Relationship between Perceived Leg Length Discrepancy at One Month and Preoperative Hip Abductor Muscle Elasticity in Patients after Total Hip Arthroplasty.

OBJECTIVE: Preoperative factors related to perceived leg length discrepancy (PLLD) after total hip arthroplasty (THA) are not well studied. This study aimed to examine the preoperative factors, including hip abductor modulus, related to PLLD one month after THA. METHODS: The study included 73 patients diagnosed with osteoarthritis secondary to developmental dysplasia of the hip and a posterior approach to surgery. Multiple logistic regression analysis was performed using the presence or absence of PLLD as the dependent variable and preoperative hip abductor's modulus of elasticity, pain, hip abduction range of motion, hip abductor muscle strength and pelvic obliquity as the independent variable. Additionally, receiver operating characteristic curves were used for the extracted variables for calculating the cutoffs, sensitivity, specificity and area under the curve (AUC) to determine the presence or absence of PLLD. The significance level was set at p<0.05. RESULTS: The hip abductor modulus (odds ratio=1.13; 95% confidence interval=1.06-1.21; p<0.001) was selected as a preoperative factor. The cutoff value to determine the presence or absence of a PLLD was 16.32 kPa. The sensitivity and specificity were 81.8% and 72.5%, respectively, and the AUC was 0.8137. CONCLUSION: The hip abductor muscle elastic modulus affected PLLD one month after THA. If the preoperative hip abductor elastic modulus is higher than the cutoff value, it may affect the appearance of PLLD at one month postoperatively.

Unique circumferential peripheral keratitis in relapsing polychondritis: A case report.

RATIONALE: Relapsing polychondritis (RP) is a rare collagen disease characterized by inflammation and destruction of cartilage throughout the body. The paper details the clinical course of a case of RP with unique circumferential peripheral keratitis. PATIENT CONCERNS: A 54-year-old Japanese woman was referred to the hospital presenting with auricular and ocular pain. DIAGNOSES: Based on the auricle biopsy results and the three presenting symptoms (bilateral auricular chondritis, inflammatory arthritis and ocular inflammation), her condition was diagnosed as RP. INTERVENTIONS: The three presenting symptoms gradually improved with prednisolone (PSL), methylprednisolone and cyclophosphamide combination therapy, followed by PSL, methotrexate and infliximab combination therapy. However, one month after the initial visit, despite ongoing treatment, a unique circumferential peripheral keratitis suddenly occurred, in which the corneal infiltration gradually clumped together and shrank at the peripheral area. The eye and ear pain showed exacerbations and remissions on reducing the dosage of steroid drugs. The general condition was improved on altering systemic therapy to PSL, methotrexate and tocilizumab. OUTCOMES: Keratitis gradually disappeared within 10 months of the initial visit. LESSONS: This is the first report of a case of RP causing unique circumferential peripheral keratitis. This keratitis occurred despite use of focal and systemic steroids and showed improvement with general recovery. This may indicate that stabilization of general condition is important for recovery from keratitis in RP.

Restoration of Photoreceptor Outer Segments up to 24 Months after Pars Plana Vitrectomy in Patients with Diabetic Macular Edema.

PURPOSE: To evaluate the ellipsoid zone (EZ) and external limiting membrane (ELM) status on optical coherence tomography images in patients with diabetic macular edema (DME) before and after pars plana vitrectomy (PPV). DESIGN: Retrospective observational analysis. PARTICIPANTS: Sixty-one eyes of 49 patients with DME. METHODS: We retrospectively reviewed the spectral-domain optical coherence tomography images of 61 eyes of 49 patients with DME who were treated with PPV and evaluated the percentage disruption of the EZ and ELM before and up to 24 months after PPV. MAIN OUTCOME MEASURES: Longitudinal changes in visual acuity (VA), central retinal thickness (CRT), and EZ and ELM spectral-domain optical coherence tomography findings in patients with DME. RESULTS: The logarithm of the minimum angle of resolution VA was 0.477 before PPV and then improved to 0.372 and 0.344 at 12 and 24 months after PPV, respectively (P < 0.005 and P < 0.001, respectively). The CRT was 505.5 µm before PPV and then decreased gradually to 345.0 and 301.4 µm at 12 and 24 months, respectively (P < 0.001 for both). The percentage disruption of the EZ was 29.3% and ELM was 9.6% before PPV and then deteriorated to 41.6% (P < 0.001) and 15.1% (P < 0.05), respectively, 1 month after PPV. The disruption of the EZ and ELM decreased gradually. The percentage disruption of the ELM recovered but did not improve by 24 months, compared with baseline (11.6%; P = 0.875), whereas the percentage disruption of the EZ recovered to baseline by 6 months (29.4%; P = 1.000) and then decreased significantly at 24 months (21.3%; P < 0.05). CONCLUSIONS: Both the EZ and ELM deteriorated after PPV. Whereas the ELM recovered but did not improve by 24 months when compared with baseline, the EZ and VA improved up to 24 months.

