Changes of Biogenic Amines and Their Metabolites in Postmortem Brains from Patients with Alzheimer-Type Dementia

Noradrenaline (NA), 3,4-dihydroxyphenylethylamine (dopamine, DA), 5-hydroxytryptamine (serotonin, 5-HT), homovanillic acid (HVA), and 5-hydroxyindoleacetic acid (5-HIAA) were measured in 22 regions of postmortem brains from four histologically verified cases with Alzheimer-type dementia (ATD) and nine histologically normal controls. Compared with the controls, concentrations of 5-HT and 5-HIAA in the ATD brains were significantly reduced in nine regions (superior frontal gyrus, insula, cingulate gyrus, amygdala, putamen, medial and lateral segments of globus pallidus, substantia nigra, lateral nucleus of thalamus) and in eight regions (amygdala, substantia innominata, caudate, putamen, medial and lateral segments of globus pallidus, medial and lateral nuclei of thalamus), respectively. NA concentrations of the ATD brains were significantly reduced in six regions (cingulate gyrus, substantia innominata, putamen, hypothalamus, medial nucleus of thalamus, raphe area). In contrast, significant reductions of DA and HVA concentrations in the ATD brains were found only in putamen and amygdala, respectively. The 5-HIAA/5-HT ratio in the ATD brains decreased significantly in locus coeruleus, while the HVA/DA ratio increased significantly in putamen and medial segment of globus pallidus. These findings suggest that the serotonergic and noradrenergic systems are affected, while the dopaminergic system is relatively unaffected in ATD brains.     

Role of Monoamine Oxidase Type A and B on the Dopamine Metabolism in Discrete Regions of the Primate Brain

The role of monoamine oxidase (MAO) type A and B on the metabolism of dopamine (DA) in discrete regions of the monkey brain was studied. Monkeys were administered (–)-deprenyl (0.25 mg/kg) or clorgyline (1.0 mg/kg) or deprenyl and clorgyline together by intramuscular injections for 8 days. Levels of DA and its metabolites, dihydroxy phenylacetic acid (DOPAC) and homovanillic acid (HVA) were estimated in frontal cortex (FC), motor cortex (MC), occipital cortex (OC), entorhinal cortex (EC), hippocampus (HI), hypothalamus (HY), caudate nucleus (CN), globus pallidus (GP) and substantia nigra (SN). (–)-Deprenyl administration significantly increased DA levels in FC, HY, CN, GP and SN (39–87%). This was accompanied by a reduction in the levels of DOPAC (37–66%) and HVA (27–79%). Clorgyline administration resulted in MAO-A inhibition by more than 87% but failed to increase DA levels in any of the brain regions studied. Combined treatment of (–)-deprenyl and clorgyline inhibited both types of MAO by more than 90% and DA levels were increased (57–245%) in all brain regions studied with a corresponding decrease in the DOPAC (49–83%) and HVA (54–88%) levels. Our results suggest that DA is metabolized preferentially, if not exclusively by MAO-B in some regions of the monkey brain.     

Globus pallidus: a target brain region for divalent metal accumulation associated with dietary iron deficiency

Recently, iron deficiency has been connected with a heterogeneous accumulation of manganese in the rat brain. The striatum is particularly vulnerable, for there is a significant negative correlation between accumulated manganese and gamma-aminobutyric acid levels. The effect of dietary iron deficiency on the distribution of zinc and copper, two other divalent metals with essential neurobiological roles, is relatively unexplored. Thus, the primary goal of this study was to examine the effect of manipulating dietary iron and manganese levels on the concentrations of copper, iron, manganese and zinc in five rat brain regions as determined with inductively coupled plasma mass spectrometry analysis. Because divalent metal transporter has been implicated as a transporter of brain iron, manganese, and to a lesser extent zinc and copper, another goal of the study was to measure brain regional changes in transporter levels using Western blot analysis. As expected, there was a significant effect of iron deficiency (P < 0.05) on decreasing iron concentrations in the cerebellum and caudate putamen; and increasing manganese concentrations in caudate putamen, globus pallidus and substantia nigra. Furthermore, there was a significant effect of iron deficiency (P < 0.05) on increasing zinc concentration and a statistical trend (P = 0.08) toward iron deficiency-induced copper accumulation in the globus pallidus. Transporter protein in all five regions increased due to iron deficiency compared to control levels (P < 0.05); however, the globus pallidus and substantia nigra revealed the greatest increase. Therefore, the globus pallidus appears to be a target for divalent metal accumulation that is associated with dietary iron deficiency, potentially caused by increased transporter protein levels.     

