Triaminepentaacetic acid compound and paramagnetic metal complex prepared from using the compound as ligand

The present invention provides a triaminepentaacetic acid compound which can be used as a ligand to coordinate to a metal ion to form a paramagnetic metal complex. The paramagnetic metal complex of the present invention can be used as a contrast agent for magnetic resonance imaging (MRI).

BACKGROUND OF THE INVENTION
 1. Field of the Invention
 The present invention relates to a series of triaminepentaacetic acid
 compounds, and more particularly to a paramagnetic metal complex prepared
 from using the compound as the ligand, which can be used as a contrast
 agent for magnetic resonance imaging (MRI).
 2. Description of the Prior Art
 In recent years, magnetic resonance imaging (MRI) has developed rapidly and
 has become one of the most important techniques for diagnosing diseases.
 In order to increase sensitivity and accuracy, it is very important to
 develop a safe, stable, and targeting MRI contrast agent. Having a high
 magnetic moment, paramagnetic metal ions such as Mn.sup.2+, Fe.sup.3+, and
 Gd.sup.+3 have potential to serve as MRI contrast agents. MRI contrast
 agents which have been approved by FDA of United States to be
 intravenously injected clinically include Gd(DTPA).sup.2- (gadopentetate
 dimeglumine), Gd(DOTA).sup.- (gadoterate megulumine), Gd(DTPA-BMA)
 (bis-methylamide) (gadodiamide injection), Gd(HP-DO3A) (gadoteridol), and
 MnDPDP (Teslascan). All of these five contrast agents belong to
 extracellular agents. Gd(DTPA-BMA) and Gd(HP-DO3A) are nonionic contrast
 agents, and Gd(DTPA).sup.2-, Gd(DOTA).sup.-, and MnDPDP are ionic ones.
 Gd(DOTA).sup.- and Gd(HP-DO3A) are macrocyclic, and MnDPDP,
 Gd(DTPA).sup.2-, and Gd(DTPA-BMA) are open-chained.
 Among the above cations, Gd.sup.3+ has the greatest magnetic moment; thus,
 it has drawn the greatest interest. However, such a cation is not suitable
 for use alone as a MRI contrast agent due to the reasons of toxicity,
 pharmacokinetics, biodistribution, and effect. In addition, when
 GdCl.sub.3 is intravenously injected to animal bodies, the LD.sub.50 is
 very high, 0.3-0.5 mmol/kg [Weinmann et al. (1984) Am. J. Roentg., 142,
 619]. Therefore, it is necessary to use an organic ligand to complex with
 Gd.sup.3+ to form a stable metal complex to inhibit its toxicity and
 change the biodistribution and effect. Having a d orbital, Mn.sup.2+ and
 Fe.sup.3+ can form a stable complex with an organic ligand because of very
 strong partial covalent bonds [Lauffer et al. (1985) J. Comput. Assist.
 Tomogr., 9, 431]. It is more difficult for trivalent cations of lanthanide
 series to form complexes with organic ligands, since the f orbital belongs
 to the inner orbital which has less orientation and the interaction
 between the cation and the ligand is totally contributed by electrostatic
 interaction.
 The toxicity of the metal complex can be derived from (1) free metal ion
 released from dissociation; (2) free organic ligand released from
 dissociation; and (3) the metal complex itself. In addition, metabolites
 may be even more toxic than the metal complex itself. Since metal ions and
 organic ligands may form bonding with proteins, enzymes, or cell membrane
 in tissues by electrostatic interaction, hydrogen bonds, or covalent
 bonds, they have higher toxicity than the metal complex itself for animal
 bodies.
 The toxicity of the metal ion is derived from coordination of ions to
 oxygen, nitrogen, or sulfur atom of macromolecules in animal bodies, thus
 changing the dynamic equilibria necessary to sustain life. For example,
 Gd.sup.3+ easily replaces Ca.sup.2+ and binds to Ca.sup.2+ binding sites
 to complex with the above atoms. The toxicity of the organic ligand is due
 to the effect to the tissues by the ligand itself. The toxicity of the
 metal complex may be derived from various reasons. For example, when a
 large dose of the metal complex is injected, it will cause a difference in
 osmolality between intracellular and extracellular compartments. Water is
 drawn out of cells as a result of the osmotic gradient, causing cellular
 and circulatory damage. Other toxicity reasons include enzyme inhibition
 or alternation of membrane functions.
 To design a new contrast agent for MRI, the stability of the metal complex
 is the main concern. The contrast agent should be effective during the
 period of time from injecting it to the body to excreting it from the
 body. Therefore, stability is required for this residence time. Three
 factors should be considered to determine the stability of a gadolinium
 complex in vivo; that is, thermodynamic stability constant, conditional
 stability constant, and selectivity constant [Cacheris et al. (1990) Magn.
 Reson. Imag., 8, 467].
 Recent reseach on MRI contrast agents can be classified in two categories
 and are described as follows:
 (1) Ionic MRI contrast agents: Such contrast agents include
 [Gd(DTPA)].sup.2-, [Gd(EOB-DTPA)].sup.2- [ethoxybenzyl diethylene
 triaminepentaacetate-gadolinium(III)], [Gd(BOPTA)].sup.2-
 [benzyloxypropionic tetraacetate-gadolinium(III)], and [Gd(DOTA)].sup.-1.
 The thermodynamic stability constants of [Gd(DTPA)].sup.2-,
 [Gd(BOPTA)].sup.2- and [Gd(DOTA)].sup.-1 are 10.sup.22.46, 10.sup.22.0,
 and 10.sup.25.3 [Vittadin et al. (1988) Invest. Radiol., 23, 246; and
 Pavone et al. (1990) Radiology, 176, 61]. Since these gadolinium complexes
 are ionic, counter ions, generally meglumine, should be added to form ion
 pair for storage. However, this will increase the osmotic pressure of the
 solution.
 (2) Non-ionic MRI contrast agents: Such contrast agents have a lower
 osmotic pressure than ionic contrast agents. Thus, non-ionic MRI contrast
 agents can be injected in a larger dose in order to achieve higher
 enhancement effect. Non-ionic MRI contrast agents includes [Gd(DTPA-BMA)]
 [diethylenetriamine pentaacetic acid bis(methylamide)-gadolinium(III)],
 [Gd(DTPA-BP)]
 [N,N-bis(2-pyridylmethyl)diethylenetriamine-N,N',N"-triacetate-gadolinium(
 III)], [Gd(HP-DO3A)]
 [10-(2-hydroxypropyl)-1,4,7,10-tetraaza-cyclododecane-1,4,7-triacetate-gad
 olinium(III)], and [Gd(DO3A)]
 [1,4,7,10-tetraazacyclododecane-1,4,7-triacetate-gadolinium(III)]. These
 non-ionic gadolinium complexes have a lower thermodynamic stability than
 ionic gadolinium complexes. For example, the thermodynamic stability
 constants of [Gd(DTPA-BMA)], [Gd(DTPA-BP], [Gd(HP-DO3A)] and [Gd(DO3A)]
 are 10.sup.16.85, 10.sup.16.83, and 10.sup.23.8 and 10.sup.21.0 [Kumar et
 al. (1994) Inorg. Chem., 33, 3567; and Brucher et al. (1991) Inorg. Chem.,
 30, 2092]. However, these non-ionic gadolinium complexes are very stable
 under the physiological conditions of bodies.
 The toxicity of the open-chained gadolinium complex, no matter ionic or
 non-ionic, is mainly related to selectivity constant. For example, the
 selectivity constant is in the order of [Gd(DTPA-BMA)]
 (10.sup.9.04)&gt;[Gd(DTPA)].sup.2- (10.sup.7.04)&gt;[Gd(DTPA-BP)]
 (10.sup.5.32), which is consistent to the order of LD.sub.50,
 [Gd(DTPA-BMA)] (14.8 mmol/kg)&gt;[Gd(DTPA)].sup.2- (5.6
 mmol/kg)&gt;[Gd(DTPA-BP)] (3.2 mmol/kg).
