Subsituted 2-(chroman-6-yloxyl)-thiazoles and their use as pharmaceuticals

Abstract

The present invention relates to substituted 2-(chroman-6-yloxy)-thiazoles of the formula I, in which Ar, R2, R3 and R4 are as defined in the claims. The compounds of the formula I are inhibitors of the sodium-calcium exchanger (NCX), especially of the sodium-calcium exchanger of subtype 1 (NCX1), and are suitable for the treatment of diverse disorders in which intracellular calcium homeostasis is disturbed, such as arrhythmias, heart failure and stroke. The invention furthermore relates to processes for the preparation of the compounds of the formula I, their use as pharmaceuticals, and pharmaceutical compositions comprising them.

We claim: 
     
         1 . A method for inhibiting the sodium-calcium-exchanger (NCX) or for treating heart failure, cardiac arrhythmias, stroke, hypertension, cardiac ischemia, renal failure or shock comprising administering to a patient in need thereof a pharmaceutically effective amount of a compound of formula I, in any of its stereoisomeric forms or a mixture of stereoisomeric forms in any ratio, or a pharmaceutically acceptable salt thereof, 
       
         
           
           
               
               
           
         
         wherein 
         Ar is selected from the series consisting of phenyl and a 5-membered or 6-membered monocyclic aromatic heterocycle, which are all unsubstituted or substituted by one or more identical or different substituents R1, wherein the heterocycle comprises 1 or 2 identical or different ring heteroatoms selected from the series consisting of nitrogen, oxygen and sulfur and is bonded via a ring carbon atom; 
         R1 is selected from the series consisting of halogen, (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl, (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-, phenyl, Het1, HO—, (C 1 -C 6 )-alkyl-O—, (C 3 -C 7 )-cycloalkyl-O—, (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-O—, phenyl-O—, Het1-O— and (C 1 -C 6 )-alkyl-S(O) n —, and two groups R1 bonded to adjacent ring carbon atoms in Ar, together with the carbon atoms carrying them, can form a 5-membered to 7-membered mono-unsaturated ring which comprises 0, 1 or 2 identical or different ring heteroatoms selected from the series consisting of nitrogen, oxygen and sulfur, and which is unsubstituted or substituted by one or more identical or different substituents selected from the series consisting of fluorine and (C 1 -C 4 )-alkyl; 
         R2 is selected from the series consisting of R5-N(R6)-C(O)—, R5-N(R6)-CH 2 —, R7-C(O)—NH—CH 2 — and R7-S(O) 2 —NH—CH 2 —; 
         R3 is selected from the series consisting of hydrogen, halogen, (C 1 -C 4 )-alkyl and (C 1 -C 4 )-alkyl-O—; 
         R4 is hydrogen or one or more identical or different substituents selected from the series consisting of halogen, (C 1 -C 4 )-alkyl and (C 1 -C 4 )-alkyl-O—; 
         R5 and R6 are independently of one another selected from the series consisting of hydrogen, (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl, (C 6 -C 10 )-bicycloalkyl, phenyl, Het1 and Het2, wherein (C 1 -C 6 )-alkyl is unsubstituted or substituted by one or more identical or different substituents R10, and (C 3 -C 7 )-cycloalkyl, (C 6 -C 10 )-bicycloalkyl and Het2 all are unsubstituted or substituted by one or more identical or different substituents R11, 
         or the groups R5 and R6, together with the nitrogen atom carrying them, form a 4-membered to 10-membered, monocyclic or bicyclic, saturated or partially unsaturated heterocycle which, in addition to the nitrogen atom carrying R5 and R6, comprises 0 or 1 further ring heteroatom selected from the series consisting of nitrogen, oxygen and sulfur, and which is unsubstituted or substituted by one or more identical or different substituents R12; 
         R7 is selected from the series consisting of (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl, phenyl, Het2 and Het3, wherein (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl and Het2 all are unsubstituted or substituted by one or more identical or different substituents R10, and phenyl and Het3 all are unsubstituted or substituted by one or more identical or different substituents R13; 
         R10 is selected from the series consisting of R14, fluorine, HO—, oxo, (C 1 -C 6 )-alkyl-O—, R15-C(O)—O—, R15-NH—C(O)—O—, HO—S(O) 2 —O—, (HO) 2 P(O)—O—, (HO) 2 P(O)—O—CH 2 —O—C(O)—O—, (C 1 -C 6 )-alkyl-S(O) n —, R16-N(R17)-, R18-C(O)—N(R17)-, R16-N(R17)-C(O)—, R19-O—C(O)— and R16-N(R17)-S(O) 2 —; 
