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Title: Agents to Treat Hypertension:


1
Agents to Treat Hypertension
2
What is Hypertension?
  • A serious disease affecting 1 in 3 adults in the
    United States
  • More commonly known as High Blood Pressure
  • Occurs when blood is forced through the heart and
    arteries under excessive pressure

3
What is Blood Pressure?
  • Blood pressure readings have two components
  • Systolic pressure
  • Heart muscles contracted
  • Diastolic pressure
  • Heart muscles relaxed
  • With hypertension
  • Arteries narrow thereby increasing blood pressure
  • Fluid volume in arteries increases which can
    increase pressure

4
Classifying Blood Pressure by Readings
Blood Pressure Category Systolic (mm Hg) Diastolic (mm Hg)
Normal lt120 lt80
Prehypertension 120-139 80-89
High Stage 1 140-159 90-99
High Stage 2 160 100
  • High Blood Pressure Elevated systolic pressure
    and/or elevated diastolic pressure.
  • The highest reading dictates classification.
  • Elevated readings must occur on multiple
    occasions to be diagnosed.

5
Classifying Hypertension by Causes
  • Primary or Essential Hypertension
  • Causes are unknown, but linked to risk factors,
    etiology is unknown.
  • Secondary Hypertension
  • 5-10 of hypertension cases
  • Caused by disease states

6
  • Some causes include kidney disease,
    atherosclerosis, hormone imbalances, pregnancy,
    and some medications,renal,endocrinal or vascular
    disorder.

7
Who is Affected by Hypertension?
  • Affects 1 billion people worldwide
  • Affects 40 million Americans (15)
  • 30 of people with hypertension dont know they
    have it

Race and Gender Prevalence
White Female 19.3
White Male  24.4
African-American Female 34.2
African-American Male  35.0
Hispanic Female 22.0
Hispanic Male  25.2
Race and Gender Death Rate
White Males 14.4
African-American Males 49.6
White Females 13.7
African-American Females 40.5
(Death rates per 100,000 people)
8
Why Should I Care?
  • Hypertension can elevate your risk for
  • Stroke
  • Blood clots
  • Bleeding
  • Heart attacks
  • Heart enlargement
  • Heart failure
  • Kidney failure
  • Atherosclerosis

9
Treatment Options for Hypertension
  • Prevention is the best treatment strategy
  • The goal of treatment
  • Lower blood pressure to prevent associated
    complications
  • Typically lt140/90 mmHg

10
  • It is a syndrome affecting arterial blood
    vessels, caused largely by the accumulation
    of macrophage white blood cells and promoted
    by low-density lipoproteins (plasma proteins that
    carry cholesterol and triglycerides) without
    adequate removal of fats and cholesterol from the
    macrophages by functional high density
    lipoproteins (HDL),
  • It is commonly referred to as a hardening or
    furring of the arteries. It is caused by the
    formation of multiple plaques within the arteries.

11
Treatment of HTN
  • There are following steps in treating HTN
  • Lifestyle modification
  • First line treatment
  • Second line treatment
  • Third line treatment

12
Treatment Options for Hypertension
  • Then first drugs used to produce symptamatic
    relief of hypertension were a-adrenergic blocking
    agents.
  • Limitations- duration of action too short.
  • Side effects precluded long term therapy.
  • Adrenergic drugs exert their effects by direct
    action on adrenergic receptors.
  • a andß receptors
  • NE activates a receptors
  • Epinephrine activates ß receptors.

13
  • a receptors fall into two groups
  • a 1 found in smooth muscles of iris,arteries,arter
    ioles,veins.
  • a 2- mediate the inhibition of adrenergic
    neurotransmitter release.
  • ß adrenergic receptors 3 types
  • ß1, ß2, ß3.

14
  • ß1- found in myocardium, stimulation increases
    the force and rate of myocardial contraction.
  • ß2- found in bronchial and vascular smooth
    muscles, stimulation causes
  • Smooth muscle dilation or relaxation.
  • ß3- on fat cells and their stimulation causes
    lipolysis

15
  • Symptathomimetic agents
  • Drugs stimulate the adrenergic nerve,directly by
    mimicing the action of NE.