Differential Changes in the Content of Amino Acid Neurotransmitters in Discrete Regions of the Rat Brain Prior to the Onset and During the Course of Homocysteine-Induced Seizures

Changes in amino acid concentrations were investigated in selected regions of rat brain prior to the onset and during the course of epileptiform seizures induced by L-homocysteine. The concentration of gamma-aminobutyric acid (GABA) decreased preictally in substantia nigra (-18%), caudate putamen (-26%), and inferior colliculus (-46%). After seizure onset, the GABA content was further reduced in substantia nigra (-31%) and additionally in hippocampus (-18%). Preictal taurine levels were elevated in globus pallidus (+26%) and caudate putamen (+13%) but returned to normal after seizure onset. However, in hippocampus, taurine decreased both preictally (-22%) and after seizure onset (-56%). Glycine was reduced preictally only in globus pallidus (-13%). After seizure onset the direction of its concentration change varied in the brain regions studied. Glutamate levels decreased preictally in hippocampus (-10%) and hypothalamus (-46%) but increased in globus pallidus (+14%). Normal levels were detectable after seizure onset in hypothalamus and globus pallidus but a further reduction in hippocampus (-59%) and significant reductions in substantia nigra (-15%) and caudate putamen (-17%) were detected. Aspartate was elevated in hippocampus, both preictally (+49%) and after seizure onset (+21%) while at the same phases in globus pallidus a consistent reduction (-30%) was observed. The glutamine content increased preictally in globus pallidus (+41%) and hypothalamus (+36%), and in all brain areas during the ictal phase of seizure, the hippocampus exhibiting a dramatic increase (approximately 300%). The contents of serine and alanine were altered in most regions studied only after seizure onset, with the exception of the hippocampus, where a decrease (-41%) of serine was observed preictally.     

Distribution of the Two Forms of Monoamine Oxidase Within Monoaminergic Neurons of the Guinea Pig Brain

The relative distribution of type A and type B monoamine oxidase (MAO) inside and outside the monoaminergic synaptosomes in preparations from hypothalamus and striatum of the guinea pig was determined by incubation of synaptosomal preparations of these regions with low concentrations of [14C]5-hydroxytryptamine (5-HT), noradrenaline, and dopamine. The deamination within the monoaminergic synaptosomes was hindered by selective amine uptake inhibitors. In the absence of these inhibitors, both intra- and extraneuronal deamination was measured. The two forms of the enzyme were differentiated with the irreversible and selective MAO-A and MAO-B inhibitors clorgyline and selegiline (l-deprenyl), respectively. [14C]5-HT was deaminated greater than 90% by MAO-A both inside and outside the 5-hydroxytryptaminergic synaptosomes prepared from the guinea pig hypothalamus. The deamination of [14C]noradrenaline within the noradrenergic synaptosomes of the hypothalamic preparation was in the ratio 75:25% for MAO-A:MAO-B; the corresponding ratio outside these synaptosomes was 45:55%. The deamination of [14C]dopamine within dopaminergic synaptosomes in the striatal preparation was 65% type A:35% type B, whereas outside these synaptosomes the ratio was 35:65%. Because the relative amounts and the distribution of the two forms of MAO in the guinea pig brain seem to be similar to those previously detected for the human brain, the MAO in the guinea pig brain may be a good model for the MAO in the human brain.     

Regional distribution of enkephalinase in the rat brain by autoradiography

The first visualization of enkephalinase (neutral metalloendopeptidase, E.C.3.4.24.11) in rat brain was obtained by autoradiography, using a new tritiated inhibitor: [3H]N-[( R,S )3-(N-hydroxy) carboxamido-2-benzyl propanoyl]glycine (3H-HCBP-Gly). The preliminary analysis of sections clearly showed a discrete localization of enkephalinase in enkephalin enriched regions, such as caudate nucleus, putamen, globus pallidus, and substantia nigra. Moreover 3H-HCBP-Gly binding also occurred in choroid plexus and spinal cord.     