 The relaxivity of the metal complex is also an important consideration for
 designing an MRI contrast agent. When the denticity of the organic ligand
 increases, the coordinated water molecules in the inner sphere of the
 metal complex decreas, thus decreasing the relaxation effect. Taking
 [Gd(EDTA)].sup.- for an example, EDTA has 6 denticities and Gd.sup.3+ has
 8-9 binding sites, thus, 2-3 inner sphere water molecules will be present
 in [Gd(EDTA)].sup.-, and the relaxivity (R.sub.1) is as high as 6.3 (mM
 s).sup.-1. DTPA, EOB-DTPA, BOPTA, DOTA, HP-DO3A and DTPA-BMA have 8
 denticities, thus, only 1 inner sphere water molecule will be present in
 their gadolinium complex, and the relaxivities are 3.7, 5.3, 5.65, 5.8,
 3.7, and 5.1 (mM s).sup.-1 respectively. Gd(III)-TREN-Me-3,2-HOPO
 [tris(3-hydroxy-1-methyl-2-oxo-1,1-didehydro-pyridine-4-carboxamido)ethyla
 mine] has 2 inner sphere water 7 molecules, and the relaxivity is increased
 to 10.5 (mM s).sup.-1 (37.degree. C., 20 MHz) [Xu et al. (1995) J. Am.
 Chem. Soc., 117, 7245]. Petre et al. modifies DTPA by introducing
 p-butylbenzyl with higher lipid solubility to the ethyl group of DTPA to
 form Gd(1RS)-1-(p-butylbenzyl)-DTPA, so as to make the contrast agent
 absorbed by livers [Petre et al. (1995) Magn. Reson. Med., 35, 532]. Also,
 Runge et al. synthesizes 2,5-BPA-DO3A and Cy.sub.2 DOTA
 (biscyclohexyl-DOTA) to increase their lipid solubility [Runge et al.
 (1996) Invest. Radiol., 31, 11]. Lammers et al. synthesizes
 N,N"-bis[N-(d-gluco-2,3,4,5,6-pentahydroxyhexyl)carbamoylmethyl]diethylene
 triamine-N,N',N"-triacetic acid (DTPA-BGLUCA) and
 N,N"-bis[N-(3-aza-D-galacto-5,6,7,8,9-pentahydroxynonyl)carbamoylmethyl]di
 ethylenetriamine-N,N',N"-triacetic acid (DTPA-BENGALAA). The purpose of
 introducing various aminoglucoses is to increase the functional group, so
 as to increase the outer sphere water molecules, thus increasing
 relaxivity [Lammers et al. (1997) Inorg. Chem., 36, 2527]. Vauthey et al.
 synthesizes
 2,11-dihydroxy-4,9-dioxa-1,12-bis[1,4,7,10-tetraaza-4,7,10-tris(carboxymet
 hyl)cyclododecyl]dodecane-gadolinium(III)) {BO[Gd(DO3A)(H.sub.2 O)]2}
 dimer. Since the dimer has two inner sphere water molecules (q=2), and the
 rotational time (.tau..sub.r) of the dimer increases twice compared with
 the monomer, therefore, the relaxivity (R.sub.1) increases from 3.4
 (monomer) to 4.61 dm.sup.3 mmol.sup.-1 s.sup.-1 (dimer) [Vauthey et al.
 (1996) Inorg. Chem., 35, 3375]. Schumann et al. synthesizes
 1,4,7,10,13,16,19,22-octaazacyclotetracosane-1,4,7,10,13,16,19,22-octaacet
 ic acid (H.sub.8 OTEC) and
 1,4,7,10,14,17,20,23-octaazacyclohexacosane-1,4,7,10,14,17,20,23-octaaceti
 c acid (H.sub.8 HEC). The two ligands have 16 coordinating sites and can
 form a bimetallic complex with lanthanide series metal ion, which have
 higher water solubility [Schumann et al. (1997) J. Chem. Ber./Recueil,
 130, 267]. Aime et al synthesize
 3,6,9,15-tetraazabicyclo[9.3.
 1]pentadeca-1(15),11,13-triene-3,6,9-triacetic acid (

DETAILED DESCRIPTION OF THE INVENTION
 The triaminepentaacetic acid compound of the present invention is
 represented by the following formula
 ##STR3##
 wherein
 R.sup.1 is --(CH.sub.2).sub.n -- or --(CH.sub.2).sub.n
 --X--(CH.sub.2).sub.n --, wherein n=1 to 5, X is --O-- or --S--;
 R.sup.2 is --(CH.sub.2).sub.m -- or --(CH.sub.2).sub.m
 --X--(CH.sub.2).sub.m --, wherein m=1 to 5, X is --O-- or --S--; and
 R.sup.1 and R.sup.2 can be the same or different.
 According to a preferred embodiment of the present invention, in formula
 (I), R.sup.1 is --(CH.sub.2).sub.n --X--(CH.sub.2).sub.n --, wherein n=2
 to 4, X is --O-- or --S--; and R.sup.2 is --(CH.sub.2).sub.m
 --X--(CH.sub.2).sub.m --, wherein m=2 to 4, X is --O-- or --S--.
 According to a second preferred embodiment of the present invention, in
 formula (I), R.sup.1 is --(CH.sub.2).sub.n --, wherein n=2 to 4; and
 R.sup.2 is --(CH.sub.2).sub.m --X--(CH.sub.2).sub.m --, wherein m=2 to 4,
 X is --O-- or --S--.
 According to a third preferred embodiment of the present invention, in
 formula (I), R.sup.1 is --(CH.sub.2).sub.n --X--(CH.sub.2).sub.n --,
 wherein n=2 to 4, X is --O-- or --S--; and R.sup.2 is --(CH.sub.2).sub.m
 --, wherein m=2 to 4.
 According to a fourth preferred embodiment of the j present invention, in
 formula (I), R.sup.1 is --(CH.sub.2).sub.n --, wherein n=2 to 4; and
 R.sup.2 is --(CH.sub.2).sub.m --, wherein m=2 to 4. Representative
 examples of the triaminepentaacetic acid according to this embodiment
 include
 TTDA (n=2, m=3) [3,6,10-tri(carboxymethyl)-3,6,10-triazadodecanedioic
 acid],
 TTRA (n=3, m=3) [3,7,11-tri(carboxymethyl)-3,7,11-triazatridecanedioic
 acid], and
 TTEA (n=3, m=4) [3,7,12-tri(carboxymethyl)-3,7,12-triazatetradecanedioic
 acid].
 The triaminepentaacetic acid compound of the present invention can be used
 as a ligand to coordinate to a metal ion to form a paramagnetic metal
 complex represented by the formula ML. M is a central metal ion, which is
 selected from the group consisting of ions of metals of Lanthanide series,
 manganese ion, iron ion, cobalt ion, copper ion, nickel ion, and chromium
 ion. Examples are Gd(+3), Fe(+3), and Mn(+3). L is the triaminepentaacetic
 acid compound of formula (I) as mentioned above. The paramagnetic metal
 complex of the present invention can be used as a contrast agent for
 magnetic resonance imaging (MRI).
 The following examples are intended to illustrate the process and the
 advantages of the present invention more fully without limiting its scope,
 since numerous modifications and variations will be apparent to those
 skilled in the art.
 EXAMPLES
 The synthesis of the DTPA derivatives is depicted as follows:
 ##STR4##
 Example 1
 Preparation of TTDA [3,6,10-tri(carboxymethyl)-3,6,10-triazadodecanedioic
 acid]
 3.0 g (25.64 mmol) of N-(2-aminoethyl)-1,3-propanediamine and 18.41 g (133
 mmol) of anhydrous potassium carbonate in 150 ml of CH.sub.3 CN
 (acetonitrile) were stirred thoroughly. Then, 25.56 g (136.19 mmol) of
 tert-butyl bromoacetate was slowly added and the mixture was stirred for
 24 hours. Removal of the solvent at reduced pressure on a rotary
 evaporator gave a residue which was partitioned between 100 ml of water
 and 100 ml of chloroform. The aqueous layer was separated and then
 extracted with two 100 ml portions of chloroform. The chloroform portions
 were combined and dried over MgSO.sub.4. Filtration and evaporation of
 solvent gave an amber oil, which was purified by chromatography on silica
 gel using ethyl acetate/n-hexane (1:4, v/v) as the eluent to give a gold
 oil. The oil was then acidified with 25 ml of concentrated aqueous
 hydrochloric acid (12 mol dm.sup.-3). The acid was removed by rotary
 evaporation and the residue taken up in water (20 ml). The solution was
 loaded onto an AG 50W.times.8 cation exchange resin column (200-400 mesh,
 H.sup.+ form, 3.5.times.20 cm) and washed with distilled water (1000 ml).