16
  • Classification
  • Centrally acting- Clonidine,Methyl dopa
  • Ganglionic blocking agents- Pempidine,hexamethoni
    um,Pentolinium
  • Adrenergic neuron blockers- Guanethidine,reserpin
    e,bethanidine,bretylium.
  • ß- adrenergic blockers -propanolol,atenolol.
  • a- adrenergic blockers - Phenoxybenzamine,
    phentolamine, indoramine.

17
  • F) Mixed a and ß adrenergic blockers- Labetolol,
    Carvediol.
  • Diuretics - Chlorthiazide.
  • Vasodilaors eg hydralazine,minoxidil,diazoxide,N
    a nitroprusside.
  • Calcium channel blockers Verapamil,Nefidipine,Dil
    tiazem,Beridil,Amlodipine.
  • Drugs acting on renin- angiotensin aldosterone
    axis
  • a)Angiotensin converting enzyme inhibitors-

18
  • Sulfhydryl containing inhibitor- captopril
  • Dicarboxylate containing inhibitor-
    enalapril,lisinopril,quinapril,ramipril,trandopril
    ,spirapril etc.
  • Phosphonate containing inhibitor fosinopril
  • Angiotensin II receptor antagonist -
    losartan,valsartan,candesartan,telmisartan etc.

19
First Line Treatment
  • Continue with lifestyle modification
  • Initial drug selection
  • Diuretic
  • Beta-blocker
  • If inadequate, continue to second line treatment

20
Available Drug Therapies
  • Drug therapies available
  • ACE (angiotensin-converting enzyme) inhibitors
  • Alpha blockers
  • Alpha-2-agonists
  • Angiotensin II receptor blockers
  • Beta blockers
  • Calcium channel blockers
  • Combined alpha and beta blockers
  • Combined ACE inhibitors and diuretics
  • Diuretics

21
Second Line Treatment
  • Adding drugs from the following categories
  • Angiotensin Converting Enzyme (ACE) Inhibitor
  • Calcium Channel Blocker
  • Angiotensin II Receptor Blocker (ARB)
  • a- blocker, a- and ß-blocker
  • If inadequate, continue to third line treatment

22
Third Line Treatment
  • Increase drug dose, or
  • Substitute another drug, or
  • Add a second drug from another class
  • If inadequate, may need to do further studies
  • Serious organ damage may be present

23
Drug Therapies
Options for Individualizing Antihypertensive Drug Therapy Options for Individualizing Antihypertensive Drug Therapy
If you have hypertension and the following Then your doctor may prescribe one of the following
Diabetes mellitus ACE Inhibitors, ARBs, Diuretics, Beta Blockers, Calcium Channel Blockers
Heart failure Diuretics, Beta Blockers, ACE Inhibitors, ARBs, spironolactone
Heart attack Beta Blockers, ACE Inhibitors, spironolactone
Isolated systolic hypertension (elevated systolic only) Diuretics, certain Long-acting Calcium Channel Blockers
Kidney Disease ACE Inhibitors, ARBs
Recurrent Stroke Prevention Diuretics, ACE Inhibitors
24
Drugs Used to Treat HTN
  • Diuretics
  • Furosemide (Lasix) Hydrochlorothizide
    (HydroDIURIL)
  • Beta blockers
  • Atenolol (Tenormin) Propranolol (Inderal)
  • ACE inhibitors
  • Captopril (Capoten) Enalapril (Vasotec)
  • ARBs
  • Irbesartan (Avapro) Losartan (Cozaar)
  • Calcium channel blockers
  • Amlodipine (Norvasc) Diltiazem (Cardizem)

25
Site Of Action of Antihypertensive Drugs
  • Action of Beta-Blockers
  • Block vasoconstriction
  • Decrease heart rate
  • Decrease cardiac muscle contraction
  • Tend to increase blood flow to the kidneys -gt
    leading to a decrease in the release of renin

26
Classification of Beta Blockers


  • ß1 receptors blockers
  • Atenolol (Tenormin)
  • Betaxolol (Kerlone)
  • Bisoprolol (Zabeta)
  • Metoprolol (Lopressor, Toprol-XL)
  • ß1, ß2 receptor blockers
  • Nadolol (Corgard)
  • Propranolol (Inderal)
  • ß1, ß2, a receptor blockers
  • Labetolol (Normodyne, Trandate)

27
  • Commonalities
  • One chiral center
  • Aromatic ring
  • Side alkyl chain
  • Secondary hydroxyl group
  • Amine

28
DRUG AFFECTING CATECHOLAMINE STORAGE AND RELEASE
  • Reserpine is a prototypical drug affecting
    vesicle storage of NE in sympathetic neurons and
    neurons of the CNS.
  • Also of epinephrine of the adrenal medulla.
  • It also affect the storage of serotonin and
    dopamine in their respective neurons in the brain.