         R11 and R12 are independently of one another selected from the series consisting of (C 1 -C 4 )-alkyl, HO—(C 1 -C 4 )-alkyl-, R16-N(R17)-(C 1 -C 4 )-alkyl-, R19-O—C(O)—(C 1 -C 4 )-alkyl-, R14, fluorine, HO—, oxo, (C 1 -C 6 )-alkyl-O—, R15-C(O)—O—, R15-NH—C(O)—O—, HO—S(O) 2 —O—, (HO) 2 P(O)—O—, (HO) 2 P(O)—O—CH 2 —O—C(O)—O—, (C 1 -C 6 )-alkyl-S(O) n —, R16-N(R17)-, R18-C(O)—N(R17)-, R16-N(R17)-C(O)—, R19-O—C(O)— and R16-N(R17)-S(O) 2 —; 
         R13 is selected from the series consisting of halogen, (C 1 -C 4 )-alkyl, HO—, (C 1 -C 4 )-alkyl-O— and R16-N(R17)-, and two substituents R13 bonded to adjacent ring carbon atoms in R7, together with the carbon atoms carrying them, can form a 5-membered to 7-membered mono-unsaturated ring which comprises 0, 1 or 2 identical or different ring heteroatoms selected from the series consisting of nitrogen, oxygen and sulfur, and which is unsubstituted or substituted by one or more identical or different substituents selected from the series consisting of fluorine and (C 1 -C 4 )-alkyl; 
         R14 is a 3-membered to 10-membered, monocyclic or bicyclic ring which is saturated, partially unsaturated or aromatic and comprises 0, 1, 2, 3 or 4 identical or different ring heteroatoms selected from the series consisting of nitrogen, oxygen and sulfur, and which is unsubstituted or substituted by one or more identical or different substituents R20; 
         R15 and R18 are independently of one another selected from the series consisting of (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl, (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-, phenyl-(C 1 -C 4 )-alkyl- and Het1-(C 1 -C 4 )-alkyl-; 
         R16 and R17 are independently of one another selected from the series consisting of hydrogen, (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl, (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-, phenyl-(C 1 -C 4 )-alkyl- and Het1-(C 1 -C 4 )-alkyl-, 
         or the groups R16 and R17, together with the nitrogen atom carrying them, form a 4-membered to 7-membered, monocyclic saturated heterocycle which, in addition to the nitrogen atom carrying R16 and R17, comprises 0 or 1 further ring heteroatom selected from the series consisting of nitrogen, oxygen and sulfur, and which is unsubstituted or substituted by one or more identical or different substituents selected from the series consisting of fluorine and (C 1 -C 4 )-alkyl; 
         R19 is selected from the series consisting of hydrogen, (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl, (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-, phenyl-(C 1 -C 4 )-alkyl- and Het1-(C 1 -C 4 )-alkyl-; 
         R20 is selected from the series consisting of halogen, (C 1 -C 4 )-alkyl, HO—(C 1 -C 4 )-alkyl-, (C 3 -C 7 )-cycloalkyl, HO—, oxo, (C 1 -C 6 )-alkyl-O—, R15-C(O)—O—, R15-NH—C(O)—O—, HO—S(O) 2 —O—, (HO) 2 P(O)—O—, (HO) 2 P(O)—O—CH 2 —O—C(O)—O—, (C 1 -C 6 )-alkyl-S(O) n —, R16-N(R17)-, R18-C(O)—N(R17)-, R18-O—C(O)—N(R17)-, NC—, R18-C(O)—, R16-N(R17)-C(O)—, R19-O—C(O)— and R16-N(R17)-S(O) 2 —; 
         Het1 is a 5-membered or 6-membered monocyclic aromatic heterocycle comprising 1 or 2 identical or different ring heteroatoms selected from the series consisting of nitrogen, oxygen and sulfur, which is unsubstituted or substituted by one or more identical or different substituents selected from the series consisting of halogen, (C 1 -C 4 )-alkyl and (C 1 -C 4 )-alkyl-O—; 
         Het2 is a 4-membered to 10-membered monocyclic or bicyclic, saturated or partially unsaturated heterocycle comprising 1 or 2 identical or different ring heteroatoms selected from the series consisting of nitrogen, oxygen and sulfur; 
         Het3 is a 5-membered to 10-membered monocyclic or bicyclic aromatic heterocycle comprising 1 or 2 identical or different ring heteroatoms selected from the series consisting of nitrogen, oxygen and sulfur; 
         n is selected from the series consisting of 0, 1 and 2, wherein all numbers n are independent of one another; 
         wherein all phenyl groups, unless specified otherwise, are unsubstituted or substituted by one or more identical or different substituents selected from the series consisting of halogen, (C 1 -C 4 )-alkyl and —O—(C 1 -C 4 )-alkyl; 
         wherein all cycloalkyl and bicycloalkyl groups, independently of any other substituents which can be present on a cycloalkyl or bicycloalkyl group, can be substituted by one or more identical substituents selected from the series consisting of fluorine and (C 1 -C 4 )-alkyl; 
         wherein all alkyl groups, independently of any other substituents which can be present on an alkyl group, can be substituted by one or more fluorine substituents. 
       