Factors affecting health-related quality of life one year after lumbar spinal fusion.

OBJECTIVE: To identify preoperative factors that affect the medical outcome study 36-item short form health survey (SF-36) score 1 year after lumbar spinal fusion. METHODS: Participants were selected from among 624 patients who underwent lumbar spinal fusion between April 1, 2009 and March 31, 2011 who were followed up for 1 year or more. The SF-36 version 2 was used to evaluate HRQOL. The following preoperative parameters were investigated: sex, age, body mass index (BMI), employment status (other than home-making), living with other family members, smoking, orthopedic disorder in another part of the body (other than lumbar spinal disease), history of lumbar spinal surgery, bladder function, and leg muscle strength. RESULTS: 94 patients were included. None of the independent preoperative factors exhibited a high degree of correlation, and the absence of multicollinearity was confirmed before further analysis was performed. The first canonical variates were age and leg muscle strength, which had a major effect on physical functioning, role physical, and role emotional 1 year after surgery, and the second canonical variates were employment status, sex, and orthopedic disorder in another part of the body, which had a major effect on general health 1 year after surgery. CONCLUSIONS: The SF-36 score 1 year after lumbar spinal fusion was affected by the preoperative factors of age, leg muscle strength, living with other family members, employment status, sex, and orthopedic disorders in another part of the body.

Reliability of measurements of hip abduction strength obtained with a hand-held dynamometer.

This study aimed to evaluate intrarater and interrater reliability when measuring hip abductor strength in the supine position using a hand-held dynamometer (HHD) (Study 1), and to elucidate the relationships between measured values and examiners' physical characteristics (Study 2). Three healthy examiners (1 female, 24 y.o. and 2 males 23 and 27 y.o) and 12 subjects (6 females, 24.5 ± 2.8 years and 6 males, 27.7 ± 3.5 years) participated in Study 1, and 20 healthy examiners (7 females, 22.3 ± 1.3 years and 13 males, 29.4 ± 8.2 years) and 2 subjects (1 female, 24 y.o. and 1 male 27 y.o) participated in Study 2. All healthy examiners were hospital employees. Hip abductor strength was measured by HHD with hand fixation and with belt fixation, and examiner age, sex, height, weight, BMI, and dominant hand grip strength were evaluated. The intraclass correlation coefficient (ICC) (1,1), a measure of intrarater reliability, was 0.89-0.95 with hand fixation and 0.96-0.97 with belt fixation. ICC (2,1), a measure of interrater reliability, was 0.76-0.79 and 0.90-0.93, respectively. In subjects with high muscle strength (the examiner's hand was moved), the examiner's dominant hand grip strength affected muscle strength values with hand fixation (standardized partial regression coefficient = 0.78, determination coefficient R(2 )= 0.61, p < 0.01). In subjects with low muscle strength (the examiner's hand was not moved), no variables had effect. When the muscle strength of the subject is weak, both methods can be used. When the muscle strength of the subject is strong, it is necessary to adjust the value obtained by the examiner's dominant hand grip strength in the hand fixation method.

Association between external limiting membrane status and visual acuity in diabetic macular oedema.

