Quantum Coherence and Ergotropy.

Constraints on work extraction are fundamental to our operational understanding of the thermodynamics of both classical and quantum systems. In the quantum setting, finite-time control operations typically generate coherence in the instantaneous energy eigenbasis of the dynamical system. Thermodynamic cycles can, in principle, be designed to extract work from this nonequilibrium resource. Here, we isolate and study the quantum coherent component to the work yield in such protocols. Specifically, we identify a coherent contribution to the ergotropy (the maximum amount of unitarily extractable work via cyclical variation of Hamiltonian parameters). We show this by dividing the optimal transformation into an incoherent operation and a coherence extraction cycle. We obtain bounds for both the coherent and incoherent parts of the extractable work and discuss their saturation in specific settings. Our results are illustrated with several examples, including finite-dimensional systems and bosonic Gaussian states that describe recent experiments on quantum heat engines with a quantized load.

Role of coherence in the nonequilibrium thermodynamics of quantum systems.

Exploiting the relative entropy of coherence, we isolate the coherent contribution in the energetics of a driven nonequilibrium quantum system. We prove that a division of the irreversible work can be made into a coherent and incoherent part. This provides an operational criterion for quantifying the coherent contribution in a generic nonequilibrium transformation on a closed quantum system. We then study such a contribution in two physical models of a driven qubit and kicked rotor. In addition, we also show that coherence generation is connected to the nonadiabaticity of a processes, for which it gives the dominant contribution for slow-enough transformations. The amount of generated coherence in the energy eigenbasis is equivalent to the change in diagonal entropy, and here we show that it fulfills a fluctuation theorem.

Irreversible work and inner friction in quantum thermodynamic processes.

We discuss the thermodynamics of closed quantum systems driven out of equilibrium by a change in a control parameter and undergoing a unitary process. We compare the work actually done on the system with the one that would be performed along ideal adiabatic and isothermal transformations. The comparison with the latter leads to the introduction of irreversible work, while that with the former leads to the introduction of inner friction. We show that these two quantities can be treated on an equal footing, as both can be linked with the heat exchanged in thermalization processes and both can be expressed as relative entropies. Furthermore, we show that a specific fluctuation relation for the entropy production associated with the inner friction exists, which allows the inner friction to be written in terms of its cumulants.

Prospective evaluation of interobserver diagnostic agreement for focal urinary bladder wall abnormalities detected by ultrasound.

INTRODUCTION: The interobserver variability of the sonographic assessment of Focal Bladder Wall Abnormalities (FBWA) between two physicians with different levels of experience was evaluated prospectively. MATERIALS AND METHODS: In the same session the two operators examined independently the urinary bladder of 87 consecutive patients (Mean Age 68 yrs; range 33-80; 75 Males; 15 Females) who underwent cystoscopy within 1-2 days. Before beginning the study, the two observers standardized the process for US exam. Weighted kappa statistics were used to determine the degree of agreement as to the presence, size, location and number of FBWA detected at cystoscopy. RESULTS: the highest level of agreement (k = 1) was reached on the presence of FBWA, whereas a substantial agreement was reached on size (k = 0.78), number (k = 0.72) and location (k = 0.62) of FBWA. CONCLUSIONS: In this study the gap in US experience between two operators did not emerge in assessing FBWA, provided a standardized technical approach is pursued.

Delayed diagnosis is associated with changes in the clinical and ultrasound features of subcutaneous endometriosis near cesarean section scars.