     
     
         2 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, in any of its stereoisomeric forms or a mixture of stereoisomeric forms in any ratio, or a pharmaceutically acceptable salt thereof, wherein
 Ar is selected from the series consisting of phenyl, thiophenyl, pyridinyl and pyrazinyl, which are all unsubstituted or substituted by one or more identical or different substituents R1;   R1 is selected from the series consisting of halogen, (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl, (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-, HO—, (C 1 -C 6 )-alkyl-O—, (C 3 -C 7 )-cycloalkyl-O—, (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-O— and (C 1 -C 6 )-alkyl-S(O) n —;   R2 is selected from the series consisting of R5-N(R6)-C(O)—, R5-N(R6)-CH 2 —, R7-C(O)—NH—CH 2 — and R7-S(O) 2 —NH—CH 2 —;   R3 is selected from the series consisting of hydrogen, halogen and (C 1 -C 4 )-alkyl;   R4 is hydrogen or one or more identical or different substituents selected from the series consisting of halogen and (C 1 -C 4 )-alkyl;   R5 and R6 are independently of one another selected from the series consisting of hydrogen, (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl, (C 6 -C 10 )-bicycloalkyl and Het2, wherein (C 1 -C 6 )-alkyl is unsubstituted or substituted by one or more identical or different substituents R10, and (C 3 -C 7 )-cycloalkyl, (C 6 -C 10 )-bicycloalkyl and Het2 all are unsubstituted or substituted by one or more identical or different substituents R11,   or the groups R5 and R6, together with the nitrogen atom carrying them, form a 4-membered to 10-membered, monocyclic or bicyclic, saturated heterocycle which, in addition to the nitrogen atom carrying R5 and R6, comprises 0 or 1 further ring heteroatom selected from the series consisting of nitrogen, oxygen and sulfur, and which is unsubstituted or substituted by one or more identical or different substituents R12;   R7 is selected from the series consisting of (C 1 -C 6 )-alkyl, Het2 and Het3, wherein (C 1 -C 6 )-alkyl and Het2 all are unsubstituted or substituted by one or more identical or different substituents R10, and Het3 is unsubstituted or substituted by one or more identical or different substituents R13;   R10 is selected from the series consisting of R14, fluorine, HO—, oxo, (C 1 -C 6 )-alkyl-O—, R15-C(O)—O—, R15-NH—C(O)—O—, HO—S(O) 2 —O—, (HO) 2 P(O)—O—, (HO) 2 P(O)—O—CH 2 —O—C(O)—O—, R16-N(R17)-, R18-C(O)—N(R17)-, R16-N(R17)-C(O)— and R19-O—C(O)—;   R11 and R12 are independently of one another selected from the series consisting of (C 1 -C 4 )-alkyl, HO—(C 1 -C 4 )-alkyl-, R16-N(R17)-(C 1 -C 4 )-alkyl-, R19-O—C(O)—(C 1 -C 4 )-alkyl-, fluorine, HO—, oxo, (C 1 -C 6 )-alkyl-O—, R15-C(O)—O—, R15-NH—C(O)—O—, HO—S(O) 2 —O—, (HO) 2 P(O)—O—, (HO) 2 P(O)—O—CH 2 —O—C(O)—O—, R16-N(R17)-, R18-C(O)—N(R17)-, R16-N(R17)-C(O)— and R19-O—C(O)—;   R13 is selected from the series consisting of halogen, (C 1 -C 4 )-alkyl, (C 1 -C 4 )-alkyl-O— and R16-N(R17)-;   R14 is a 3-membered to 10-membered, monocyclic or bicyclic ring which is saturated, partially unsaturated or aromatic and comprises 0, 1, 2 or 3 identical or different ring heteroatoms selected from the series consisting of nitrogen, oxygen and sulfur, and which is unsubstituted or substituted by one or more identical or different substituents R20;   R15 and R18 are independently of one another selected from the series consisting of (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl and (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-;   R16 and R17 are independently of one another selected from the series consisting of hydrogen, (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl and (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-,   or the groups R16 and R17, together with the nitrogen atom carrying them, form a 5-membered to 6-membered, monocyclic saturated heterocycle which, in addition to the nitrogen atom carrying R16 and R17, comprises 0 or 1 further ring heteroatom selected from the series consisting of nitrogen, oxygen and sulfur, and which is unsubstituted or substituted by one or more identical or different substituents selected from the series consisting of fluorine and (C 1 -C 4 )-alkyl;   R19 is selected from the series consisting of hydrogen, (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl and (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-;   R20 is selected from the series consisting of halogen, (C 1 -C 4 )-alkyl, HO—(C 1 -C 4 )-alkyl-, (C 3 -C 7 )-cycloalkyl, HO—, oxo, (C 1 -C 6 )-alkyl-O—, R15-C(O)—O—, R15-NH—C(O)—O—, HO—S(O) 2 —O—, (HO) 2 P(O)—O—, R16-N(R17)- and NC—;   Het2 is a 4-membered to 10-membered monocyclic or bicyclic, saturated or partially unsaturated heterocycle comprising 1 or 2 identical or different ring heteroatoms selected from the series consisting of nitrogen, oxygen and sulfur;   Het3 is a 5-membered to 10-membered monocyclic or bicyclic aromatic heterocycle comprising 1 or 2 identical or different ring heteroatoms selected from the series consisting of nitrogen, oxygen and sulfur;   n is selected from the series consisting of 0, 1 and 2, wherein all numbers n are independent of one another;   wherein all cycloalkyl and bicycloalkyl groups, independently of any other substituents which can be present on a cycloalkyl or bicycloalkyl group, can be substituted by one or more identical substituents selected from the series consisting of fluorine and (C 1 -C 4 )-alkyl;   wherein all alkyl groups, independently of any other substituents which can be present on an alkyl group, can be substituted by one or more fluorine substituents.   
     