 The crude product was eluted with 0.5 mol dm.sup.-3 NH.sub.3 (aq). The
 solution was concentrated by rotary evaporation and the white residue
 applied to an AG1.times.8 anion exchange resin column (200-400 mesh,
 HCO.sub.2 H form, 3.5.times.20 cm). The column was washed with distilled
 water and eluted with 0.5 mol dm.sup.-3 formic acid. The eluate was
 concentrated by rotary evaporation for 12 hours to give a white solid.
 Yield: 6.58 g (58%). .sup.1 H-NMR (D.sub.2 O, pD 2.9): 3.83 (s, 8H,
 terminal, NCH.sub.2 COOH), 3.80 (s, 2H, central, NCH.sub.2 COOH), 3.51 (s,
 4H, NCH.sub.2 CH.sub.2 N), 2.28 (t, 4H, NCH.sub.2 CH.sub.2 CH.sub.2 N),
 2.16 (m, 2H, NCH.sub.2 CH.sub.2 CH.sub.2 N). .sup.13 C-NMR (D.sub.2 O):
 .delta. 176.52, 175.01, 173.45, 60.46, 60.23, 58.76, 56.37, 55.03, 54.41,
 53.56, 23.04. Anal. Calcd (found) for C.sub.15 N.sub.25 N.sub.3 O.sub.10
 2H.sub.2 O: C, 40.63 (40.61); H, 6.59 (6.74); N, 9.47 (9.31).
 Example 2
 Preparation of TTRA [3,7,11-tri(carboxymethyl)-3,7,11-triazatridecanedioic
 acid]
 2.0 g (15.24 mmol) of N-(3-aminopropyl)-1,3-propanediamine and 10.5 g (76
 mmol) of anhydrous potassium carbonate in 150 ml of CH.sub.3 CN
 (acetonitrile) were stirred thoroughly. Then, 15.46 g (79.25 mmol) of
 tert-butyl bromoacetate was slowly added and the mixture was stirred for
 24 hours. Removal of the solvent at reduced pressure on a rotary
 evaporator gave a residue which was partitioned between 100 ml of water
 and 100 ml of chloroform. The aqueous layer was separated and then
 extracted with two 100 ml portions of chloroform. The chloroform portions
 were combined and dried over MgSO.sub.4. Filtration and evaporation of
 solvent gave an amber oil, which was purified by chromatography on silica
 gel using ethyl acetate/methanol as the eluent to give a gold oil. The oil
 was then acidified with 25 ml of concentrated aqueous hydrochloric acid
 (12 mol dm.sup.-3) The acid was removed by rotary evaporation and the
 residue taken up in water (20 ml). The solution was loaded onto an AG
 50W.times.8 cation exchange resin column (200-400 mesh, H.sup.+ form,
 3.5.times.20 cm) and washed with distilled water (1000 ml). The crude
 product was eluted with 0.5 mol dm.sup.-3 NH.sub.3 (aq). The solution was
 concentrated by rotary evaporation and the white residue applied to an
 AG1.times.8 anion exchange resin column (200-400 mesh, HCO.sub.2 H form,
 3.5.times.20 cm). The column was washed with distilled water and eluted
 with 0.5 mol dm.sup.-3 formic acid. The eluate was concentrated by rotary
 evaporation for 12 hours to give a white solid. Yield: 4.74 g (68%).
 .sup.1 H-NMR (D.sub.2 O, pD 3.51): 3.82 (s, 8H, terminal, NCH.sub.2 COOH),
 3.76 (s, 2H, central, NCH.sub.2 COOH), 3.32 (m, 8H, NCH.sub.2 CH.sub.2
 CH.sub.2 N), 2.16 (m, 4H, NCH.sub.2 CH.sub.2 CH.sub.2 N). .sup.13 C-NMR
 (D.sub.2 O): .delta. 174.78, 173.82, 60.28, 58.82, 56.13, 54.72, 22.68.
 Anal. Calcd (found) for C.sub.16 N.sub.27 N.sub.3 O.sub.10 2H.sub.2 O: C,
 42.01 (41.80); H, 6.83 (6.98); N, 9.18 (9.09).
 Example 3
 Preparation of TTEA
 [3,7,12-tri(carboxymethyl)-3,7,12-triazatetradecanedioic acid]
 2.0 g (13.77 mmol) of N-(3-aminopropyl)-1,4-butanediamine and 9.52 g (68.85
 mmol) of anhydrous potassium carbonate in 150 ml of CH.sub.3 CN
 (acetonitrile) were stirred thoroughly. Then, 13.97 g (71.60 mmol) of
 tert-butyl bromoacetate was slowly added and the mixture was stirred for
 24 hours. Removal of the solvent at reduced pressure on a rotary
 evaporator gave a residue which was partitioned between 100 ml of water
 and 100 ml of chloroform. The aqueous layer was separated and then
 extracted with two 100 ml portions of chloroform. The chloroform portions
 were combined and dried over MgSO.sub.4. Filtration and evaporation of
 solvent gave an amber oil, which was purified by chromatography on silica
 gel using ethyl acetate/methanol as the eluent to give a gold oil. The oil
 was then acidified with 20 ml of concentrated aqueous hydrochloric acid
 (12 mol dm.sup.-3). The acid was removed by rotary evaporation and the
 residue taken up in water (20 ml). The solution was loaded onto an AG
 50W.times.8 cation exchange resin column (200-400 mesh, H.sup.+ form,
 3.5.times.20 cm) and washed with distilled water (1000 ml). The crude
 product was eluted with 0.5 mol dm.sup.-3 NH.sub.3 (aq). The solution was
 concentrated by rotary evaporation and the white residue applied to an
 AG1.times.8 anion exchange resin column (200-400 mesh, HCO.sub.2 H form,
 3.5.times.20 cm). The column was washed with distilled water and eluted
 with 0.5 mol dm.sup.-3 formic acid. The eluate was concentrated by rotary
 evaporation for 12 hours to give a white solid. Yield: 4.85 g (72%).
 .sup.1 H-NMR (D.sub.2 O, pD 3.43): 3.83 (s, 4H, terminal, NCH.sub.2 COOH),
 3.80 (s, 4H, central, NCH.sub.2 COOH), 3.76 (s, 2H, NCH.sub.2 COOH),
 3.26-3.78 (m, 8H, NCH.sub.2), 2.17 (t, 2H, NCH.sub.2 CH.sub.2 CH.sub.2 N),
 1.78 (m, 4H, NCH.sub.2 CH.sub.2 CH.sub.2 CH.sub.2 N). .sup.13 C-NMR
 (D.sub.2 O): .delta. 173.77, 173.53, 173.47, 60.35, 58.79, 58.22, 56.99,
 55.81, 54.58, 23.99, 23.59, 22.60. Anal. Calcd (found) for C.sub.17
 N.sub.29 N.sub.3 O.sub.10 3H.sub.2 O: C, 41.72 (41.77); H, 7.21 (7.55); N,
 8.58 (8.75).
 Example 4
 Preparation of [Gd(TTDA)].sup.2-.7H.sub.2 O
 1.5 g (3.38 mmol) of TTDA.2H.sub.2 O obtained from example 1, 0.59 g (1.65
 mmol) of gadolinium chloride, and 15 ml of deionized water were mixed and
 reluxed for 24 hours. After reaction is completed, 10 ml of methanol was
 slowly added and colorless crystals were formed. Yield: 1.47 g (63%).
 Anal. Calcd (found) for C.sub.15 H.sub.25 N.sub.3 O.sub.10 7H.sub.2 O: C,
 26.07 (26.01); H, 4.96 (4.85); N, 6.08 (5.92).