29
  • Agents that block adrenergic neurotransmitter
    synthesis and / or release. Reserpine,guanethidine
    , pargyline.

30
  • Mechanism of action Interferes with the Mg2-
    and ATP-dependent uptake of biogenic amines,
  • depleting NE, dopamine, and serotonin.
  • Reserpine decreases both cardiac output and PVR.

31
  • Rawolfia is an indole alkaloid obtained from the
    root of Rawolfia serpentina.
  • Other alkaloids possessing the same activity are
    deserpidine and rescinnamine.

32
  • Reserpine extremely binds tightly with the
    ATPdriven MOA transporter that transports NE and
    other biogenic amines from the cytoplasm to the
    storage vesicles.
  • This binding leads to a blockade of the
    transporter.

33
  • NE transported into the storage vesicle is
    metabolized by mitochondrial MAO in the
    cytoplasm.
  • There is a gradual loss of vesicle stored NE as
    it is used up by release
  • resulting from sympathetic nerve activity.

34
  • Storage vesicles eventually become dysfunctional.
  • The end result is depletion of NE in the
    sympathetic neuron.

35
CATECHOLAMINE DEPLETORS-RESERPINE
36
  • Slow onset of action
  • Sustained effect (weeks)
  • Used in the treatment of hypertension
  • May precipitate depression
  • Both orally and parenterally.

37
  • Selective a2 AGONIST
  • CLONIDINE(CATAPRESS)
  • Phenyliminoimidazolidine derivative
  • Antihypertensive effect followed by long lasting
    hypotensive effect.
  • Stimulate a2receptors in brain.
  • Decrease in peripheral resistance and B.P

38
Direct acting adrenergic receptor agonists
a2 receptors
Clonidine (Catapres) Methyldopa
(Aldomet) Guanabenz ( Wytensinr R Guanfacine
(Tenex) Tizanidine (Zanaflex)
39
  • Chemical name-
  • N-(2,6-dichlorophenyl)-4,5-dihydro-1H-imidazol-2-a
    mine
  • CLONIDINE RH
  • 4-HYDROXYCLONIDINE ROH
  • Phenyl imino imidazoline derivtive that possess
    selective a2 adrenergic receptor
  • Antihypertensive agent.

40
  • Phenyliminoimidazolidine
  • Selective a2 receptor agonist
  • The basicity of the guanidine group (pKa 13.6)
    is decreased (to pKa 8.0) because of the
    attachment to the dichlorophenyl ring
  • Administration Oral, parenteral, transdermal

41
Guanethidine(Ismelin) 2- (hexahydro-1H-azocinyl)e
thylguanidine Guanidine act by interfering with
adrenergic transmission.Attached to either an
alicyclic or aromatic lipophilic ring
42
  • Uses Hypertension, Vasodilation, increases
    venous capacitance.
  • Possess guanidino moiety (pKa gt 12)
  • They are essentially completely protonated.
  • Do not get into the CNS.
  • Prevents NE release from sympathetic nerve
    terminals.

43
  • VASODILATORS
  • Drugs that act directly on the vascular smooth
    muscle, decreases vascular resistance and
    arterial B.P.
  • Hydralazine Relax smooth muscle (SM) of
    arterioles (and sometimes veins).

44
Vasodilators
  • Types of vasodilators
  • Arteriodilators
  • reduce afterload
  • Venodilators
  • reduce preload
  • Mixed vasodilators

45
  • Moderate to severe hypertension.
  • Used in conjugation with hypertension and ß
    blocker
  • 1-hydrazino-pthalazine.

46
  • Therapeutic use
  • Hydralazine Dilates arterioles but not veins.
  • Effect does not last long when used
    alone(tachyphylaxis) but combination therapy can
    be very effective for even severe hypertension.

47
  • Best effect is achieved when used together with
    ß-blockers and loop diuretics.