     
         3 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, in any of its stereoisomeric forms or a mixture of stereoisomeric forms in any ratio, or a pharmaceutically acceptable salt thereof, wherein
 Ar is selected from the series consisting of phenyl, thiophenyl, pyridinyl and pyrazinyl, which are all unsubstituted or substituted by one or more identical or different substituents R1;   R1 is selected from the series consisting of halogen, (C 1 -C 6 )-alkyl, HO— and (C 1 -C 6 )-alkyl-O—;   R2 is selected from the series consisting of R5-N(R6)-C(O)—, R5-N(R6)-CH 2 —, R7-C(O)—NH—CH 2 — and R7-S(O) 2 —NH—CH 2 —;   R3 is selected from the series consisting of hydrogen, halogen and (C 1 -C 4 )-alkyl;   R4 is hydrogen or one or more identical or different substituents selected from the series consisting of halogen and (C 1 -C 4 )-alkyl;   R5 and R6 are independently of one another selected from the series consisting of hydrogen, (C 1 -C 6 )-alkyl and (C 3 -C 7 )-cycloalkyl, wherein (C 1 -C 6 )-alkyl is unsubstituted or substituted by one or more identical or different substituents R10, and (C 3 -C 7 )-cycloalkyl is unsubstituted or substituted by one or more identical or different substituents R11,   or the groups R5 and R6, together with the nitrogen atom carrying them, form a 4-membered to 10-membered, monocyclic or bicyclic, saturated heterocycle which, in addition to the nitrogen atom carrying R5 and R6, comprises 0 or 1 further ring heteroatom selected from the series consisting of nitrogen and oxygen, and which is unsubstituted or substituted by one or more identical or different substituents R12;   R7 is selected from the series consisting of (C 1 -C 6 )-alkyl and Het3, wherein (C 1 -C 6 )-alkyl is unsubstituted or substituted by one or more identical or different substituents R10, and Het3 is unsubstituted or substituted by one or more identical or different substituents R13;   R10 is selected from the series consisting of R14, fluorine, HO—, oxo, (C 1 -C 6 )-alkyl-O—, R15-C(O)—O—, R15-NH—C(O)—O—, HO—S(O) 2 —O—, (HO) 2 P(O)—O—, (HO) 2 P(O)—O—CH 2 —O—C(O)—O—, R16-N(R17)-, R18-C(O)—N(R17)-, R16-N(R17)-C(O)— and R19-O—C(O)—;   R11 and R12 are independently of one another selected from the series consisting of (C 1 -C 4 )-alkyl, HO—(C 1 -C 4 )-alkyl-, R16-N(R17)-(C 1 -C 4 )-alkyl-, fluorine, HO—, oxo, (C r  C 6 )-alkyl-O—, HO—S(O) 2 —O—, (HO) 2 P(O)—O—, R16-N(R17)- and R18-C(O)—N(R17)-;   R13 is selected from the series consisting of halogen, (C 1 -C 4 )-alkyl, (C 1 -C 4 )-alkyl-O— and R16-N(R17)-;   R14 is a 3-membered to 10-membered, monocyclic or bicyclic ring which is saturated, partially unsaturated or aromatic and comprises 0, 1, 2 or 3 identical or different ring heteroatoms selected from the series consisting of nitrogen, oxygen and sulfur, and which is unsubstituted or substituted by one or more identical or different substituents R20;   R15 and R18 are independently of one another selected from the series consisting of (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl and (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-;   R16 and R17 are independently of one another selected from the series consisting of hydrogen, (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl and (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-,   or the groups R16 and R17, together with the nitrogen atom carrying them, form a 5-membered to 6-membered, monocyclic saturated heterocycle which, in addition to the nitrogen atom carrying R16 and R17, comprises 0 or 1 further ring heteroatom selected from the series consisting of nitrogen, oxygen and sulfur, and which is unsubstituted or substituted by one or more identical or different substituents selected from the series consisting of fluorine and (C 1 -C 4 )-alkyl;   R19 is selected from the series consisting of hydrogen, (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl and (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-;   R20 is selected from the series consisting of halogen, (C 1 -C 4 )-alkyl, HO—(C 1 -C 4 )-alkyl-, (C 3 -C 7 )-cycloalkyl, HO—, oxo, (C 1 -C 6 )-alkyl-O—, R15-C(O)—O—, R15-NH—C(O)—O—, HO—S(O) 2 —O—, (HO) 2 P(O)—O—, R16-N(R17)- and NC—;   Het3 is a 5-membered to 10-membered monocyclic or bicyclic aromatic heterocycle comprising 1 or 2 identical or different ring heteroatoms selected from the series consisting of nitrogen, oxygen and sulfur;   wherein all cycloalkyl groups, independently of any other substituents which can be present on a cycloalkyl group, can be substituted by one or more identical substituents selected from the series consisting of fluorine and (C 1 -C 4 )-alkyl;   wherein all alkyl groups, independently of any other substituents which can be present on an alkyl group, can be substituted by one or more fluorine substituents.   
     