AIM: To evaluate the association between the foveal external limiting membrane (ELM) status and visual acuity (VA) in diabetic macular oedema (DMO). METHODS: We retrospectively reviewed the spectral domain optical coherence tomography images of 127 eyes from 127 patients with DMO and evaluated the correlation between the logarithm of the minimal angle of resolution (logMAR) VA and the statuses of the foveal ELM, inner segment/outer segment (IS/OS) and cone outer segment tips (COST); foveal macular thickness (FMT); and presence or absence of hard exudates (HE), serous retinal detachment (SRD) and vitreous adhesion. The integrity of the ELM, IS/OS, and COST was classified into three categories (absent, disrupted and complete). RESULTS: There was a strong correlation between VA and the statuses of the ELM (r=0.699, p<0.001), IS/OS (r=0.716, p<0.001) and COST (r=0.471, p<0.001). There was no correlation between FMT and logMAR VA (r=-0.036, p=0.687). However, when we analysed the correlation between FMT and VA by dividing patients into those with FMT ≤250 µm and those with FMT >250 µm, there was a positive correlation between FMT and VA in eyes with FMT ≤250 µm (r=-0.601, p<0.0001) and a negative correlation in eyes with FMT>250 µm (r=0.290, p<0.01). Other factors HE, SRD and vitreous adhesion did not correlate with VA. CONCLUSIONS: In DMO, the ELM status may be as closely related to VA as the IS/OS status.

What predicts 36-item health survey version 2 after total hip arthroplasty.

OBJECTIVE: To identify the factors having the greatest effect on the Medical Outcomes Study 36-Item Short-Form Health Survey, version 2 (SF-36v2) score after total hip arthroplasty (THA). DESIGN: Retrospective review. SETTING: Private 150-bed hospital. PARTICIPANTS: Patients (N=659) who underwent initial THA for osteoarthritis (OA) of the hip between April 2007 and January 2009. A total of 138 patients who fulfilled the inclusion criteria were seen at the first follow-up, while 108 patients were included in the second follow-up; all 30 patients excluded at the second follow-up underwent contralateral THA between follow-ups. The average time ± SD from surgery to first follow-up was 195.1±67.7 days, and that to second follow-up was 443.0±108.5 days. Patients' average age ± SD was 61.1±9.9 years at first follow-up and 61.3±10.3 years at second follow-up. Women accounted for 85.5% of patients at first follow-up and 85.2% at second follow-up. INTERVENTIONS: Not applicable. MAIN OUTCOME MEASURES: Eight subscales of the SF-36v2, age, sex, body mass index, complications, living alone, contralateral hip OA, range of hip joint motion, walking aids, and preoperative mental health (MH) values from the SF-36v2. RESULTS: Canonical correlation analysis showed that contralateral hip OA had a major effect on the SF-36v2 score at the first follow-up. At the second follow-up, excluding the 30 patients who had undergone contralateral THA, physical function measured by the SF-36v2 was strongly affected by age, and other items were strongly affected by preoperative MH. CONCLUSIONS: When using the SF-36v2 as an assessment scale after THA, adjustments should be made for contralateral hip OA. Moreover, age and preoperative MH should also be considered.

Fourier transform general formula for systematic potentials.

For calculating molecular integrals of systematic potentials, a three-dimensional (3D) Fourier transform general formula can be derived, by the use of the Abel summation method. The present general formula contains all 3D Fourier transform formulas which are well known as Bethe-Salpeter formulas (Bethe and Salpeter, Handbuch der Physik, Bd. XXXV, 1957) as special cases. It is shown that, in several of the Bethe-Salpeter formulas, the integral does not converge in the meaning of the Riemann integral but converges in the meaning of a hyper function as the Schwartz distribution. For showing an effectiveness of the present general formula, the convergence condition of molecular integrals is derived generally for all of the present potentials. It is found that molecular integrals can be converged in the meaning of the Riemann integral for the present potentials, except for those for extra super singular potentials. It is also found that the convergence condition of molecular integrals over the Slater-type orbitals is exactly the same as that of the corresponding integrals over the Gaussian-type orbitals for the present systematic potentials. For showing more effectiveness, the molecular integral over the gauge-including atomic orbitals is derived for the magnetic dipole-same-dipole interaction.

The significance of cone outer segment tips as a prognostic factor in epiretinal membrane surgery.