Inhibition of MAO-B by (−)-deprenyl alters dopamine metabolism in the macaque (Macaca facicularis) brain

The present study has examined whether MAO-B has a role in DA metabolism in the primate CNS in situ. Eleven macaques (macaca facicularis) were used in this study to examine the effects of (-)-deprenyl (1 mg/kg, i.v., 2 and 24 hours). (-)-Deprenyl administration completely and selectively blocked MAO-B activity and blocked DA metabolism in the caudate nucleus and frontal cortex. DA metabolism in the substantia nigra was not affected by MAO-B inhibition. Changes in DA metabolism were accompanied by changes in 5-hydroxytryptamine (5HT) turnover: 5-hydroxyindole acetic acid (5HIAA) levels increased in the caudate and decreased in the frontal cortex. Levels of 2-phenylethylamine (PE), a putative modulator of dopaminergic transmission, were increased by MAO-B inhibition in all three brain regions examined. It is concluded that in some regions of the primate brain, in contrast to the rat, MAO-B has an important role in DA metabolism.     

In vivo release of transmitters in the cat basal ganglia

The release of transmitters was studied in various structures of the basal ganglia in cats implanted with several push-pull cannulas. Local depolarization enhanced Met-enkephalin release in the globus pallidus. Activation of striatonigral substance P(SP) neutrons stimulated the transmitter release from terminals. Unilateral electrical stimulation of the caudate nucleus evoked GABA release in both substantia nigrae and pallidoentopeduncular nuclei. The unilateral facilitation or interruption of nigral SP transmission modified dopamine (DA) release in the ipsilateral caudate nucleus in contrast, modifications of GABAergic or glycinergic nigral transmissions induced bilateral symmetrical effects, whereas bilateral asymmetrical changes in DA release in the two caudate nuclei were seen during the unilateral modification of nigral DA transmission. Changes in the dendritic release of DA induced changes in serotonin release both in the substantia nigra and in the ipsilateral caudate nucleus. Finally, it will be shown that acetylcholinesterase can be released from the substantia nigra and the caudate nucleus through processes dependent on nerve activity.     

Differential Transmitter Release from Nerve Terminals Isolated from Basal Ganglia and Substantia Nigra

Abstract: The K⁺-induced release of amino acids and dopamine from synaptosomes of basal ganglia and substantia nigra of sheep was studied. K⁺ (56 mM) caused an increase in the release of GABA from caudate, putamen, globus pallidus, and substantia nigra, the increased release being 227, 171, 198, and 366%, respectively, compared with samples incubated without stimulation. The release of glutamate was also increased by 56 mM-K⁺ (136–183%) from all regions except the globus pallidus, and a significant release of aspartate was only seen in response to K⁺ stimulation of synaptosomes from putamen (50%). Veratrine (75 μM) also stimulated a similar pattern of amino acid release from these regions. Regional correlation was shown between the presence of an uptake system for an amino acid and its evoked release. [¹⁴C]Dopamine formed from L-[U-¹⁴C]tyrosine was released only from caudate and putamen synaptosomes by K⁺ stimulation, the increases being 105% and 74%, respectively. Synthesis of [¹⁴C]dopamine from L-[U-¹⁴C]tyrosine occurred only in synaptosomes prepared from these two regions and was not detected in synaptosomes from substantia nigra or globus pallidus although whole-tissue homogenates of substantia nigra were able to synthesise dopamine.     

Role of monoamine oxidase-B in medroxyprogesterone acetate (17-acetoxy-6 alpha-methyl-4-pregnene-3, 20-dione) induced changes in brain dopamine levels of rats

The effect of medroxyprogesterone acetate (MPA) on brain monoamine levels and monoamine oxidase (MAO) activity was studied in adult, healthy, non-pregnant female rats. MpA was injected in a single dose of 100 mg/kg i.m. Dopamine (DA), noradrenaline (NA), 5-hydroxytryptamine (5-HT) levels and MAO activity were estimated fluorometrically in rat brian. No change in DA, NA, 5-HT or MAO activity was observed after 7 days of MPA treatment while a significant decrease in DA levels along with a significant increase in MAO activity was observed after 21 days of MPA treatment. However, there was no change in NA and 5-HT levels after 21 days of MPA administration. The selective reduction of DA by MPA could be due to an increase in MAO-B activity. MPA does not appear to increase MAO-A activity because neither of the specific substrates (NA and 5-HT) of MAO-A was found to be decreased inspite of the increase in MAO activity as estimated by the kynuramine method. These findings suggest the importance of MAO-B also in DA metabolism in rat brain.     