     
         4 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, in any of its stereoisomeric forms or a mixture of stereoisomeric forms in any ratio, or a pharmaceutically acceptable salt thereof, wherein the compound of formula I is a compound of formula Ie, 
       
         
           
           
               
               
           
         
       
     
     
         5 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, in any of its stereoisomeric forms or a mixture of stereoisomeric forms in any ratio, or a pharmaceutically acceptable salt thereof, wherein R2 is selected from the series consisting of R5-N(R6)-C(O)— and R5-N(R6)-CH 2 —. 
     
     
         6 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, in any of its stereoisomeric forms or a mixture of stereoisomeric forms in any ratio, or a pharmaceutically acceptable salt thereof, wherein R2 is selected from the series consisting of R7-C(O)—NH—CH 2 — and R7-S(O) 2 —NH—CH 2 —. 
     
     
         7 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, in any of its stereoisomeric forms or a mixture of stereoisomeric forms in any ratio, or a pharmaceutically acceptable salt thereof, wherein the compound of formula I is a compound of formula Ie, 
       
         
           
           
               
               
           
         
         wherein 
         Ar is phenyl which is unsubstituted or substituted by one or more identical or different substituents R1; 
         R1 is selected from the series consisting of halogen, (C 1 -C 6 )-alkyl, HO— and (C 1 -C 6 )-alkyl-O—; 
         R2 is selected from the series consisting of R5-N(R6)-C(O)— and R5-N(R6)-CH 2 —; 
         R3 is selected from the series consisting of hydrogen, halogen and (C 1 -C 4 )-alkyl; 
         R4 is hydrogen or one or more identical or different substituents selected from the series consisting of halogen and (C 1 -C 4 )-alkyl; 
         one of the groups R5 and R6 is hydrogen and the other of the groups R5 and R6 is selected from the series consisting of (C 1 -C 6 )-alkyl and (C 3 -C 7 )-cycloalkyl, wherein (C 1 -C 6 )-alkyl is unsubstituted or substituted by one or more identical or different substituents R10, and (C 3 -C 7 )-cycloalkyl is unsubstituted or substituted by one or more identical or different substituents R11; 
         R10 is selected from the series consisting of R14, fluorine, HO—, (C 1 -C 6 )-alkyl-O—, R15-C(O)—O—, R15-NH—C(O)—O—, HO—S(O) 2 —O—, (HO) 2 P(O)—O—, (HO) 2 P(O)—O—CH 2 —O—C(O)—O—, R16-N(R17)- and R18-C(O)—N(R17)-; 
         R11 is selected from the series consisting of (C 1 -C 4 )-alkyl, HO—(C 1 -C 4 )-alkyl-, R16-N(R17)-(C 1 -C 4 )-alkyl-, fluorine, HO—, (C 1 -C 6 )-alkyl-O—, HO—S(O) 2 —O—, (HO) 2 P(O)—O—, R16-N(R17)- and R18-C(O)—N(R17)-; 
         R14 is a 3-membered to 10-membered, monocyclic or bicyclic ring which is saturated, partially unsaturated or aromatic and comprises 0, 1, 2 or 3 identical or different ring heteroatoms selected from the series consisting of nitrogen, oxygen and sulfur, and which is unsubstituted or substituted by one or more identical or different substituents R20; 
         R15 and R18 are independently of one another selected from the series consisting of (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl and (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-; 
         R16 and R17 are independently of one another selected from the series consisting of hydrogen, (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl and (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-, 
         or the groups R16 and R17, together with the nitrogen atom carrying them, form a 5-membered to 6-membered, monocyclic saturated heterocycle which, in addition to the nitrogen atom carrying R16 and R17, comprises 0 or 1 further ring heteroatom selected from the series consisting of nitrogen, oxygen and sulfur, and which is unsubstituted or substituted by one or more identical or different substituents selected from the series consisting of fluorine and (C 1 -C 4 )-alkyl; 
         R20 is selected from the series consisting of halogen, (C 1 -C 4 )-alkyl, HO—(C 1 -C 4 )-alkyl-, (C 3 -C 7 )-cycloalkyl, HO—, oxo, (C 1 -C 6 )-alkyl-O—, R15-C(O)—O—, R15-NH—C(O)—O—, HO—S(O) 2 —O—, (HO) 2 P(O)—O—, R16-N(R17)- and NC—; 
         wherein all cycloalkyl groups, independently of any other substituents which can be present on a cycloalkyl group, can be substituted by one or more identical substituents selected from the series consisting of fluorine and (C 1 -C 4 )-alkyl; 
         wherein all alkyl groups, independently of any other substituents which can be present on an alkyl group, can be substituted by one or more fluorine substituents. 
       