48
  • USES
  • Mild to moderate hypertension.
  • Topical use in baldness
  • Adverse Effects
  • Due to vasodilatation
  • Reflex tachychardia, palpitation, may ? angina.
    Compensatory increase in fluid and electrolytes,
    edema
  • (Better combine with ß-blocker diuretic)

49
Minoxidil (Loniten)
  • 2,4-diamino-6-piperidinopyramidine-3-oxide.

50
  • Minoxidil Opens K channels in SM by its active
    metabolite, minoxidil sulfate, and stabilizes
    membrane at its resting potential.
  • Patients with renal failure and severe
    hypertension, who do not respond well to
    hydralazine, may be given minoxidil.

51
  • It isinactive and biotranformed in liver by
    sulfotransferase into Minoxidil sulfate N-SO-3
    called Kchannel opener.

52
  • Mechanism
  • Like diazoxide, opens K channels, relaxes smooth
    muscle of BV Cause arterial venous
    dilatation, ? PR, ? BP
  • ? Intracellular Ca, ? ses the excitability
    smooth muscles.

53
ACE-Inhibitors
  • ACE is a zinc metalloproteinase
  • It catalyses the hydrolysis of a dipeptide
    fragment, His-Leu, from a decapeptide,
    angiotensin
  • Asp-Arg-Val-Tyr-Ile-His-Pro-Phe-His-Leu ?
    Asp-Arg-Val-Tyr-Ile-His- Pro-Phe His-Leu
  • The reaction produces angiotensin II, an
    octapeptide

ACE
Angiotensin I
Angiotensin II
54
  • ACE is membrane-bound enzyme anchored to the cell
    membrane thru a single transmembrane domain
    located near the carboxy-terminal extremity.
  • Zinc containing glycoprotein with a MW of
    1,30,000.
  • Nonspecific peptidyldipeptidrolase hydrolase
    widely distributed in mammalian tissues.
  • It cleaves dipeptides from the carboxy terminus
    of a no of endogenous peptides.
  • The impt binding points at the active site of ACE
    is a cationic site to attract a COO- ion and a
    zinc that can polarize a carbonyl grp of an amide
    function to hydrolysis

55

  • O

  • C
  • (CH2)n---------- Zn binding
    grp

  • NRing

56
BIOCHEMISTRY OF THE RENIN ANGIOTENSIN SYSTEM

  • RENIN
  • NH2end-ASP-ARG-VAL-TYR-ILE-HIS-PRO-PHE-HIS-LEU----
    VAL-

  • ILE-HIS-R COOH END
  • ( ANGIOTENSINOGEN)

  • ACE
  • ASP-ARG-VAL-TYR-ILE-HIS-PRO-PHE-HIS----L
    EU
  • ( ANGIOTENSIN I)
  • AP
  • ASP-ARG-VAL-TYR-ILE-HIS-PRO-PHE-HIS----LE
    U
  • ( ANGIOTENSIN
    II)
  • ANGIOTENSINASES
  • ARG-VAL-TYR-ILE-HIS-PRO-PHE
  • (
    ANGIOTENSIN III)
  • INACTIVE PRODUCTS

57
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58
  • Renin produced a potent vasopressor response
    when injected in a host.
  • The angiotensin was used as a cofactor for renin
    to produce vasoconstriction.
  • Identified as a decapeptide called angiotensin.
  • Angiotensin existed in two forms--- biologically
  • inactive decapeptide angiotensin I and the
    active decapeptide angiotensin II.

59
  • The precursor of angiotensin, angiotensinogen is
    a glycoprotein of molecular weight 58,000
    61,000.
  • 1.Renin,an aspartyl protease(MW 35,000-40,000)
    cleaves Leu-Val bond from the aspartic acid end
    of the angiotensin polypeptide to release the
    decapeptide angiotensin I.
  • 2. Cleavage of dipeptide(His-Leuminal) frm the
    carboxy terminal of angiotensinI by ACE to form
    the octapeptide angiotensinII ,potent
    vasoconstrictor.