 Discussion on Thermodynamic Constants
 1. Protonation Constants:
 Potentiometric titrations were performed with an automatic titrator system
 to determine the protonation constants of the organic ligands and the
 stability constants of the metal complexes. The autotitrating system
 consists of a 702 SM Titroprocessor, a 728 stirrer, and a PT-100
 combination pH electrode (Metrohm). The pH electrode was calibrated using
 two standard buffer solutions with pH 7.0.+-.0.05 and pH 4.0.+-.0.05
 respectively. The ionic strength was 0.10 mol dm.sup.-3 Me.sub.4 NNO.sub.3
 ((CH.sub.3).sub.4 NNO.sub.3). The ligands used in this experiment should
 have high purity. If the important functional groups of the ligand have
 not been protonated, suitable acid should be added to make it protonated
 before titration. The titrant used was 0.1 mol dm.sup.-3 NaOH with a
 titration amount of 0.005 ml/time.
 The protonation constants of the ligand were calculated using a FORTRAN
 computer program PKAS. The overall stability constants of the various
 metal complexes formed in aqueous solution were determined from the
 titration data with the FORTRAN computer program BEST. The average
 difference between observed and calculated -log[H.sup.+ ] was &lt;0.04
 throughout all titrations. The species distribution diagrams were
 calculated with the FORTRAN programs SPE and SPEPLOT.
 The potentiometric titration curves of the organic ligands TTDA, TTRA, and
 TTEA are shown in FIG. 1 to FIG. 4. The protonation constants of the
 organic ligands is calculated using the FORTRAN computer program PKAS and
 are shown in Table 1. From FIG. 1, it is shown that there are two
 buffering regions (pH 2.5-5.5 and pH 6-9) in the TTDA titration curve.
 When the number of mole base per mole ligand (value a) is equal to 2, the
 curve is rising steeply. This is due to the large difference between the
 third (logK.sub.3.sup.H =5.12) and fourth protonation constant
 (logK.sub.4.sup.H =2.8) of TTDA. When a=3, the curve is rising steeply
 again, which is due to the large difference between the second
 (logK.sub.2.sup.H =8.92) and third protonation constant (logK.sub.3.sup.H
 =5.12) of TTDA. The difference between the first (logK.sub.1.sup.H =10.60)
 and second protonation constant (logK.sub.2.sup.H =8.92) is not obvious.
 From FIG. 3, it is shown that there are two buffering regions (pH 3-8 and
 pH 8-10) in the TTRA titration curve. When a=2, the curve is rising
 steeply. This is due to the large difference between the third
 (logK.sub.3.sup.H =7.00) and fourth protonation constant (logK4.sup.H
 =3.10) of TTRA. When a=3, the curve is rising steeply again, which is due
 to the large difference between the second (logK.sub.2.sup.H =9.12) and
 third protonation constant (logK.sub.3.sup.H =7.00).
 From FIG. 4, it is shown that there are two buffering regions (pH 2.8-8 and
 pH 8-10) in the TTEA titration curve. When a=2, the curve is rising
 steeply. This is due to the large difference between the third
 (logK.sub.3.sup.H =7.71) and fourth protonation constant (logK.sub.4.sup.H
 =3.04) of TTEA. When a=3, the curve is rising steeply again, which is due
 to the large difference between the second (logK.sub.2.sup.H =9.46) and
 third protonation constant (logK.sub.3.sup.H =7.71).
 In the titration curve, the steep rising curve indicates that the two
 protonation constants differ greatly, and the smooth rising curve
 indicates that the two protonation constants differ little.
 TABLE 1
 The protonation constants of the organic ligands
 TTDA, TTRA, TTEA, DTPA-BMA, and DTPA at
 25.0 .+-. 0.1.degree. C. in aqueous Me.sub.4 NNO.sub.3 (I = 0.10 mol
 dm.sup.-3)
 log K.sub.n.sup.H
 DTPA-
 Equilibrium TTDA TTRA TTEA BMA DTPA
 [HL]/[L][H] 10.60(2) 10.63(3) 10.69(0) 9.51(2) 10.49
 [H.sub.2 L]/[HL][H] 8.92(2) 9.12(2) 9.46(3) 4.49(1) 8.60
 [H.sub.3 L]/[H.sub.2 L][H] 5.12(2) 7.00(3) 7.71(2) 3.53(1) 4.28
 [H.sub.4 L]/[H.sub.3 L][H] 2.80(9) 3.10(5) 3.04(5) 2.64
 .SIGMA. PK.sub.a 27.44 29.85 30.90 17.53 26.01
 DTPA-BMA = diethylenetriamine pentaacetic acid
 bis(methylamide)-gadolinium(III)
 DTPA = diethylenetriaminepentaacetic acid
 From Table 1, it can be seen that the basicity (.SIGMA.pK.sub.a) of TTDA,
 TTRA, and TTEA is 27.44, 29.85, and 30.90 respectively, which increases by
 1.43, 3.84, and 4.89 compared with the basicity (.SIGMA.pK.sub.a =26.01)
 of DTPA. This indicates that when the carbon number between amino groups
 increases, the basicity increases. The first protonation constants of
 TTDA, TTRA, and TTEA are very close, and the second protonation constants
 are very close too. The third protonation constant decreases in the order
 TTEA (logK.sub.3.sup.H =7.71)&gt;TTRA (logK.sub.3.sup.H =7.00)&gt;TTDA
 (logK.sub.3.sup.H =5.12)&gt;DPTA (logK.sub.3.sup.H =4.28) This can be
 explained by considering the chain length (carbon number) between the
 amino groups. In general, the protonation constant increases with the
 chain length between the amino groups.
 2. Thermodynamic Stability Constants:
 The complexes of Zn.sup.2+, Ca.sup.2+, Cu.sup.2+, and Gd.sup.3+ with
 ligands TTDA, TTRA, and TTEA may have a stability constant higher than 10.
 Therefore, the stability constant is determined using the following two
 methods:
 (1) Direct Potentiometric Titration: The metal ion and ligand is mixed in
 1:1 molar ratio. NaOH is used as the titrant with 0.005 ml/time to titrate
 the mixed solution. The stability constant of the metal complex is
 calculated from the titration data by the program BEST.
 (2) Ligand-ligand Competition Titration: The metal ion, ligand, and EDTA is
 mixed in 1:1:1 molar ratio. NaOH is used as the titrant with 0.005 ml/time
 to titrate the mixed solution. The titration interval is 10-15 minutes to
 ensure the equilibrium of the competition reaction. The stability constant
 of the metal complex is calculated from the titration data by the program
 BEST.
 From the direct potentiometric titration, the titration curves of the TTDA,
 TTRA, and TTEA with metal ions Ca.sup.2+, Zn.sup.2+, and Cu.sup.2+ are
 shown in FIGS. 1-3. Referring to FIG. 1, it can be seen that the Ca.sup.2+
 -TTDA (molar ratio 1:1) complex has very similar pH value to the single
 TTDA solution. This indicates that in the beginning, Ca.sup.2+ does not
 immediately coordinate with the unprotonated or protonated organic ligand
 to form metal complex. As to Zn.sup.2+ and Cu.sup.2+ metal ions, they bind
 with TTDA ligand in the beginning; therefore, the pH value is lower than
 that of the single TTDA solution. The potentiometric curves of TTDA with
 Ca.sup.2+, Zn.sup.2+, and Cu.sup.2+ rise rapidly in the pH 3.5-10 range.
 The inflection point is at a=4 and a=5, indicating that the complex is
 present in the form of [MHL].sup.2- at a=4, and five protons are
 dissociated at a=5.
 Referring to FIG. 3, the potentiometric curve of TTRA-Ca.sup.2+ rises
 rapidly in the pH 3-6.5 range and those of TTRA with Zn.sup.2+ and
 Cu.sup.2+ rise rapidly in the pH 3.5-9 range. The inflection points of the
 metal complexes of TTRA with Ca.sup.2+, Zn.sup.2+ and Cu.sup.2+ are a=3,
 4, and 5 respectively, indicating that different metal complexes have
 different proton numbers dissociated.