PURPOSE: To evaluate the prognostic value of the cone outer segment tips (COST) and other features using spectral-domain optical coherence tomography (SD-OCT) in patients undergoing epiretinal membrane (ERM) surgery. DESIGN: Retrospective observational case series. METHODS: Fifty eyes of 49 patients that underwent vitrectomy for idiopathic ERM were studied. Best-corrected visual acuity (BCVA) and SD-OCT images were examined preoperatively and at 1 and 6 months postoperatively. The SD-OCT features evaluated included central foveal thickness (CFT) and the status and defect diameter of the external limiting membrane (ELM), the photoreceptor inner/outer segment (IS/OS) junction, and the COST line. The associations between SD-OCT parameters and BCVA were analyzed. RESULTS: There was no ELM disruption found, and thus the eyes were categorized into 3 groups: Group A, with a continuous IS/OS and COST line; Group B, with a continuous IS/OS but disrupted COST line; and Group C, with a disrupted IS/OS and COST line. At 6 months, Group A showed a significantly better BCVA than Group B (P<.005), and poorer BCVA was noted in Group C (P=.034). Defect diameters of IS/OS and COST line were also significantly correlated with BCVA postoperatively. The BCVA at 6 months was better in order of Group A, B, and C as assigned at baseline (P<.05) or 1 month (P<.001). There was no significant correlation between CFT and BCVA. CONCLUSIONS: The status of the COST line, in conjunction with the IS/OS junction, is a useful prognostic factor after ERM surgery.

Effects of Hura crepitans and its active ingredient, daphne factor F3, on dihydrotestosterone-induced neurotrophin-4 activation and hair retardation.

Neurotrophin (NT)-4 is known to be an inducer of catagen in the hair cycle, but little is known of its role in the pathogenesis of androgenetic alopecia (AGA). We previously studied the gene expression of dermal papilla cells from AGA patients and controls and found that NT-4 was up-regulated in the AGA patients. In the present study, the etiological relationship between NT-4 and androgen, which is one of the causes of AGA, and the effect of an NT-4 inhibitor on hair growth were investigated. We established a NT-4 luciferase reporter assay system using a roughly 2-kb region upstream of the NT-4 transcriptional start site and investigated an accelerating effect of androgen on NT-4 transcription. We also screened for a NT-4 inhibitor by using the NT-4 reporter assay and evaluated the effects of NT-4 inhibitors on hair growth by using dihydrotestosterone (DHT)-implanted mice. The results show that transcriptional activity of NT-4 was accelerated by androgen, and extract of Hura crepitans L. inhibited the DHT-induced NT-4 transcriptional activation and ameliorated the retardation of hair regrowth by DHT-implanted mice. We also isolated the active ingredient in H. crepitans and found its structure to be that of 6,7-epoxy-5-hydroxyresiniferonol-14-(2,4-tetradecadienoate), i.e., daphne factor F3. These findings demonstrated that NT-4 activity accelerated by androgen might contribute to the pathogenesis of AGA and indicated that NT-4 inhibitors such as H. crepitans and daphne factor F3 might have a salutary effect on AGA.

Corneal spherical aberration of eyes with cataract in a Japanese population.

PURPOSE: To investigate the distribution of corneal spherical aberration in Japanese eyes with cataract for implantation of aspheric intraocular lenses (IOLs). METHODS: Corneal spherical aberration (Zernike coefficient Z04) in the central 6-mm zone was measured with a wavefront analyzer (KR9000PW, Topcon) in 257 eyes of 168 Japanese patients with cataract. Axial length was also measured for each eye. RESULTS: Mean corneal spherical aberration was 0.203+/-0.100 microm (range: -0.103 to 0.497 microm). A significant negative correlation was found between axial length and corneal spherical aberration (r =/-0.135, P=.036). CONCLUSIONS: Corneal spherical aberration varied among cataract patients and correlated with axial length. Japanese patients showed a relatively smaller corneal spherical aberration than previous studies of Caucasians. Preoperative measurement of wavefront aberrations is thus important in using aspheric IOLs.

Identification of death-associated protein kinases inhibitors using structure-based virtual screening.

Death-associated protein kinases (DAPKs) function in the early stages of eukaryotic programmed cell death. DAPKs are now emerging as targets for drug discovery in novel therapeutic approaches for ischemic diseases in the brain, heart, kidney, and other organs. Using a structure-based virtual screening approach, we discovered potent and selective DAPKs inhibitors. 6 was found to be the most potent inhibitor with enzyme selectivity (IC(50) = 69 nM for DAPK1).

Isolation of SIP, a protein that interacts with SPB, a possible transcriptional regulatory factor in Rhodobacter sphaeroides.

SPB is a transcriptional factor in Rhodobacter sphaeroides that represses expression of the puf operon under aerobic or semi-aerobic light conditions. Here, we identified a 17,500 Da protein designated SIP (SPB interaction protein) that interacts with SPB, as determined by binding to an SPB-His(x6) fusion protein-Ni column. The SPB-SIP interaction in vivo was confirmed by an immunoprecipitation assay. The level of transcripts and protein of SIP did not differ for all growth conditions tested, indicating that regulation of the SIP-SPB interaction, if any, is not through modulation of sip or spb expression but rather by modification of the proteins.