60
  • The N-terminal aspartate residue of angiotensin
    II is removed to form angiotensin III ,a reaction
    catalyzed by glutamyl aminopeptidase.
  • AIII has a less potent but significant regulatory
    effect on Na excretion by the renal tubules.
  • Na and K balance and arterial B.P is modified by
    vasodilators called kinins.
  • Callidin tissue enzymes
    Bradykinin PGrelease


  • ACE

  • Inactive pdts vasodilatation


61
Angiotensisn Inhibitors
Angiotensin-I
Bradykinin
Angiotensin Converting Enzyme (ACE)
Angiotensin Receptor Blockers
Angiotensin-II
-
Inactived
ACE Inhibitors
Vasoconstriction
-
Vasodilatation
? Aldosterone
-
? BP
? BP
? BP
? BP
62
History Highlights ACE-Inhibitors
  • Discovered in 1960s
  • Venom of pit vipers intensified the response to
    bradykinin, a vasodilator
  • Response was caused by peptides
  • that inhibited kininase II, an enzyme
  • that inactivated bradykinin
  • Later found that kininase II ACE
    (angiotensin-converting enzyme)
  • First Drug- Teprotide
  • Nonapeptide that lowered blood pressure caused by
    primary hypertension
  • Not orally active

http//www.szgdocent.org/resource/rr/c-viper.htm
63
Carboxypeptidase
  • Carboxypeptidase is a zinc metalloproteinase that
    could be isolated
  • Carboxypeptidase splits a terminal amino acid
    from a peptide chain
  • In the presence of L-benzylsuccinic acid the
    reaction is inhibited

2
64
Carboxypeptidase
  • Key features of the carboxypeptidase active site
  • Charged arginine
  • Forms an ionic bond with the terminal carboxylic
    acid
  • Zinc ion
  • Binds to carbonyl of terminal peptide
  • S1 pocket
  • Allows for the side chain of the terminal amino
    acid

2
65
L-Benzylsuccinic Acid
  • Inhibits carboxypeptidase
  • Key features
  • Benzyl group to fill the S1 pocket
  • Carboxylate anion for ionic interactions with
    arginine
  • Second carboxylate to act as a ligand for the
    zinc ion
  • Lack of a peptide bonds prevents it from being
    hydrolyzed and removed from the active site

2
66
ACE-Inhibitors
  • From the carboxypeptidase the ACE active site
    contains
  • Arginine
  • Zinc ion
  • S pockets
  • Inhibitor used Succinyl proline
  • Proline is located on the terminus of teprotide
  • Distance between the dipeptide and peptide were
    thought to be greater than the distance between
    the amino acid and peptide chain
  • Analogous to benzylsuccinic acid

2
67
ACE-Inhibitors
  • Next developments increased binding affinity
  • Captopril
  • Methyl group to fill S1
  • Thiol added to interact with zinc
  • Enalaprilat
  • Glutarylproline replaced succinyl proline to
    better fit the S1 pocket
  • Lisinopril
  • Similar to enalaprilat with a aminobutyl
    substitutent replacing methyl substitutent

2
2
68
ACE-Inhibitors
1
69
Sulfhydryl-containing ACE-Inhibitors
  • Captopril
  • Active compound
  • 75 bioavailability, which can be reduced by food
  • Take 1 hour prior to food consumption
  • Eliminated in the urine
  • Captopril, captopril disulfide dimmers, and
    captopril-cysteine disulfide

http//home.caregroup.org/clinical/altmed/interact
ions/Drugs/Captopril.htm
70
Dicarboxyl-containing ACE-Inhibitors
  • Enalapril
  • Prodrug, activated in vivo
  • to enalaprilat
  • C2H5 group is hydrolyzed by
  • esterases in the liver
  • Eliminated by the kidneys
  • Enalapril and enalaprilat
  • Bioavailability of 60, not reduced by food
  • Enalaprilat
  • Active dicarboxylic acid
  • Not orally stable
  • IV administration only

71
Dicarboxyl-containing ACE-Inhibitors
  • Lisinopril
  • Active molecule
  • Lysine analogue of enalaprilat
  • Characterized by
  • Slow, variable, incomplete absorption (30- not
    reduced by food)
  • Eliminated intact by the kidneys
  • Benazepril
  • Prodrug, activated to be benazeprilat
  • Eliminated by kidney and liver via urine and bile
  • High potency in vitro with a low uptake, 37-
    can be reduced when food is present

72
Dicarboxyl-containing ACE-Inhibitors
  • Trandolapril
  • Prodrug, activated to trandolaprilat
  • Active form has 70 bioavailability, slowed by
    food
  • Eliminated in urine (33) and feces (66)
  • Quinapril
  • Prodrug, activated to quinaprilat
  • 60 absorption, slowed by food
  • Two half-lives in the body
  • Initial 2 hours
  • Prolonged 25 hours
  • Due strong binding with tissue ACE