 The thermodynamic constants determined by the program BEST are shown in
 Table 2. The stability constants of TTDA with Gd.sup.3+, Ca.sup.2+,
 Zn.sup.2+, and Cu.sup.2+ are in the order [Gd(TTDA)].sup.2-
 (22.77)&gt;[Cu(TTDA)].sup.3- (19.31)&gt;[Zn(TTDA)].sup.3-
 (18.59)&gt;[Ca(TTDA)].sup.3- (14.45). For Ca.sup.2+, TTDA complex has a
 greater stability constant than DTPA complex. For Zn.sup.2+ and Cu.sup.2+,
 TTDA complex has a smaller stability constant than DTPA complex. For
 Gd.sup.3+, TTDA complex has a similar stability constant to DTPA complex,
 [Gd(TTDA)].sup.2- (22.77)=[Gd(DTPA)].sup.2- (22.46).
 TABLE 2
 Thermodynamic constants
 of the of Gd.sup.3+, Zn.sup.2+, Ca.sup.2+, and Cu.sup.2+ complexes of
 organic ligands TTDA, TTRA, TTEA, DTPA-BMA,
 and DTPA at 25.0 .+-. 0.1.degree. C. in
 aqueous Me.sub.4 NNO.sub.3 (I = 0.10 mol dm.sup.-3)
 log K
 Parameter TTDA TTRA TTEA DTPA-BMA DTPA
 [GdL]/[Gd][L] 22.77 15.89 -- 16.95 22.46
 [GdHL]/[GdL][H] -- 5.95 -- --
 log K.sub.GdL' (pH 7.4) 18.04 10.93 -- 14.84 18.14
 [CaL]/[Ca][L] 14.45 13.52 13.48 7.72 10.75
 [CaHL]/[CaL][H] 6.06 8.02 8.2 5.11 6.11
 log K.sub.CaL' (pH 7.4) 9.72 8.56 8.13 5.11 6.43
 [ZnL]/[Zn][L] 18.59 19.37 19.91 12.13 18.70
 [ZnHL]/[ZnL][H] 7.41 4.15 4.7 4.04 5.60
 log K.sub.ZnL' (pH 7.4) 13.86 14.41 14.56 10.02 14.38
 [CuL]/[Cu][L] 19.31 17.92 17.33 13.17 21.38
 [CuL]/[CuL][H] 5.52 8.68 9.5 3.36 4.81
 log K.sub.CuL' (pH 7.4) 14.58 12.96 11.97 11.06 17.06
 The stability constants of TTRA with Gd.sup.3+, Ca.sup.2+, Zn.sup.2+, and
 Cu.sup.2+ are in the order [Zn(TTRA)].sup.3- (19.37)&gt;[Cu(TTRA)].sup.3-
 (17.92)&gt;[Gd(TTRA)].sup.3- (15.89)&gt;[Ca(TTRA)].sup.3- (13.52). For
 Gd.sup.3+, TTRA complex has a smaller stability constant than TTDA
 complex. The stability constants of TTEA with Ca.sup.2+, Zn.sup.2+, and
 Cu.sup.2+ are 13.48, 19.91, and 17.33 respectively. The stability of TTEA
 with Gd.sup.3+ can not be determined by potentiometric titration. This is
 because the f orbital of Gd.sup.3+ is ball-shaped, and the bonding between
 Gd.sup.3+ and the ligand is totally provided by electrostatic interaction.
 In TTEA, the carbon number among three amino groups is 3 and 4
 respectively; therefore, TTEA is very difficult to complex with metal
 ions. However, both of TTDA and TTRA, which have eight binding sites
 (three amino groups and five carboxyl groups), can complex with Gd.sup.3+.
 The stability constants logK.sub.GdL of TTDA and TTRA are 22.77 and 15.89
 respectively, indicating that the stability constant is related to the
 binding angle. However, for Ca.sup.2+, Zn.sup.2+, and Cu.sup.2+, the
 influence is less because of the d orbital.
 In addition, comparing TTDA, DTPA-BMA and DTPA, it can be found that the
 thermodynamic stability constants of complexes with the same metal ion is
 related to the basicity of the ligand. The more basic the ligand, the
 larger stability constant the metal complex. The thermodynamic stability
 constant for the same metal ion is in the order
 [M(TTDA)]=[M(DTPA)]&gt;[M(DTPA-BMA)] (M.sup.n+ =Gd.sup.3+, Zn.sup.2+,
 Ca.sup.2+, and Cu.sup.2+. The reason is because the ionic bonding between
 the metal ion and the carboxyl groups of the ligand is stronger than the
 ionic-dipolar interaction between the metal ion and the amide groups of
 the ligand.
 The thermodynamic stability constants of complexes with the same ligand is
 in the order GdL&gt;CuL&gt;ZnL&gt;CaL, which is mainly related to the
 charge density. The ion radii of Gd.sup.3+, Zn.sup.2+, Ca.sup.2+, and
 Cu.sup.2+ is 1.22 .ANG. (CN=8), 0.88 .ANG. (CN=6), 1.26 .ANG. (CN=8), and
 0.87 .ANG. (CN=6) respectively. It can be found that when the metal ion
 has a greater charge density, the metal complex formed has a larger
 thermodynamic stability constant.
 The protonated species distribution of TTDA, TTRA, and TTEA is shown in
 FIG. 5 to FIG. 9. In FIG. 5 shows that in the pH 5-9 range, the dominant
 species of TTDA ligand is the second protonated species [H.sub.2
 L].sup.3-. When pH=7.0, the concentration of [H.sub.2 L].sup.3- is the
 maximum (97.5%). In the pH 3-5 range, the dominant species is the third
 protonated species [H.sub.3 L].sup.2-. When pH=3.7, the concentration of
 [H.sub.3 L].sup.2- is the maximum (87.75%). In the pH 9-10.5 range, the
 dominant species is the first protonated species [HL].sup.4-. When pH=9.8,
 the concentration of [HL].sup.4- is the maximum (77.5%). In the pH 2-3
 range, the dominant species is the fourth protonated species [H.sub.4
 L].sup.-. When pH=2.3, the concentration of [H.sub.4 L].sup.- is the
 maximum (60.9%). In the pH range greater than 11, the dominant species is
 the deprotonated species [L].sup.5-.
 In FIG. 6 shows that in the pH 2-3.5 range, the dominant species of TTRA
 ligand is the fourth protonated species [H.sub.4 L].sup.-. When pH=2.7,
 the concentration of [H.sub.4 L].sup.- is the maximum (55.9%). In the pH
 3.5-7 range, the dominant species is the third protonated species [H.sub.3
 L].sup.2-. When pH=5, the concentration of [H.sub.3 L].sup.2- is the
 maximum (97.7%). In the pH 7-9 range, the dominant species is the second
 protonated species [H.sub.2 L].sup.3-. When pH=8.1, the concentration of
 [H.sub.2 L].sup.3- is the maximum (86.5%). In the pH 9.5-10.5 range, the
 dominant species is the first protonated species [HL].sup.4-. When pH=9.9,
 the concentration of [HL].sup.4- is the maximum (71.6%). In the pH range
 greater than 12, the dominant species is the deprotonated species
 [L].sup.5-. In the pH range less than 2, the dominant species is the
 totally protonated species [H.sub.5 L].
 In FIG. 7 shows that in the pH 2.5-3.5 range, the dominant species of TTEA
 ligand is the fourth protonated species [H.sub.4 L].sup.-. When pH=2.8,
 the concentration of [H.sub.4 L].sup.- is the maximum (45.9%). In the pH
 3.5-7.5 range, the dominant species is the third protonated species
 [H.sub.3 L].sup.2-. When pH=5.2, the concentration of [H.sub.3 L].sup.2-
 is the maximum (99.0%). In the pH 8-9.5 range, the dominant species is the
 second protonated species [H.sub.2 L].sup.3-. When pH=8.6, the
 concentration of [H.sub.2 L].sup.3- is the maximum (78.8%). In the pH
 9.5-11 range, the dominant species is the first protonated species
 [HL].sup.4-. When pH=10.1, the concentration of [HL].sup.4- is the maximum
 (67.2%). In the pH range greater than 12, the dominant species is the
 deprotonated species [L].sup.5-. In the pH range less than 2, the dominant
 species is the totally protonated species [H.sub.5 L].