INTRODUCTION: The aim of the present study was to highlight the sonographic and clinical characteristics of large (≥30 mm in diameter) scar endometriomas near Pfannenstiel incisions, assuming that large size is a marker of delayed diagnosis. METHODS: We compared clinical, ultrasound (US) and color Doppler findings in 13 patients (mean age 31.3 years) with 13 large scar endometriomas (L-SEs) (mean lesion diameter 41.8 mm; range 30-60 mm) and 17 women (mean age 30.7 years) with 19 small scar endometriomas (S-SEs) (mean lesion size 18.3 mm; range 7-26 mm). RESULTS: Compared with the S-SE group, the L-SE group had a significantly longer mean interval between the last cesarean section and hospital admission (5.5 vs. 3.3 years; p < 0.01) and longer mean duration of symptoms before admission (43 vs. 17.4 months; p < 0.01). The L-SE group also had a significantly higher percentage of patients who had undergone at least one inconclusive diagnostic examination (Computed Tomography, Magnetic Resonance Imaging, fine needle biopsy, or laparoscopy) (39% vs. 0%; p < 0.05). As for US findings, L-SEs more frequently displayed cystic regions and fistulous tracts (p < 0.05), loss of round/oval shape (p < 0.05), and increased vascularity (p < 0.05). CONCLUSIONS: Delayed diagnosis of scar endometrioma reflected by a longer and more complex medical history results in larger than usual endometriomas with peculiar US findings, which are even more likely to be misinterpreted by physicians and radiologists.

Factors predicting complete necrosis rate after ultrasound-guided percutaneous laser thermoablation of small hepatocellular carcinoma tumors in cirrhotic patients: a multivariate analysis.

PURPOSE: To assess factors affecting the effectiveness of percutaneous laser ablation (PLA) under ultrasound (US) guidance in terms of complete ablation achievement. MATERIAL AND METHODS: The clinical records of 86 hepatocellular carcinoma (HCC) tumors (mean diameter 23.7 mm) in 60 cirrhotic patients (mean age 68.3 years; 36 males; 57 HCV+; 53 Child's class A, seven Child's class B) treated by means of PLA were reviewed. PLA was performed with a continuous-wave Nd:YAG laser by a single operator who positioned two to four 300-microm optic fibers advanced in 21-gauge needles into target lesions under US guidance. Triphasic computed tomography (CT) studies were used to verify treatment effectiveness 1 month after PLA completion. The association between characteristics of the lesion and outcome (complete or incomplete ablation) was evaluated by logistic regression, taking into account the following predictive factors: tumor size, pattern of growth (infiltrating or not) at imaging, location, first diagnosis of HCC (naïve tumors vs. non-naïve tumors), number of sessions (1/ > 1), total delivered energy, and years of treatment in 2001-2002 (first period) vs. 2003-2004 (second period). RESULTS: Complete ablation was obtained in 62 nodules (72%). Statistically significant predictors of incomplete ablation after the first PLA course at both univariate and multivariate analysis included: infiltrating growth pattern (odds ratio (OR) 12.3, P<0.002), non-naïve tumors (OR 8.7, P<0.001), and first period of treatment (OR 10.3, P<0.002). CONCLUSION: The effectiveness of US-guided PLA for HCC tumors < or =4 cm turned out to be negatively affected by both operator-related (the beginning of the operator's experience with the technique) and tumor-related factors (non-naïve, infiltrating HCC tumors).

Diagnosis of benign and malignant portal vein thrombosis in cirrhotic patients with hepatocellular carcinoma: color Doppler US, contrast-enhanced US, and fine-needle biopsy.

BACKGROUND: We assessed the role of contrast-enhanced ultrasound (CEUS) in the differential diagnosis between benign and malignant portal vein thrombosis in patients who had cirrhosis with hepatocellular carcinoma (HCC). METHODS: Fifty-four consecutive patients who had cirrhosis, biopsy-proved HCC, and thrombosis of the main portal vein and/or left/right portal vein on US were prospectively studied with color Doppler US (CDUS) and CEUS. CEUS was performed at low mechanical index after intravenous administration of a second-generation contrast agent (SonoVue, Bracco, Milan, Italy). Presence or absence of CDUS signals or thrombus enhancement on CEUS were considered diagnostic for malignant or benign portal vein thrombosis. Twenty-eight patients also underwent percutaneous portal vein fine-needle biopsy (FNB) under US guidance. All patients were followed-up bimonthly by CDUS. Shrinkage of the thrombus and/or recanalization of the vessels on CDUS during follow-up were considered definitive evidence of the benign nature of the thrombosis, whereas enlargement of the thrombus, disruption of the vessel wall, and parenchymal infiltration over follow-up were considered consistent with malignancy. CDUS, CEUS, and FNB results were compared with those at follow-up. RESULTS: Follow-up (4 to 21 months) showed signs of malignant thrombosis in 34 of 54 patients. FNB produced a true-positive result for malignancy in 19 of 25 patients, a false-negative result in six of 25 patients, and a true-negative result in three of three patients. CDUS was positive in seven of 54 patients. CEUS showed enhancement of the thrombus in 30 of 54 patients. No false-positive result was observed at CDUS, CEUS, and FNB. Sensitivities of CDUS, CEUS, and FNB in detecting malignant thrombi were 20%, 88%, and 76% respectively. Three patients showed negative CDUS and CEUS and positive FNB results; follow-up confirmed malignant thrombosis in these patients. One patient showed negative CDUS, CEUS, and FNB findings. However, follow-up of the thrombus showed US signs of malignancy. Another FNB confirmed HCC infiltration of the portal vein. CONCLUSION: CEUS seems to be the most sensitive and specific test for diagnosing malignant portal vein thrombosis in patients with cirrhosis.