Role of thrombospondin-1 in T cell response to ocular pigment epithelial cells.

Ocular pigment epithelium (PE) cells promote the generation of T regulators (PE-induced Treg cells). Moreover, T cells exposed to PE acquire the capacity to suppress the activation of bystander T cells via TGFbeta. Membrane-bound TGFbeta on iris PE cells interacts with TGFbeta receptors on T cells, leading to the conversion of T cells to CD8(+) Treg cells via a cell contact-dependent mechanism. Conversely, soluble forms of TGFbeta produced by retinal PE cells can convert CD4(+) T cells into Treg cells in a manner that is independent of cell contact. In this study, we looked at the expression of immunoregulatory factors (TGFbeta, thrombospondins, CD59, IL-1 receptor antagonist, etc.) in PE cells as identified via an oligonucleotide microarray. Several thrombospondin-binding molecules were detected, and thus we focused subsequent analyses on thrombospondins. Via the conversion of latent TGFbeta to an active form that appears to be mediated by thrombospondin 1 (TSP-1), cultured iris PE and retinal PE cells induce a PE-induced Treg cell fate. After conversion, both ocular PE and PE-induced Treg cells express TSP-1. Regulatory T cell generation was amplified when the T cells also expressed TSP-1. In addition, PE-induced Treg cells significantly suppressed activation of bystander T cells via TSP-1. These results strongly suggest that the ability of ocular PE and PE-induced Treg cells to suppress bystander T cells depends on their capacity to produce TSP-1. Thus, intraocular TSP-1 produced by both ocular parenchymal cells and regulatory T cells is essential for immune regulation in the eye.

Fellow eye of patients with retinal detachment associated with macular hole and bilateral high myopia.

PURPOSE: To estimate the risk of retinal detachment in the fellow eye of patients with bilateral high myopia who had retinal detachment associated with macular hole (MH-RD) in one eye. METHODS: The present study examined retrospectively 56 patients with bilateral high myopia who had MH-RD. To determine the incidence of involvement of the fellow eye, patients who completed a follow up of 12 months or longer were eligible for the current study. RESULTS: Of 56 patients with MH-RD due to high myopia, 54 had unilateral detachment at presentation and two had bilateral detachment. Of the 54 highly myopic fellow eyes without retinal detachment at presentation, 37 eyes underwent 12 or more months of documented follow up. Mean follow up after initial surgery to the primary eye was 6.5 +/- 4.9 years. During follow up, a macular hole without retinal detachment was noted in one (2.7%) of these 37 eyes. Three other eyes (8.1%) had MH-RD at 1, 2 and 7 years, respectively, after the initial surgery to the primary eye. At the final visit, 12 eyes (32%) had visual acuity of > or =6/9, whereas 12 eyes (32%) had visual acuity of < or =6/60. CONCLUSIONS: When patients with bilateral high myopia have MH-RD in one eye, they would be expected to be at increased risk of retinal detachment in the fellow eye.

Visual field defect after radial optic neurotomy for central retinal vein occlusion.

PURPOSE: To evaluate visual field defects after radial optic neurotomy (RON) in eyes with central retinal vein occlusion (CRVO). METHODS: Eight patients (eight eyes) underwent RON for macular edema associated with CRVO. Goldmann perimetry was performed on each patient both before and after surgery. RESULTS: Postoperative Goldmann perimetry showed a temporally located wedge-shaped visual field defect consistent with neural damage secondary to RON in seven eyes (88%). After surgery, the visual field decreased from preoperative values by 7% at 3 months (P = 0.30) and by 21% at 12 months (P = 0.0023). Although three patients (38%) were aware of the postoperative visual field defect, only one patient (13%) considered this defect to be a visual disability. CONCLUSIONS: After RON, most patients showed a postoperative defect in the temporal visual field consistent with the incision to the optic disk. However, this visual field defect appears to be well tolerated by most patients.

Immobilization of octadecyl ammonium chloride on the surface of titanium and its effect on microbial colonization in vitro.