 The species distribution of the TTDA-Gd.sup.3+ complex is shown in FIG. 8.
 It can be seen that below pH 1.5, the solution is present in the form of
 free Gd.sup.3+ ion, and above pH 3.9, the solution is present in the form
 of metal complex. The maximum concentration is 99.7%. The species
 distribution of the TTRA-Gd.sup.3+ complex is shown in FIG. 9. It can be
 seen that below pH 4.0, the solution is present in the form of free
 Gd.sup.3+ ion, and above pH 6, the solution is present in the form of
 metal complex. At pH 6.5, the maximum concentration is 98%.
 3. Conditional Stability Constants:
 To understand the stability of the metal complex in vivo, the conditional
 stability constant is more important than the thermodynamic stability
 constant. The conditional stability constant is the stability constant of
 a metal complex under physiological conditions (pH 7.4).
 The reaction of forming a metal complex from a metal ion and an organic
 ligand can be depicted as follows:
EQU M+L.revreaction.ML (1)
 M: metal ion, L: organic ligand, ML: metal complex The conditional
 stability constant is defined by equation (2):
 ##EQU1##
 The relationship between the conditional stability constant and the
 thermodynamic stability constant is defined by equation (3):
 ##EQU2##
 L.sub.T is the concentration of the uncomplexed organic ligand, which is
 expressed by equation (4):
EQU L.sub.T ={[L]+[HL]+[H.sub.2 L]+ . . . } (4)
 Substituting equation (4) into equation (3):
EQU K.sub.cond =K.sub.therm {1+K.sub.1.sup.H [H.sup.+ ]+K.sub.1.sup.H
 K.sub.2.sup.H [H.sup.+ ].sup.2 + . . . }.sup.-1 =K.sub.therm.alpha..sub.H
 (5)
 wherein .alpha..sub.H ={1+K.sub.1.sup.H [H.sup.+ ]+K.sub.1.sup.H
 K.sub.2.sup.H [H.sup.+ ].sup.2 + . . . }.sup.-1
 The conditional stability constant of [Gd(TTDA)].sup.2- and
 [Gd(TTRA)].sup.2- at various pH levels can be calculated by formula (5)
 The results are shown in Table 2. The stability constant under
 physiological conditions (pH 7.4) is in the order [Gd(TTDA)].sup.2-
 (22.77)=[Gd(DTPA)].sup.2- (22.46)&gt;[Gd(DTPA-BMA)]
 (16.95)&gt;[Gd(TTRA)].sup.2- (15.89). FIG. 10 shows the pH dependence of
 the conditional stability constant for the gadolinium complexes. At high
 pH (pH&gt;11.0), the organic ligand is totally deprotonated, and the
 conditional stability constant of the metal complex is the thermodynamic
 stability constant. At pH 11.0, the stability constants (log K.sub.ML) of
 [Gd(TTDA)].sup.2- and [Gd(DTPA)].sup.2- are larger than that of
 [Gd(DTPA-BMA)] by 5.8 and 5.5 respectively. At pH 7.4, the stability
 constants of [Gd(TTDA)].sup.2- and [Gd(DTPA)].sup.2- are larger than that
 of [Gd(DTPA-BMA)] by 3.3 and 3.2 respectively. At pH 4.0, the
 thermodynamic stability constants and the conditional stability constants
 of [Gd(TTDA)].sup.2-, [Gd(DTPA)].sup.2-, and [Gd(DTPA-BMA)] are all the
 same (11.25). At pH 11, the conditional stability constant of
 [Gd(TTRA)].sup.2- is 15.89 and is decreased to 1.14 at pH 4.0. The results
 show that the conditional stability constant (log K.sub.cond) of the
 gadolinium complex is very related to the basicity of the organic ligand.
 TTDA and DTPA have close basicity, and their conditional stability
 constants are similar. However, at pH=4.0, since [Gd(TTRA)].sup.2- has
 very large basicity, its conditional stability constant is only 4.14,
 which is much lower than those of [Gd(TTDA)].sup.2-, [Gd(DTPA)].sup.2- and
 [Gd(DTPA-BMA)].
 4. The Selectivity Constants:
 The toxicity of the MRI contrast agent is mainly due to the free metal ion
 (such as free Gd.sup.3+) from the dissociation of the MRI contrast agent.
 Metal ions such as Zn.sup.2+, Ca.sup.2+, and Cu.sup.2+ in the animal body
 compete with Gd.sup.3+ in the gadolinium complex, thus free Gd.sup.3+ is
 formed. The free Gd.sup.3+ will bind to the ligand in the body, such as
 amino acid, citric acid, or serum protein, to form complex, thus causing
 physiological unequivalence.
 Among Zn.sup.2+, Ca.sup.2+, and Cu.sup.2+, Zn.sup.2+ is the main cause of
 the dissociation of the gadolinium complex in the animal body. That is
 because the Zn.sup.2+ concentration in plasma is very high (10-50 .mu.M).
 Zn.sup.2+ can bind to a large amount of ligand to form a stable complex;
 thus, a large amount of Gd.sup.3+ is formed. As to the other metal ions in
 the animal body, Cu.sup.2+ concentration in plasma is only 1-10 .mu.m.
 Although Ca.sup.2+ concentration in plasma is very high (2.5-4 mM), the
 Ca.sup.2+ complexes with TTDA, DTPA, and DPTA-BMA have a low stability
 constant; thus, gadolinium complex will not be dissociated to form free
 gadolinium ion. In addition, as to Fe.sup.3+, the bonding of Fe.sup.3+ and
 the ligand for ferritin and hemosiderin is very strong; thus, replacement
 reaction with the gadolinium complex will not occur.
 The selectivity constant of the ligand for Gd.sup.3+ over M.sup.+ is
 defined as log K(Gd.sup.3+ /M.sup.n+) (M.sup.n+ =Zn.sup.2+, Ca.sup.2+, and
 Cu.sup.2+). Table 3 shows the selectivity constants of [Gd(TTDA)].sup.2-,
 [Gd(TTRA)].sup.2-, [Gd(DTPA-BMA)], and [Gd(DTPA)].sup.2- over Zn.sup.2+,
 Ca.sup.2+, and Cu.sup.2+. It is found that the selectivity constant of
 [Gd(TTDA)].sup.2- over Zn.sup.2+ is similar to that of [Gd(DTPA-BMA)],
 which is higher than that of [Gd(DTPA)].sup.2-, indicating that TTDA shows
 more favorable selectivity toward Gd.sup.3+ over Zn.sup.2+ than DTPA.
 5. Modified Selectivity Constants:
 Taking the thermodynamic stability constant of the gadolinium complex and
 the stability constant of the ligand with Zn.sup.2+, Ca.sup.2+, and
 Cu.sup.2+ into consideration, a modified selectivity constant can be
 obtained, which is expressed by K.sub.sel ' and calculated by the equation
 (6):
EQU K.sub.sel '=K.sub.therm (.alpha..sub.H.sup.-1 +.alpha..sub.CaL.sup.-1
 +.alpha..sub.CuL.sup.-1 +.alpha..sub.ZnL.sup.-1).sup.-1 (6)
 wherein
EQU .alpha..sub.H.sup.-1 =1+K.sub.1.sup.H [H.sup.+ ]+K.sub.1.sup.H
 K.sub.2.sup.H [H.sup.+ ].sup.2 + (7)
EQU .alpha..sub.CaL.sup.-1 =1+K.sub.CaL [Ca.sup.2+ ] (8)
EQU .alpha..sub.CuL.sup.-1 =1+K.sub.CuL [Cu.sup.2+ ] (9)
EQU .alpha..sub.ZnL.sup.-1 =1+K.sub.ZnL [Zn.sup.2+ ] (10)
 Knowing that the concentration of Ca.sup.2+, Cu.sup.2+, and Zn.sup.2+ in
 plasma is 2,5 mM, 1 .mu.m, and 50 .mu.m and the stability constant of the
 metal complex, the log K.sub.sel ' of the gadolinium complex at pH 7.4 can
 be calculated. The results are shown in Table 3. The modified selectivity
 constant is in the order [Gd(DTPA-BMA)] (9.03)&gt;[Gd(TTDA)].sup.2-
 (8.44)&gt;[Gd(DTPA)].sup.2- (7.07)&gt;[Gd(TTRA)].sup.2- (2.64). In
 addition, it is known that LD.sub.50 of [Gd(DTPA-BMA)] is 14.8 mmol/kg and
 that of [Gd(DTPA)].sup.2- is 5.6 mmol/kg, it can be concluded that the
 toxicity of the linear gadolinium complex is not related to the
 thermodynamic stability constant, but related to the selectivity stability
 constant. Therefore, it can be predicted that LD.sub.50 of
 [Gd(TTDA)].sup.2- may be higher than that of [Gd(DTPA)].sup.2- and the
 acute toxicity is lower.