     
     
         8 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, in any of its stereoisomeric forms or a mixture of stereoisomeric forms in any ratio, or a pharmaceutically acceptable salt thereof, wherein the compound of formula I is a compound of formula Ie, 
       
         
           
           
               
               
           
         
         wherein 
         Ar is phenyl which is unsubstituted or substituted by one or more identical or different substituents R1; 
         R1 is selected from the series consisting of halogen, (C 1 -C 6 )-alkyl, HO— and (C 1 -C 6 )-alkyl-O—; 
         R2 is selected from the series consisting of R5-N(R6)-C(O)— and R5-N(R6)-CH 2 —; 
         R3 is selected from the series consisting of hydrogen, halogen and (C 1 -C 4 )-alkyl; 
         R4 is hydrogen or one or more identical or different substituents selected from the series consisting of halogen and (C 1 -C 4 )-alkyl; 
         one of the groups R5 and R6 is hydrogen and the other of the groups R5 and R6 is selected from the series consisting of (C 1 -C 6 )-alkyl and (C 3 -C 7 )-cycloalkyl, wherein (C 1 -C 6 )-alkyl is unsubstituted or substituted by one or more identical or different substituents R10, and (C 3 -C 7 )-cycloalkyl is unsubstituted or substituted by one or more identical or different substituents R11; 
         R10 is selected from the series consisting of fluorine, HO—, (C 1 -C 6 )-alkyl-O—, R15-C(O)—O—, R15-NH—C(O)—O—, HO—S(O) 2 —O—, (HO) 2 P(O)—O—, (HO) 2 P(O)—O—CH 2 —O—C(O)—O—, R16-N(R17)- and R18-C(O)—N(R17)-; 
         R11 is selected from the series consisting of (C 1 -C 4 )-alkyl, HO—(C 1 -C 4 )-alkyl-, R16-N(R17)-(C 1 -C 4 )-alkyl-, fluorine, HO—, (C 1 -C 6 )-alkyl-O—, HO—S(O) 2 —O—, (HO) 2 P(O)—O—, R16-N(R17)- and R18-C(O)—N(R17)-; 
         R15 and R18 are independently of one another selected from the series consisting of (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl and (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-; 
         R16 and R17 are independently of one another selected from the series consisting of hydrogen, (C 1 -C 6 )-alkyl, (C 3 -C 7 )-cycloalkyl and (C 3 -C 7 )-cycloalkyl-(C 1 -C 4 )-alkyl-, 
         or the groups R16 and R17, together with the nitrogen atom carrying them, form a 5-membered to 6-membered, monocyclic saturated heterocycle which, in addition to the nitrogen atom carrying R16 and R17, comprises 0 or 1 further ring heteroatom selected from the series consisting of nitrogen, oxygen and sulfur, and which is unsubstituted or substituted by one or more identical or different substituents selected from the series consisting of fluorine and (C 1 -C 4 )-alkyl; 
         wherein all cycloalkyl groups, independently of any other substituents which can be present on a cycloalkyl group, can be substituted by one or more identical substituents selected from the series consisting of fluorine and (C 1 -C 4 )-alkyl; 
         wherein all alkyl groups, independently of any other substituents which can be present on an alkyl group, can be substituted by one or more fluorine substituents. 
       
     
     