Seeding from hepatocellular carcinoma after percutaneous ablation: color Doppler ultrasound findings.

BACKGROUND: We describe the clinical and color Doppler ultrasound findings in a series of cases of seeding from hepatocellular carcinoma (HCC) observed in patients treated with percutaneous ablation therapy (PAT) over a 15-year period. METHODS: We reviewed the clinical and imaging records of 12 patients with cirrhosis (nine men and three women, age range 51-82 years, mean age 63 years) that showed neoplastic seeding from HCC occurring after one or more PAT procedures. Five of 12 cases of seeding were observed as a complication of 1080 PAT procedures (0.46%) performed in 545 patients (0.96%) by two of the authors (L.T., G.F.) over a long period (15 years) at different institutions. The other seven patients had been treated with PAT procedures at other institutions and had come to our attention during post-treatment follow-up. RESULTS: The 12 patients who had seeding nodules had undergone the following PAT procedures: multisession conventional percutaneous ethanol injection (PEI) without anesthesia (four patients), single-session PEI with general anesthesia (three patients), single-session PEI with general anesthesia plus multisession conventional PEI (four patients), and single-session PEI plus radiofrequency ablation (one patient). Seeding nodules ranged from 0.9 to 6.0 cm (mean 1.7 cm). Eleven of 12 seeding nodules appeared as hypervascular hypoechoic nodules with smooth and regular margins and multiple intralesional vascular signals. CONCLUSIONS: Clinical and imaging findings of seeding from HCC should be recognized by physicians who perform follow-up ultrasound examinations of patients who are treated with PAT. Early diagnosis of seeding can be reliably made by scanning the abdominal wall with small probes in the area where the previous PAT has been performed. Hypoechoic hypervascular pattern of the seeding nodule allows definitive diagnosis.

Hydatid liver cyst: an 11-year experience of treatment with percutaneous aspiration and ethanol injection.

OBJECTIVE: To report an 11-year experience of treatment of hydatid liver cysts with double percutaneous aspiration and injection of alcohol. METHODS: Of the 129 patients with 174 hydatid liver cysts admitted to our department between January 1988 and January 1999, 79 patients with 119 vital hydatid liver cysts were selected for double percutaneous aspiration and injection of alcohol. Under ultrasonographic guidance, cystic cavities were first drained through fine needles, and then 95% sterile ethanol was injected and left in situ. The same procedure was repeated 3 days later without reaspiration of the injected alcohol. General anesthesia without endotracheal intubation was performed in 21 selected cases. RESULTS: Double percutaneous aspiration and injection of alcohol was completed in 78 patients with 118 hydatid liver cysts. In 1 case the procedure could not be accomplished because of an intracystic hemorrhage. A total of 254 punctures were performed, and the ethanol injected per session ranged between 12 and 250 mL. The mean hospital stay was 2.9 days (range, 2-7 days). The overall median follow-up was 48 months (range, 6-122 months). At the last ultrasonographic examination, 45.8% of the treated hydatid liver cysts had a solid pattern, 47.4% were no longer appreciable, and 6.8% had a minimal liquid component. Intracystic relapse occurred in 5% of the patients. In no case were any new cysts observed either in different hepatic segments or in any extrahepatic location. The morbidity rate was 9%, and 1 death occurred (mortality rate, 1.3%). CONCLUSIONS: Over a long period, double percutaneous aspiration and injection of alcohol proved to be a substantially safe, effective, and low-cost procedure for hydatid liver cyst treatment.