 TABLE 3
 The selectivity of [Gd(TTDA)].sup.2-,
 [Gd(TTRA)].sup.2-, [Gd(DTPA-BMA)] and [Gd(DTPA)].sup.2- over Zn.sup.2+,
 Ca.sup.2+, and Cu.sup.2+.
 Parameter TTDA TTRA DTPA-BMA DTPA
 log K(Gd/Zn) 4.18 -- 4.82 3.76
 log K(Gd/Cu) 3.46 -- 3.78 1.08
 log K(Gd/Ca) 8.32 2.37 9.73 11.71
 log K sel' 8.44 2.64 9.03 7.07
 The stability of the metal complex in the animal body is very important for
 MRI contrast agent, and pM value is one of the important data. The pM
 value is defined as -log M.sup.n+ ].sub.free at pH 7.4 can be calculated
 by equation (11)
 ##EQU3##
 wherein
EQU .alpha..sub.L =1+.beta..sub.n.sup.H [H.sup.+.sup.n =1+K.sub.1.sup.H
 [H.sup.+ ]+K.sub.1.sup.H K.sub.2.sup.H [H.sup.+ ].sup.2 + (12)
EQU .alpha..sub.ML =1+.beta..sub.MH.sub..sub.n .sub.L.sup.H [H.sup.+ ].sup.n
 =1+K.sub.MHL [H.sup.+ ]+K.sub.MH.sub..sub.2 .sub.L [H.sup.+ ].sup.2 +
 (13)
 T.sub.L represents the total concentration of the ligand, and T.sub.M the
 total concentration of the metal ion. In the examples, T.sub.L is
 1.1.times.10.sup.-5 mol dm.sup.-3 and T.sub.M is 1.0.times.10.sup.-6 mol
 dm.sup.-3. Thus, pM of the metal complex at pH 7.4 can be calculated, and
 the results are shown in Table 4. It can be seen that the pM values of
 [M(DTPA)] and [M(TTDA)] are higher than that of [M(DTPA-BMA)]
 (M=Gd.sup.3+, Ca.sup.2+, Zn.sup.2+, and Cu.sup.2+). The reason is that the
 basicities of DTPA and TTDA are stronger than that of DTPA-BMA; therefore,
 the DTPA and TTDA complexes with the metal are more stable and the
 complexes will not be dissociated to form free metal ions. The pM value is
 related to the stability constant of the metal complex. That is to say,
 the larger the stability constant of the metal complex, the smaller the
 free metal ion concentration.
 TABLE 4
 TTDA TTRA TTEA DTPA-BMA DTPA
 logK.sub.ML pM logK.sub.ML pM logK.sub.ML pM logK.sub.ML
 pM logK.sub.ML pM
 Gd.sup.3+ 22.77 17.03 15.89 9.80 -- -- 16.95(6) 13.68
 22.46 17.14
 Ca.sup.2+ 15.45 9.73 13.52 8.20 13.48 7.64 7.72(7) 3.95
 10.75 5.45
 Zn.sup.2+ 18.95 13.22 19.37 13.67 19.91 13.08 12.13(4) 8.86
 18.70 13.39
 Cu.sup.2+ 19.31 13.58 17.92 13.12 17.33 12.63 13.17(2) 9.90
 21.38 16.06
 6. Inner-sphere Water Molecules:
 The chemical shift (d.i.s.) of the Dy(III)-induced .sup.17 O is determined
 by .sup.17 O-NMR. The relationship between the Dy(III) complex
 concentration and d.i.s. is shown in equation (14)
EQU d.i.s.=q.DELTA.[Dy(ligand).sub.n ](H.sub.2 O).sub.q /[H.sub.2 O] (14)
 The slope of equation (14) is q.DELTA./[H.sub.2 O], and q refers to the
 inner-sphere water molecule. In FIG. 11, the slope for [Dy(TTDA)].sup.2-
 is -48.8, and that for DyCl.sub.3 is -445.6. It is known that Dy(III) can
 bind with eight water molecules at low concentration, and q is in a linear
 relationship with the slope. Thus, it can be calculated that q is 0.90 for
 [Dy(TTDA)].sup.2- ; that is to say, [Dy(TTDA)].sup.2- contains one
 inner-sphere water molecule. In the same manner, the q values for
 [Dy(DTPA)].sup.2-, [Dy(DOTA)].sup.-, and [Dy(EDTA)].sup.- are 1.3, 0.8,
 and 2.3 respectively. This indicates that the inner-sphere water molecules
 for [Dy(DTPA)].sup.2- and [Dy(DOTA)].sup.- are only one, which is less
 than that for [Dy(EDTA)].sup.- (2-3 inner-sphere water molecules).
 7. The Effect of pH Value on Relaxivity:
 The relaxivities R.sub.1 for the complexes [Gd(TTDA)].sup.2- and
 [Gd(DTPA-BMA)] at various pH values are given in FIG. 12. The relaxivity
 curve exhibits no pH dependence over the range 4-10. Therefore, no ligand
 dissociation occurred with this pH range and the hydration number remains
 constant. However, in the pH range less than 4.0, R.sub.1 increase with
 the decrease of pH. The reason is that the oxygen atoms on the carboxyl
 groups may be partially protonated, thus the carboxyl groups can not
 coordinate with the gadolinium ion. This increases the inner-sphere water
 molecules on the gadolinium ion, and the R.sub.1 increases.
 The relaxivities (R.sub.1) of various gadolinium complexes at various pH
 are shown in Table 5. It can be found that at pH=6.75, the R.sup.1 of
 [Gd(TTDA)].sup.2- is 3.85; at pH=7.5, the R.sub.1 of [Gd(DTPA)].sup.2- is
 3.71; and at pH=6.3, the R.sup.1 of [Gd(DTPA-BMA)] is 3.74. It can be
 concluded that the R.sub.1 for various gadolinium complexes are similar.
 In addition, it is also found that in the pH range 3-10, the average
 relaxivities for [Gd(TTDA)].sup.2- and [Gd(DTPA-BMA)] are 4.10 and 4.05
 dm.sup.-3 mmol.sup.-1 s.sup.-1, which are similar too. It is found that
 [Gd(DTPA-BMA)] contains one inner-sphere water molecule by the X-ray
 single crystal analysis, and [Dy(TTDA)].sup.2- also contains one
 inner-sphere water molecule by the .sup.17 O-NMR analysis. Since the
 [Gd(TTDA)].sup.2- has the similar structure to [Dy(TTDA)].sup.2-, it can
 be deduced that [Gd(TTDA)].sup.2- contains one inner-sphere water
 molecule. That is why the R.sub.1 of [Gd(TTDA)].sup.2- is similar to those
 of [Gd(DTPA)].sup.2- and [Gd(DTPA-BMA)].