         9 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, or a pharmaceutically acceptable salt thereof, wherein the compound of formula I is selected from the series consisting of:
 2-(2-o-Tolyl-chroman-6-yloxy)-thiazole-5-carboxylic acid[2-(2-oxo-imidazolidin-1-yl)-ethyl]-amide,   2-(2-o-Tolyl-chroman-6-yloxy)-thiazole-5-carboxylic acid(2-hydroxy-ethyl)-amide,   2-(2-Phenyl-chroman-6-yloxy)-thiazole-5-carboxylic acid cyclopropylamide,   2-((S)-2-o-Tolyl-chroman-6-yloxy)-thiazole-5-carboxylic acid(2-hydroxy-ethyl)-amide,   2-(2-Oxo-pyrrolidin-1-yl)-N-[2-(2-o-tolyl-chroman-6-yloxy)-thiazol-5-ylmethyl]-acetamide,   Isoxazole-5-carboxylic acid[2-(2-o-tolyl-chroman-6-yloxy)-thiazol-5-ylmethyl]-amide,   2-(2-o-Tolyl-chroman-6-yloxy)-thiazole-5-carboxylic acid propylamide,   4-Methyl-2-(2-o-tolyl-chroman-6-yloxy)-thiazole-5-carboxylic acid(isoxazol-5-ylmethyl)-amide,   2-[2-(5-Fluoro-2-methyl-phenyl)-chroman-6-yloxy]-thiazole-5-carboxylic acid(2-hydroxy-ethyl)-amide,   2-[2-(5-Fluoro-2-methyl-phenyl)-chroman-6-yloxy]-thiazole-5-carboxylic acid propylamide,   Phosphoric acid mono-(2-{[2-((S)-2-o-tolyl-chroman-6-yloxyl)-thiazole-5-carbonyl]-amino}-ethyl)ester,   2-(2-Phenyl-chroman-6-yloxy)-thiazole-5-carboxylic acid(6,7-dihydro-5H-pyrrolo[2,1-c][1,2,4]triazol-3-ylmethyl)-amide,   2-(2-Phenyl-chroman-6-yloxy)-thiazole-5-carboxylic acid propylamide,   2-(2-Phenyl-chroman-6-yloxy)-thiazole-5-carboxylic acid(2-chloro-pyridin-4-ylmethyl)-amide,   2-(2-Phenyl-chroman-6-yloxy)-thiazole-5-carboxylic acid(1,5-dimethyl-1H-pyrazol-4-ylmethyl)-amide,   1,3,5-Trimethyl-1H-pyrazole-4-sulfonic acid[2-(2-phenyl-chroman-6-yloxy)-thiazol-5-ylmethyl]-amide,   2-((R)-2-o-Tolyl-chroman-6-yloxy)-thiazole-5-carboxylic acid(2-hydroxy-ethyl)-amide, and   [2-(2-Phenyl-chroman-6-yloxy)-thiazol-5-ylmethyl]-pyridin-4-ylmethyl-amine.   
     
     
         10 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, in any of its stereoisomeric forms or a mixture of stereoisomeric forms in any ratio, wherein the compound of formula I is 2-(2-o-tolyl-chroman-6-yloxy)-thiazole-5-carboxylic acid(2-hydroxy-ethyl)-amide. 
     
     
         11 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, wherein the compound of formula I is 2-((S)-2-o-tolyl-chroman-6-yloxy)-thiazole-5-carboxylic acid(2-hydroxy-ethyl)-amide. 
     
     
         12 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, in any of its stereoisomeric forms or a mixture of stereoisomeric forms in any ratio, or a pharmaceutically acceptable salt thereof, wherein the compound of formula I is isoxazole-5-carboxylic acid[2-(2-o-tolyl-chroman-6-yloxy)-thiazol-5-ylmethyl]-amide. 
     
     
         13 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, in any of its stereoisomeric forms or a mixture of stereoisomeric forms in any ratio, wherein the compound of formula I is 2-(2-o-tolyl-chroman-6-yloxy)-thiazole-5-carboxylic acid propylamide. 
     
     
         14 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, in any of its stereoisomeric forms or a mixture of stereoisomeric forms in any ratio, wherein the compound of formula I is 2-[2-(5-fluoro-2-methyl-phenyl)-chroman-6-yloxy]-thiazole-5-carboxylic acid(2-hydroxy-ethyl)-amide. 
     
     
         15 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, or a pharmaceutically acceptable salt thereof, wherein the compound of formula I is phosphoric acid mono-(2-{[2-((S)-2-o-tolyl-chroman-6-yloxy)-thiazole-5-carbonyl]-amino}-ethyl)ester. 
     
     
         16 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of the compound of formula I, wherein the compound of formula I is 2-((R)-2-o-tolyl-chroman-6-yloxy)-thiazole-5-carboxylic acid(2-hydroxy-ethyl)-amide. 
     
     
         17 . The method according to  claim 1 , comprising administering to the patient in need thereof a pharmaceutically effective amount of phosphoric acid mono-(2-{[2-((S)-2-o-tolyl-chroman-6-yloxyl)-thiazole-5-carbonyl]-amino}-ethyl)ester disodium salt. 
     
     
         18 . The method according to  claim 1  for treating heart failure. 
     
     
         19 . The method according to  claim 1  for treating cardiac arrhythmias. 
     
     
         20 . The method according to  claim 18 , wherein the heart failure is acute congestive heart failure. 
     
     
         21 . The method according to  claim 18 , wherein the heart failure is chronic congestive heart failure. 
     
     
         22 . The method according to  claim 19 , wherein the cardiac arrhythmias is atrial fibrillation.