Increased Nigral Iron Content and Alterations in Other Metal Ions Occurring in Brain in Parkinson's Disease

Levels of iron, copper, zinc, manganese, and lead were measured by inductively coupled plasma spectroscopy in parkinsonian and age-matched control brain tissue. There was 31-35% increase in the total iron content of the parkinsonian substantia nigra when compared to control tissue. In contrast, in the globus pallidus total iron levels were decreased by 29% in Parkinson's disease. There was no change in the total iron levels in any other region of the parkinsonian brain. Total copper levels were reduced by 34-45% in the substantia nigra in Parkinson's disease; no difference was found in the other brain areas examined. Zinc levels were increased in substantia nigra in Parkinson's disease by 50-54%, and the zinc content of the caudate nucleus and lateral putamen was also raised by 18-35%. Levels of manganese and lead were unchanged in all areas of the parkinsonian brain studied when compared to control brains, except for a small decrease (20%) in manganese content of the medial putamen. Increased levels of total iron in the substantia nigra may cause the excessive formation of toxic oxygen radicals, leading to dopamine cell death.     

Brain Dialysis: In Vivo Metabolism of Dopamine and Serotonin by Monoamine Oxidase A but Not B in the Striatum of Unrestrained Rats

A dialysis cannula was implanted into rat striatum while the animals were anesthetized, and the area was perfused with Ringer solution while the animals were unanesthetized after at least 3 days following surgery. Concentrations of the metabolites of 3,4-dihydroxyphenylethylamine (DA) and 5-hydroxytryptamine (5-HT) in the perfusate were determined by HPLC with electrochemical detection. Levels of the DA metabolites 3,4-dihydroxyphenylacetic acid (DOPAC) and homovanillic acid (HVA) in the perfusate significantly decreased after pargyline administration (50 mg/kg i.p.), which may inhibit not only monoamine oxidase (MAO)-B but also MAO-A in these high doses. The level of the 5-HT metabolite 5-hydroxyindoleacetic acid (5-HIAA) also decreased after pargyline treatment, although change in the relative level of 5-HIAA was less than that of DOPAC or HVA. To clarify the mechanisms for the metabolism of monoamines in rat striatum, highly specific MAO-A and -B inhibitors were used in the following experiments. Treatment with l-deprenyl (10 mg/kg), a specific inhibitor for MAO-B, did not cause any statistically significant change in DOPAC, HVA, and 5-HIAA levels. No significant change was found in rat striatal homogenates at 2 h after the same treatment with l-deprenyl. In contrast, low-dose treatment (1 mg/kg) with clorgyline, a specific inhibitor for MAO-A, caused a significant decrease in levels of these three metabolites in both the perfusates and tissue homogenates. In addition to the above three metabolites, the level of 3-methoxytyramine, which is an indicator of the amount of DA released, greatly increased after treatment with a low dose (1 mg/kg) of clorgyline.(ABSTRACT TRUNCATED AT 250 WORDS)     

Susceptibility-Weighted Imaging Manifestations in the Brain of Wilson’s Disease Patients

Purpose

It is well known that patients with Wilson’s disease (WD) suffer copper metabolism disorder. However, recent studies point to an additional iron metabolism disorder in WD patients. The purpose of our study was to examine susceptibility-weighted imaging (SWI) manifestations of WD in the brains of WD patients.

Methods

A total of 33 patients with WD and 18 normal controls underwent conventional MRI (Magnetic resonance imaging) and SWI. The phase values were measured on SWI-filtered phase images of the bilateral head of the caudate nuclei, globus pallidus, putamen, thalamus, substantia nigra, and red nucleus. Student’s t-tests were used to compare the phase values between WD groups and normal controls.

Results

The mean phase values for the bilateral head of the caudate nuclei, globus pallidus, putamen, thalamus, substantia nigra, and red nucleus were significantly lower than those in the control group (P < 0.001), and bilateral putamen was most strongly affected.

Conclusions

There is paramagnetic mineralization deposition in brain gray nuclei of WD patients and SWI is an effective method to evaluate these structures.     