 TABLE 5
 Relaxivity R.sub.1 /
 Complex pH dm.sup.3 mmol.sup.-1 s.sup.-1
 [Gd(DTPA)].sup.2- 7.5 .+-. 0.1 3.71 .+-. 0.05
 [Gd(DTPA-BMA)] 6.3 .+-. 0.1 3.74 .+-. 0.05
 [Gd(TTDA)].sup.2- 6.7 .+-. 0.1 3.85 .+-. 0.03
 Study on Imaging for the Animals
 1-1. Materials and Methods:
 Sodium pentobarbital was injected into the tail veins of 250-350 mg rats
 (which have a healthy liver or tumorous liver) in a dosage of 40-50 mg/kg.
 The rats were placed on the head coil of an 1.5 T magnetic resonance
 imaging instrument. The T1-weighted (TR/Te, 15/6.1 msec) image was
 obtained by turbo field echo with the number of signal average. The field
 of view (FOV), the cross-sectional thickness, and the image matrix were 22
 cm, 4 mm, and 128.times.256 respectively.
 Before injecting the contrast agent, a set of T1-weighted baseline images
 were taken. In the first five minutes, the images were taken at a very
 short time interval in order to evaluate the dynamic enhancement
 condition. Afterwards, the images were taken every 10, 20, 30, 40, 50, and
 60 minutes in order to observe the continuous enhancement effect.
 1-2. Image Analysis:
 By means of the computer software contained in the MRI instrument, the
 region of interest (ROI) can be determined by the operator. The signal
 intensities (SI) of liver, phantom, and kidney were measured. The
 enhancement percentage of an organ (liver or kidney) and the enhancement
 percentage of liver relative to kidney were calculated by the following
 equations. The statistical method used was Wilcoxon Signed Rank Test.
 ##EQU4##
 ##EQU5##
 2. Results and Discussions of Magnetic Resonance Imaging:
 FIG. 13 shows the enhancement(%) of liver and kidney of a healthy rat after
 injecting 0.1 mmol/kg of [Gd(TTDA)].sup.2- versus time. FIG. 14 shows the
 enhancement(%) of liver of a healthy rat after injecting 0.1 mmol/kg of
 [Gd(DTPA)].sup.2- (Magnevist, a commercial MRI contrast agent) versus
 time. FIG. 15 shows the contrast enhancement(%) of liver relative to
 kidney of a healthy rat after injecting 0.1 mmol/kg of [Gd(TTDA)].sup.2-
 versus time.
 As to the [Gd(TTDA)].sup.2- injection, from FIG. 13, it can be seen that
 after the [Gd(TTDA)].sup.2- injection, the liver enhancement increases
 rapidly and reaches 116.+-.17% the maximum within 1 minute after
 injection, and remains the maximum afterwards until 60 minutes after
 injection. The kidney enhancement reaches 300.+-.100% the maximum within 1
 minute after injection, and then decreases gradually. At 60 minutes after
 injection, the kidney enhancement decreases to 76.+-.8%. From FIG. 15, it
 can be seen that the contrast enhancement of liver relative to kidney
 first decreases and then increases. It is 1.47.+-.0.45 before the
 enhancement, decreases to 0.71.+-.0.04 within 1 minute after injection,
 increases to 1 within 5 minutes, and increases to 1.59.+-.0.16 60 minutes
 after injection. FIG. 16 shows the coronal cross-sectional ureter image of
 of the healthy rat after injecting 0.1 mmol/kg of [Gd(TTDA)].sup.2-. It
 can be seen that 3 minutes after injection (FIG. 16(B)), the ureter image
 is enhanced.
 As to the [Gd(DTPA)].sup.2- (commercial MRI contrast agent) injection, from
 FIG. 14, it can be seen that after injecting 0.1 mmol/kg of
 [Gd(DTPA)].sup.2-, the liver enhancement reaches 57.+-.9% the maximum
 within 1 minute and then decreases to 24.+-.7% after 30 minutes. FIG. 17
 shows the coronal cross-sectional kidney image of the healthy rat after
 injecting 0.1 mmol/kg of [Gd(DTPA)].sup.2-. It can be seen that the kideny
 enhancement reaches the maximum at 1 minute after injection and then
 decreases gradually. At 30 minutes after injection, the enhancement
 decreases to 109.+-.14%. From the results of the [Gd(TTDA)].sup.2- and
 [Gd(DTPA)].sup.2- injection, it can be concluded that [Gd(TTDA)].sup.2-
 can be rapidly expelled out of the rat body via the kidney and can provide
 higher liver enhancement effect compared to Gd(DTPA)].sup.2-.
 FIG. 18 shows the axial cross-sectional image of the tumorous liver of the
 rat after injecting 0.1 mmol/kg of [Gd(TTDA)].sup.2- versus time. It shows
 that the tumorous liver enhancement reaches 94.+-.11% the maximum within 1
 minute after injection, and the image remains the maximum enhancement for
 30 minutes. However, the tumorous liver signal is still lower than the
 singal of the adjacent healthy liver, indicating that the tumorous liver
 is negative enhancement relative to the healthy liver.
 In summary, after injecting 0.1 mmol/kg of [Gd(TTDA)].sup.2- to the healthy
 rat, the kidney enhancement reaches the maximum within 1 minute and then
 gradually decreases. The ureter image is enhanced within 3 minutes after
 injection. This indicates that [Gd(TTDA)].sup.2- can be rapidly expelled
 out of the rat body via the kidney. The healthy liver has continuous
 enhancement for 60 minutes, indicating that [Gd(TTDA)].sup.2- has liver
 enhancement effect. The tumorous liver has continuous enhancement for 30
 minutes, and the tumorous liver signal is lower than the signal of the
 adjacent healthy liver, indicating that the tumorous liver is negative
 enhancement relative to the healthy liver. Accordingly, [Gd(TTDA)].sup.2-
 is a potential MRI contrast agent.
 Conclusion
 According to the above, the present invention discusses the protonation
 constants of three DTPA derivative ligands, TTDA, TTRA, and TTEA, the
 stability constants of the metal complexes formed from Gd, Zn, Ca, or Cu
 with the three ligands, the selectivity constants of the organic ligands
 for the gadolinium complex over the calcium, zinc, or copper ion, the
 conditional stability constants of the metal complexes under physiological
 conditions (pH 7.4), the modified selectivity constants of the metal
 complexes, and pM values of the dissociated metal ions. From the
 conditional stability constants, selectivity constants, and modified
 selectivity constants results, it can be seen that [Gd(TTDA)].sup.2- has
 very high stability in the animal body. Finally, the relaxivities R.sup.1
 for the complex [Gd(TTDA)].sup.2- at various pH values are also discussed.
 From the above thermodynamic parameters results, it can be found that
 although [Gd(TTDA)].sup.2- is an ionic complex, its thermodynamic
 stability constant is very close to that of [Gd(DTPA)].sup.2-, a
 commerciallized MRI contrast agent. However, as to the selectivity
 constant and modified selectivity constant which are related to the
 toxicity (LD.sub.50), the selectivity constants of TTDA over zinc and
 copper ions are higher than those of DTPA, and the modified selectivity
 constant of [Gd(TTDA)].sup.2- (logK.sub.sel '=8.44) is higher than that of
 [Gd(DTPA)].sup.2- (logK.sub.sel '=7.04) indicating that the acute toxicity
 of [Gd(TTDA)].sup.2- may be lower than [Gd(DTPA)].sup.2-. In addition, the
 relaxivity of [Gd(TTDA)].sup.2- (R.sub.1 =3.85 dm.sup.3 mmol.sup.-1
 s.sup.-1) is close to that of [Gd(DTPA)].sup.2- (R.sub.1 =3.70 dm.sup.3
 mmol.sup.-1 s.sup.-1). Moreover, the magnetic resonance images also show
 good results. In conclusion, [Gd(TTDA)].sup.2- could make a good MRI
 contrast agent.
 The foregoing description of the preferred embodiments of this invention
 has been presented for purposes of illustration and description. Obvious
 modifications or variations are possible in light of the above teaching.
 The embodiments were chosen and described to provide the best illustration
 of the principles of this invention and its practical application to
 thereby enable those skilled in the art to utilize the invention in
 various embodiments and with various modifications as are suited to the
 particular use contemplated. All such modifications and variations are
 within the scope of the present invention as determined by the appended
 claims when interpreted in accordance with the breadth to which they are
 fairly, legally, and equitably entitled.