The aim of our study was twofold: to immobilize an organosilicon quaternary ammonium salt (3-(trimethoxysilyl)-propyldimethyl-octadecyl ammonium chloride, Si-QAC) on the surface of pure titanium and to investigate the antimicrobial activity of Si-QAC-immobilized titanium against microbial adherence and biofilm formation. The results of ToF-SIMS analysis of Si-QAC-titanium suggested the possibility of immobilizing Si-QAC on titanium surface through Ti-O-Si coupling, and that Si-QAC treatment significantly reduced both the adherence and colonization of Candida albicans and Streptococcus mutans isolates. The antimicrobial activity was achieved through at least two mechanisms: the first was attributed to the octadecyl alkyl chain which inhibited initial adherence, and the second was attributed to the quaternary ammonium salt which killed initial adherent cells as well as retarded or inhibited subsequent microbial growth. Further, thermocycling did not significantly reduce the antimicrobial activity of Si-QAC-titanium, and no significant cytotoxicity of Si-QAC-titanium was observed in either cell viability test or proinflammatory cytokine production test using human gingival fibroblasts. These results, taken together, favorably suggested that Si-QAC treatment would be a helpful means to inhibit dental plaque or denture plaque formation.

Accurate and fast algorithm of the molecular incomplete gamma function with a complex argument.

Several efficient algorithms for the accurate and fast calculation of the molecular incomplete gamma function Fm(z) with a complex argument z are developed. The complex incomplete gamma function is arising in molecular integrals over the gauge-including atomic orbitals. Two kinds of algorithms are recommended: (1) a high-precision version and (2) a fast version. The high-precision version is able to guarantee 15 significant figures (10(-15) in the relative error) and the fast version is able to guarantee 12 significant figures (10(-12) in the relative error), at worst, within the double-precision arithmetic. The fast version is about 5-20 times faster than the high-precision version. For most molecular calculations, the fast version will give a satisfied precision.

Participation of pigment epithelium in ocular immune privilege. 3. Epithelia cultured from iris, ciliary body, and retina suppress T-cell activation by partially non-overlapping mechanisms.

PURPOSE: The ocular microenvironment is immunosuppressive and anti-inflammatory. Since various ocular pigmented epithelia contribute to this microenvironment, we studied the relative capacities of pigment epithelial (PE) cells cultured from the iris, ciliary body, and retina of mouse eyes to suppress T-cell activation in vitro. METHODS: Pigment epithelium was cultured from iris, ciliary body, and retina for 14 days, then assayed for the capacity, directly or across transwell membranes, to suppress mixed lymphocyte reactions and anti-CD3 stimulation of T cells. Potential molecules responsible for suppression were examined by attempting to block suppression with appropriate reagents, and by using mice with pertinent mutant or disrupted genes. RESULTS: We found that PE cells from all three ocular tissue sources profoundly suppressed T-cell activation in vitro. While iris PE suppressed poorly when separated from T cells by a transwell membrane (implying that cell contact is necessary), retina PE suppressed fully even in the presence of such a membrane (implying that soluble factors were responsible). Ciliary body PE used both soluble factors as well as cell contact to achieve suppression. Suppression could not be ascribed to TGFbeta, IFNgamma, TNFalpha, CD48, or ICAM-1, or to interactions between CD40 and CD154, or CD95 and CD95 ligand. Galectin-1, a galactoside-binding protein, was found to be expressed on all cultured PE cells, but only retinal pigment epithelium (RPE) from galectin-1 KO mice showed reduced capacity to inhibit T-cell activation. CONCLUSIONS: Cultured pigment epithelia from iris, ciliary body, and retina comparably suppress T-cell activation in vitro, but by partially different mechanisms. Although RPE cells suppress in part through expression of galectin-1, the molecular mediators of suppression by iris and ciliary body PE remain to be identified.

Molecular integrals over the gauge-including atomic orbitals. II. The Breit-Pauli interaction.

Each accompanying coordinate expansion (ACE) formula is derived for each of the orbit-orbit interaction, the spin-orbit coupling, the spin-spin coupling, and the contact interaction integrals over the gauge-including atomic orbitals (GIAOs) by the use of the solid harmonic gradient (SHG) operator. Each ACE formula is the general formula derived at the first time for each of the above molecular integrals over GIAOs. These molecular integrals are arising in the Breit-Pauli two-electron interaction for a relativistic calculation. We may conclude that we can derive a certain ACE formula for any kind of molecular integral over solid harmonic Gaussian-type orbitals by using the SHG operator. The present ACE formulas will be useful, for example, for a calculation of a molecule in a uniform magnetic field, for a relativistic calculation, and so on, with the GIAO as a basis function.