Manganese accumulates in iron-deficient rat brain regions in a heterogeneous fashion and is associated with neurochemical alterations

Previous studies have shown that iron deficiency (ID) increases brain manganese (Mn), but specific regional changes have not been addressed. Weanling rats were fed one of three semipurified diets: control (CN), iron deficient (ID), or iron deficient/manganese fortified (IDMn+). Seven brain regions were analyzed for Mn concentration and amino acid (glutamate, glutamine, taurine, γ-aminobutyric acid) concentrations. Both ID and IDMn+ diets caused significant (p<0.05) increases in Mn concentration across brain regions compared to CN. The hippocampus was the only brain region in which the IDMn+ group accumulated significantly more Mn than both the CN and ID groups. ID significantly decreased GABA concentration in hippocampus, caudate putamen, and globus pallidus compared to CN rats. Taurine was significantly increased in the substantia nigra of the IDMn+ group compared to both ID and CN. ID also altered glutamate and glutamine concentrations in cortex, caudate putamen, and thalamus compared to CN. In the substantia nigra, Mn concentration positively correlated with increased taurine concentration, whereas in caudate putamen, Mn concentration negatively correlated with decreased GABA. These data show that ID is a significant risk factor for central nervous system Mn accumulation and that some of the neurochemical alterations associated with ID are specifically attributable to Mn accumulation.     

The regional distribution of dopamine and serotonin uptake and transmitter concentrations in the human brain

The regional distribution of the dopamine and serotonin uptake sites in human brain have been assessed and compared with the distribution of the transmitters and their metabolites measured in the same brains and also with a limited regional distribution of the uptake sites in rat and sheep brain. The affinity of the uptake sites for both transmitters was determined and found to be c. 0.2 μ M in all 3 species. Most dopamine uptake in all species was in caudate and putamen samples. Many regions of the human brain showed no dopamine uptake and little dopamine uptake was seen in sheep cortex or nigral preparations. Dopamine and metabolite concentrations were highest in the caudate, putamen and substantia nigra. Most serotonin uptake was seen in the hypothalamus in all 3 species; less was observed in the striatal regions; the cortical and nigral preparations of sheep brain showed little serotonin uptake though cortical preparations of rat brain had high levels of uptake. In the human brain, other regions did not show serotonin uptake. Highest concentrations of serotonin were found in the substantia nigra and medulla, intermediate concentrations in the putamen, globus pallidus, hypothalamus, olfactory tubercle and thalamus; very low concentrations of serotonin were found in other regions. The use of the human uptake site for pharmacological studies and as a marker for monoaminergic afferents in human health and disease is discussed.     

Effects of Chronic Ethanol Consumption and Aging on Dopamine, Serotonin, and Metabolites

Abstract: This study examined the hypothesis that chronic ethanol consumption results in significant abnormalities in both the dopaminergic and the serotonergic system of aged rats. Levels of dopamine (DA), serotonin [5-hydroxytryptamine (5-HT)], 3,4-dihydroxyphenylacetic acid (DOPAC), and 5-hydroxyindole-3-acetic acid (5-HIAA) were determined in brain areas of both the nigrostriatal and mesocorticolimbic DA systems in 5-, 14-, and 24-month-old male Fischer 344 rats. Aging was associated with a reduced concentration of DA in the striatum (ST), ventral tegmental area (VTA), and ventral pallidum (VP) and an increased concentration of 5-HIAA in the ST, globus pallidus, nucleus accumbens, frontal cortex, and VP. In addition, there was an increase in the 5-HIAA/5-HT ratio in all brain areas analyzed. Six weeks of ethanol consumption was accompanied by significant changes in mesocorticolimbic brain areas. In the VTA of 5-month-old ethanol-fed rats DA content was decreased to the levels found in aged rats, e.g., 24 months of age. Ethanol also significantly lowered 5-HT and 5-HIAA contents in the VTA and reduced DOPAC and 5-HIAA levels in the VP. In addition, ethanol blunted the normal age-related increase in 5-HIAA/5-HT ratio in the VTA, VP, and substantia nigra. It is interesting that although the age-related changes were found in both nigrostriatal and mesocorticolimbic brain areas, the ethanol-associated effects were found only in brain areas of the mesocorticolimbic system. The changes in DA and 5-HT function that accompany aging and ethanol consumption may contribute to the problems in motor function and ethanol abuse found in the aged.     