Single-step treatment of gallbladder and bile duct stones: a combined endoscopic-laparoscopic technique.

BACKGROUND: The introduction of laparoscopic cholecystectomy has given rise to a debate as to whether endoscopic retrograde cholangiopancreatography (ERCP) should be performed before or after cholecystectomy in patients with bile duct stones. METHODS: This study evaluated the efficacy of treatment of cholecystocholedocholithiasis in a single step by performing ERCP during surgery in 52 patients (35 women, 17 men; mean age 57.0 years; age range 20 to 89 years). Laparoscopic intraoperative cholangiography via the cystic duct was carried out to confirm the presence of duct stones. A soft-tipped guidewire was passed through the cystic duct and papilla into the duodenum. A papillotome was inserted endoscopically over the guidewire. Endoscopic sphincterectomy was performed and the stones removed with balloon and basket catheters. RESULTS: Endoscopic stone removal was successful in 94% of cases without complications related to ERCP or surgery. Although operative time was lengthened by about 20 minutes, the hospital stay was as short and equal to that for simple laparoscopic cholecystectomy (3 days on average). CONCLUSIONS: The single-step combined endoscopic-laparoscopic technique is safe and effective for treatment of patients with gallbladder and bile duct stones.

Hemobilia, intrahepatic hematoma and acute thrombosis with cavernomatous transformation of the portal vein after percutaneous thermoablation of a liver metastasis.

A 53-year-old-man underwent US-guided percutaneous thermal ablation with a cooled-tip needle of three liver metastases from gastric cancer. Six days later, the patient was re-admitted for melena, scleral jaundice, and anemia. Abdominal US disclosed echogenic material in the gallbladder lumen (hemobilia) and a focal lesion with mixed echotexture in segment III (hepatic hematoma). On day 5 portal cavernomatosis was diagnosed at US and confirmed by color Doppler and a helical CT exam. The case described emphasizes that radio-frequency interstitial hyperthermia may cause not only traumatic injury of the liver parenchyma but also thermally mediated damage of vascular structures.

Ultrasound-guided percutaneous treatment of hepatocellular carcinoma by radiofrequency hyperthermia with a 'cooled-tip needle'. A preliminary clinical experience.

OBJECTIVE: Radiofrequency hyperthermia using the newly-developed 'cooled-tip' needle has recently been proposed as a therapeutic modality for hepatocellular carcinoma (HCC). Herein we report our preliminary results on feasibility and effectiveness of the thermal ablation of mono- or pauci-focal hepatocellular carcinoma with the cooled-tip needle. MATERIALS AND METHODS: We treated 15 cirrhotic patients (mean age 68.8 years; 12 males; 14 HCV-positive; 13 in Child's Class A and 2 in Class B) with 20 hepatocellular carcinoma nodules (mean diameter 28.1 mm; range 10-43 mm; nine lesions with diameter greater than 3 cm). None of the patients had portal thrombosis and/or extrahepatic spread. We used a radiofrequency generator (100 W of power) connected to a 18 g perfusion electrode needle with an exposed tip of 2-3 cm. The circuit was closed through a dispersive electrode positioned under the patient's thighs. A peristaltic pump infused a chilled (2-5 degrees C) saline solution to guarantee the continuous cooling of the needle tip. The needle was placed into target lesions under US guidance. The interventional procedure was carried out in general anesthesia without intubation. Dynamic helical CT was carried out 15-20 days after thermal ablation to assess therapeutic efficacy. RESULTS: In all, 38 areas of coagulation necrosis (at 1000-1200 mA for 10-15 min) were generated in 24 sessions in the 20 hepatocellular carcinoma nodules (mean 1.9 lesions per nodule and 1.2 sessions per nodule). Complete necrosis as assessed at dynamic CT (lack of enhancement during the arteriographic phase) was achieved in 75% of cases in a single session; after a second RF session success rate was 90% (18 out of 20 nodules). A self-limited pleurisy along with a 5-fold increase in transaminases occurred in one patient; a 3-fold elevation of transaminases was encountered in three other patients. During the follow-up (median 15 months) five patients had recurrent hepatocellular carcinoma with a 1-year disease free interval of 64%. Of the three recorded deaths, two were due to intrahepatic tumor diffusion. CONCLUSIONS: In our experience radiofrequency hyperthermia with the cooled-tip needle afforded an effective and safe percutaneous ablative method for HCC in cirrhosis and shortened treatment time.

