = nRT Air %

Nitrogen N≡N 78%

Oxygen O=O 20.1%

Argon Ar <1%

Carbon dioxide

O=C=O 0.04%

Deadly Gas: Chlorine Cl-ClChemical Weapons: At around 5:00 p.m. on 22 April 1915 around Ypres, Belgium, the Germans under the guidance of Fritz Haber released 171 tons of chlorine gas over a 6.5 km in Ypres.

They used 5,730 gas cylinders, weighing 41 kg each relying on the prevailing winds to carry the gas towards the French.

The French troops had c. 6,000 casualties, many of whom died within ten minutes, primarily from asphyxiation and tissue damage in the lungs, many more were blinded.

Chlorine gas forms hypochlorous and hydrochloric acids when combined with water, destroying moist tissues such as lungs and eyes.

Question: did Cl2 sync into the trenches?

Fritz Haber and Carl Bosch developed the Haber process, which is the catalytic formation of ammonia from hydrogen and atmospheric nitrogen under conditions of high temperature and pressure.

Fritz Haber: “father of chemical warfare”

Cl2 + H2O èHClO + HCl

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Gases, Inhaled Drugs and Pulmonary Drug Delivery

• Lungs: 50 to 75 m2

• CO2, O2 exchange• Tuberculosis (TB): Inhaled drugs can

be delivered directly and at lower dose. Eg: Isoniazid which has highly toxic liver side effects. Some antibiotics can be inhaled

• Inhalable therapeutics are less invasive than intravenous

• Common in asthma, COPD, cystic fibrosis, diabetes (Afrezza®, inhalable insulin powder), ..

• Facts to know:– Air composition and partial pressures

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Xenon as an anesthetic

• heavy, odorless noble gas• Xe is a general anesthetic about to

appear on the European market, Xe-133 isotope is approved.

• Xenon is a high-affinity NMDA receptor antagonist. It inhibits the neurotoxicity of ketamine and nitrous oxide (aka laughing gas N2O )

• 133Xe is an inhaled radiopharmaceutical imaging agent used to image the lungs and evaluate pulmonary function.

Other NMDAR antagonists:AmantadineKetamineMethoxetaminePhencyclidine (PCP)Nitrous oxideDextromethorphanMemantineEthanol (also GABA agonist..)Riluzole ,HU-211Lead (Pb2+)ConantokinsHuperzine AAtomoxetine 8

N = 54MW=131.3

NMDAR is N-Methyl-D-aspartate receptor

Some gaseous anesthetics• Halogenated Ethers

– Desflurane– Isoflurane (nirvana)– Sevoflurane (1975, fast, WHO

)• Haloalkanes (rarely used)

– Chloroform – Trichloroethylene

• Others– Ethylene – Nitrous oxide (laughing gas)– Xenon

• Issues: flammability, oil-gas solubility, toxicity, rate of onset, and metabolism,

• Concern: environment/ozone depletion due to Chloro-Fluoro-Carbons (CFC). Regulated by Montreal Protocol on Ozone Depleting Substances.

Blockade of NMDA receptors and/or hyperactivity of GABAaor Glycine neurotransmission. GABAa PAMs, NMDAant

Desflurane and sevoflurane are replacing isoflurane and halothane in modern anesthesiology

Blood : Gas partition coefficient: 0.68

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Mean gas-phase drug velocities at room temperature• Single molecules in gas phase carry the same translational energy• Therefore, molecules with larger weight move slower

Let us derive the mean velocity of a molecule of mass M at temperature T:

Kinetic energy of 1 mole of gas molecules in 3D is 3 times ½RT½Mv2 = E = 3/2RT

Mv2 = 3RT (M is mass of one mole of molecules, m is the mass of one molecule)

v = ( 3RT / M)½ = (3kBT/m) ½

Problem examples:• For one mole of N2 gas M = 14 · 2 = 28 g = 0.028 kg (in SI units) • Root-mean square velocity at T = 300K = (273+27) • v = (3*8.314*300/0.028)1/2 = 517 m/s ~ 1,156 miles/hour• Oxygen ( O2 ) is heavier: 484 m/s • Aspirin in Gas phase ( 180. g/mol): vAsp = vO2(MO2/MAsp)½ ~ 153 m/s • Compare with the speed of sound! (343 m/s)

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1m/s ≈ 2.237miles/h

Diffusion and Effusion• One of the elimination routes for drugs

is from plasma to lungs and into the air (however evaporation is not effusion)

• Diffusion ≡ The gradual mixing of molecules by random molecular motion.

• Smell propagates fast • Diffusion is a random walk. The

molecule bumps into others each few hundred nanometers.

• Effusion ≡ gases mixing or escaping through a small hole (or holes) .

• Skin will be emitting microscopic amounts of systemically taken drugs by effusion

From http://aston.chem.purdue.edu/research/ambient-ionization-methods

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Graham’s Law • Effusion is proportional to

speeds of molecules• Effusion rate is inversely

proportional to square rootof molecular mass.

where: • Rate1 is the rate of effusion of the

first gas. • Rate2 is the rate of effusion for

the second gas. • M1 is the molar mass of gas 1 • M2 is the molar mass of gas 2.