Decreased Proline Endopeptidase Activity in the Basal Ganglia in Huntington''s Disease

Soluble proline endopeptidase (EC 3.4.21.26) activity was measured by a fluorometric assay in eight human brain areas (caudate nucleus, lateral globus pallidus, medial globus pallidus, substantia nigra-zona compacta, substantia nigra-zona reticulata, frontal cortex-Brodmann area 10, temporal cortex-Brodmann area 38, and hippocampus), in 10 control and 10 Huntington's disease brains. An abnormally low activity (22% of control activity) was found in the caudate nucleus of Huntington's disease brains; significantly decreased activity was also detected in the lateral globus pallidus and medial globus pallidus (37% and 40% of control, respectively).     

Neuroprotection by bioactive components in medicinal and food plant extracts

Neurodegenerative diseases of the human brain comprise a variety of disorders that affect an increasing percentage of the population. Some of these are age dependent (e.g. Alzheimer's and Parkinson's diseases) and some are infection dependent, e.g. human immunodeficiency virus (HIV/AIDS). The vulnerable brain regions in HIV/AIDS individuals include the dentate nucleus in the cerebellum, the red nucleus, substantia nigra (SN) in the mid-brain, the subthalamic nucleus, thalamic fasciculus in the diencephalons, the globus pallidus and striatum (or neostriatum, which consists of caudate and putamen) in the forebrain. Lesion in these regions may lead to progressive dementia, which is similar to what is observed in Alzheimer's disease and Parkinson's disease. The entry of calcium into the cytoplasm of cells at concentrations that can activate oxidative enzymes such as phospholipase A(2) and xanthine oxidase, deplete cells of cysteine and glutathione, cause mitochondrial release of free radicals and cell death. Glutamate and its receptors are key molecular elements at the interface between neurons and glia. Dietary factors can modulate physiological functions (including brain function) thereby increasing the economic productivity of a population as a function of health. A greater understanding of the molecular mechanisms of neuroprotection, oxidative stress and immune function will facilitate definition of the prophylactic potentials of diet, nutritional/food supplements, medicinal plants and herbal extracts.     

Behavioral and biochemical assessment of time-related changes in globus pallidus and striatal dopamine induced by intranigrally administered neurotensin

Microinjection of neurotensin (NT; 2 and 5 μg) into the substantia nigra zona compacta caused an increase in dopamine (DA) and DA metabolites in the rodent globus pallidus and striatum which persisted for at least 20 hours after peptide administration. Similar NT treatments given unilaterally into the nigra caused circling away from the injected side in amphetamine-pretreated rats, but were without effect when microinjected into saline-pretreated animals. Circling also occurred when the animals were given amphetamine 20 hours after intranigral NT administration. Contralateral rotation was observed with unilateral intranigral injections of gamma-hydroxybutyric acid (GHB; 400 μg) or with lower intranigral GHB doses (250 μg) in amphetamine-pretreated animals. The effects of GHB and NT differed in the manner in which the animals rotated as well as in the profile of DA and DA metabolite changes induced by these drugs. These studies indicated that: (1) dopaminergic functions of the globus pallidus are influenced, like the striatum, by manipulations of the substantia nigra; (2) NT and GHB likely act via different mechanisms to effect nigral dopamine-containing cells; and (3) NT was capable of inducing changes in dopamine neurons which had long term consequences.     

磁敏感加权成像在帕金森病中的应用研究

目的:探索帕金森病(PD)的磁敏感加权成像(SWI)的表现。方法:34例帕金森病患者作为病例组和30例正常人作为对照组,采用GE1.5T磁共振成像系统,行常规的快速自旋回波T1、T2加权像后,加扫三维磁敏感加权成像覆盖基底节区及中脑。使用SWI后处理软件在校正相位图上两次测量双侧尾状核头、苍白球、壳核、黑质、红核的相位值,最终的相位值取两次测量的平均值。结果:病例组患者黑质、壳核的相位值较对照组明显降低,差异具有统计学意义(P<0.05),PD患者黑质及壳核铁沉积增加。病例组壳核的相位值与PD病程之间存在负相关。对照组中尾状核头、壳核、黑质相位值左侧低于右侧。结论:SWI是显示PD患者脑内铁沉积的有效的检查方法。