73
Dicarboxyl-containing ACE-Inhibitors
  • Ramipril
  • Prodrug, active form ramiprilat
  • Created via cleavage of ester moiety
  • Rapidly absorbed, slowed by food
  • Triphasic elimination half-life
  • Initial 2-4 hours
  • Extensive tissue distribution
  • Intermediate 9-18 hours
  • Clearance of free ramiprilat from plasma
  • Terminal 50 hours
  • Dissociation from tissue ACE

74
Dicarboxyl-containing ACE-Inhibitors
  • Moexipril
  • Prodrug, active form is moexiprilat
  • 13 bioavailability for moexiprilat due to
    incomplete absorption of moexipril
  • Take 1 hour prior to food consumption
  • Perindopril
  • Prodrug, active form is perindoprilat
  • 75 bioavailability for the prodrug
  • 35 bioavailability for the active form, reduced
    in the presence of food
  • Eliminated by the kidneys

http//www.geocities.com/lubolahchev/Moexipril.htm
l
http//www.fortunecity.com/roswell/spells/260/c990
0109.gif
75
Phosphorous-containing ACE-Inhibitors
  • Fosinopril
  • Prodrug converted to fosinoprilat
  • Slow absorption, slowed further by food
  • 36 uptake
  • Eliminated by kidneys and liver
  • Dual elimination allows for use despite the
    presence of renal disease

http//en.wikipedia.org/wiki/Monopril
76
Side Effects of ACE-Inhibitors
  • Hypotension with the first dose
  • Dry cough 5-20 of people
  • Hyperkalemia (High K levels)
  • Acute renal failure
  • Fetopathic effects in pregnant women
  • Skin rash
  • Dysgeusia, loss of taste

http//www.beauregard.org/bldpress.htm
77
The Future of ACE-Inhibitors
  • In 2003 X-ray crystallography revealed the
    structure of ACE joined with lisinopril.
  • Indicated that the arginine is actually a lysine
    residue
  • Possibility of new inhibitors with greater
    binding capabilities and greater selectivity

http//www.cbi.cnptia.embrapa.br/jorgehf/index2.h
tml
78
Sources
Print Sources 1. Brunton, Laurence L., John S.
Lazo, and Keith L. Parker, eds. The
Pharmacological Basis of Therapeutics. 11 ed.
New York McGraw-Hill, 2006. 2. Patrick, Graham
L. An Introduction to Medicinal Chemistry. 3 ed.
New York Oxford University Press, 2005. Online
Sources 3. www.aurorahealthcare.org 4.
www.healthatoz.com 5. www.americanheart.org 6.
www.drugdigest.org 7. http//www.beauregard.org/bl
dpress.htm 8. http//www.everybody.co.nz/page-3f71
418a-d1e1-43d7-9ac0-fdcb4a79a3e3.aspx 9.
http//www.merck.com/media/mmhe2/figures/fg022_2.g
if 10. http//member.rivernet.com.au/balehirs/drHt
2.jpg 11. http//www.physicaltherapy.ca/cardio/Hyp
ertension1.html 12. http//www.szgdocent.org/resou
rce/rr/c-viper.htm 13. http//home.caregroup.org/c
linical/altmed/interactions/Drugs/Captopril.htm 14
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http//www.medsafe.govt.nz/profs/Datasheet/p/prinz
idepic1.gif 16. http//www.alchemchina.com/product
s/apis_b.files/Benazepril.gif 17.
http//www.drugs.com/pdr/images/10/04044002.jpg 18
. http//www.medicinescomplete.com/mc/clarke/curre
nt/images/clk1438c001.gif 19. http//www.smspharma
.com/images/ramipril_img.gif 20.
http//www.geocities.com/lubolahchev/Moexipril.htm
l 21. http//www.fortunecity.com/roswell/spells/26
0/c9900109.gif 22. http//en.wikipedia.org/wiki/Mo
nopril 23. http//www.beauregard.org/bldpress.htm
24. http//www.cbi.cnptia.embrapa.br/jorgehf/inde
x2.html
For more detailed citations, please see
accompanying paper.
79
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