Thomas Graham 1805 –1869, Scotland, then Univ. of London,

1

2

2

1

MM

RateRate

=

½Mv2 = E = 3/2RTv ~ M-1/2

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What is pressure?• Pressure = Force / Area• Force if due to microscopic collisions• The energies or atoms differ• Maxwell-Boltzmann distribution of gas

velocities. Fast ones can activate a reaction.

• Averages and distributions

Area = 4p v2

v

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Prob. ~ n e – Ek/RT = n e – ½mv2 /RT

Prob(v) = cv2 e – (½mv2 ) /RT

(the Boltzmann distribution makes its first appearance)

Advanced materials

Gas Law and Molecular Movement

PV = nRT• P – pressure in Nm-2

• V – volume in m3

• n – number of moles• Density: r = m/V = M·P/RT • Gas constant R is 8.314 kcal/mol•KUnits of pressure (Pascal in SI):1 bar = 105 Nm-2 = 105 Pa1 atm = 760 torr (or mmHg) = 1.013 bar~ 1kg/cm2 ,or 10m of water, or 760mm of mercury

Blaise Pascal Evangelista Torricelli

Mercury

Robert Boyle’s law: PV = const

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Pressure Units and Definitions

• Pascal = Newton/meter2 = kg/(m s2)• Vapor pressure in 40 to 80 psig• What is PSIG? – PSI and PSIA : pound-force per square inch [absolute]

– PSIG: PSI Gauge means relative to atmospheric pressure

• Pa = N/m2 1atm=14.7psi; 1psig=6895Pa• Blood pressure (120/80 mmHg): 2.32/1.55 psig

– Absolute pressure in blood is Patm+ Pgauge15

Gauge vs Absolute pressure

16The Gauge Pressure can be both positive and negative (if below Patm)

Therapeutic Oxygen Gas Cylinders

How to see a jiggling molecule

• Brownian motionMean velocity of molecules

and particles is v ~ M-½

• a dust particle that is million times larger moves only 1000 times slower

Robert Brown, 1773-1858, British botanist In 1827, while examining pollen grains and the spores of mosses and Equisetum suspended in water under a microscope, Brown observed minute particles within vacuoles in the pollen grains executing a continuous jittery motion

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Barometric Formula: Partial Pressure vs Altitudes (h)

• Ph = P0 • e -M g h/RT

• h½ ~ M-1

• M - molecular mass (kg)• g - gravitational acceleration

9.80665 m/s2,

• h – altitude [m]• Acetazolamide, a Carbonic

Anhydrase inhibitor, helps fighting altitude sickness

Mosquito, vector of malaria, senses CO2 concentration gradient

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Review. PV = nRT, 3RT=Mv2

• SI units for length: m, Å, nm, µm• Size of drugs, proteins, membrane, cells• Mole, Avogadro (6): NA ~ 6 1023

• Kinetic energy = ½ mv2 = ½ m(vx2+vy

2+vz2)

• Conservation of total (potential and kinetic) energy, can be changed by work W = Force� distance

• Equipartition & abs. T: ½ mv2 = 3/2 RT • Celsius (273.15) and Fahrenheit• Energy units: J, cal, kcal, Cal, • Gas constant (8.p) 8.314 JK-1mol-1• Boltzmann constant (kB = R/NA)• RT at 300K : 0.6kc & 2.5 kJ• Energies of drug binding, photon,

unfolding

• Molecular velocities: 3/2RT=EK

• Vroot_mean_square=(3RT/M)½

• Graham’s law V ~(T/M)½

• Newton's Laws ma=dp/dt =F• Momentum conservation laws• Brownian movement• Pressure, units, origin• Gas Law: PV = nRT• Barometric: Ph = P0 • e -M g h/RT

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Math reminders (advanced/optional):• Derivatives, ex , ln x • Exponent and logarithm• ln xy = ln x + ln y• ln x/y = ln x – ln y• ln xn = n ln x ln 1/x = -lnx• ln x = ln10 log x ~ 2.3 log x

Deriving the Gas Law

• dp / dt = F 1 mole of gas:• Dp / Dt = Fmean

• Dp = 2mvx

• Dt = 2 L / vx

• Pressure = Fmean/A • = 2mvx

2 /(2LA)= mvx2 /V

• Notice that mvx2 = ⅓mv2 = ⅓ 3RT=RT

• Multiplying by V: PV = RT

• For n moles: PV = n RTNotice: Ek = mv2/2 = 3/2RT

X axis

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Optional, supplementary

Review of Differentiation

Two notations (Lagrange and Leibniz):

f’(x) and df/dx Rules• Constant, f(x) = a, f ’(x) = 0• Power: If f(x) = xn , f ’(x)= nxn-1

• Product: (fg)’ = f’g + fg’• Quotient: • Chain rule: df/dx = (df/dg) (dg/dx)

E.g. d(e-2x)/dx = (e-2x)(-2)

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Optional, supplementary

Important functions & derivatives

• d eax /dx = a eax

Rate is proportional to the value.Bacteria, viruses, Exponential growth (a>0)Drug decomposition, Exponential decay (a<0)

Comment about ln Y vs. X plots

• d ln x /dx = 1/x (e=2.718..)

ln xy = ln x + ln yln xn = n ln xln x = ln10 log x ~ 2.3 log x

0

y=ln(x)

x

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Optional, supplementary