[Echo-guided radiofrequency percutaneous ablation of hepatocellular carcinoma in cirrhosis using a cooled needle]. / Ablazione percutanea ecoguidata del carcinoma epatocellulare su cirrosi mediante radiofrequenza con "ago freddo".

INTRODUCTION: Radiofrequency hyperthermia using the newly-developed "cooled-tip" needle is one of the latest US-guided percutaneous treatments of hepatocellular carcinoma arising in cirrhosis. The continuous cooling of the needle tip allows tissue heating and necrosis far from the electrode without tissue charring, which was the major drawback of the old monopolar technique. Herein we report our preliminary results on feasibility and effectiveness of the thermoablation of mono- or paucifocal hepatocellular carcinoma with the cooled-tip needle. MATERIAL AND METHODS: November, 1996, to January, 1998, we treated thirteen cirrhotic patients (mean age 69.5 yrs, 10 men, 12 HCV-positive; 11 in Child's Class A and 2 in Class B) with 19 hepatocellular carcinoma nodules (mean diameter: 27 mm; range: 10-41 mm; 6 with diameter > 3 cm). None of the patients had portal thrombosis and/or extrahepatic spread. We used a radiofrequency generator (100 W power) connected to an 18 G perfusion electrode needle with an exposed tip of 2-3 cm. The circuit is closed through a dispersive electrode positioned under the patient's thighs. A peristaltic pump infuses a chilled (2-5 degrees C) saline solution to guarantee the continuous cooling of the needle tip. The needle was placed into target lesions under US guidance. The interventional procedure was carried out under general anesthesia using Propofol without intubation. Dynamic CT (more recently with the helical technique) was carried out 15-20 days after thermoablation to assess treatment efficacy. RESULTS: In all, 31 thermal injuries (at 1000-1200 mA for 10-15 minutes) were caused in 21 sessions in the 19 hepatocellular carcinoma nodules (mean: 1.5 lesions per nodule and 1.6 sessions per patient). Complete necrosis as assessed at dynamic CT (no enhancement during the arteriographic phase) was achieved in 16 of 19 nodules (84%). No side-effects occurred. During the follow-up (median: 11 months) no death occurred and five patients had recurrent hepatocellular carcinoma appearing either as single nodule or as multinodular liver involvement. CONCLUSIONS: In our experience radiofrequency hyperthermia with the cooled-tip needle permits effective and safe percutaneous ablation of HCC in cirrhosis. In addition, treatment time is short and lesions > 3 cm can be treated. Further experience is needed to better define the role of percutaneous thermoablation in the treatment strategy of hepatocellular carcinoma.

Relapsing neoplastic seeding after percutaneous ethanol injection for hepatocellular carcinoma. Clinical and ultrasonographic findings in a cirrhotic patient.

A case of neoplastic implant after percutaneous ethanol injection (PEI) therapy for hepatocellular carcinoma (HCC) occurring in two steps is described. A 74-year-old male cirrhotic patient underwent PEI for a 5-cm HCC nodule. To obtain complete tumoral necrosis, 80 ml were injected under sonographic guidance in four sessions. Ten months after the completion of PEI a subcutaneous nodule was palpated in the abdominal wall within the area of needle punctures. Histologic examination of the excised nodule confirmed the sonographic and Power Doppler diagnosis of metastatic HCC. At the US exam scheduled three months later a non-palpable subcutaneous nodule of 16 mm was appreciated near the surgical wound. Once again metastatic HCC was demonstrated at pathological examination. Copyright 1997 Elsevier Science Ireland Ltd.

One-shot percutaneous ethanol injection of liver tumors under general anesthesia: preliminary data on efficacy and complications.

PURPOSE: To verify the efficacy of ultrasound (US)-guided injection of large amounts of ethanol into large or multiple liver lesions, in a single session under general anesthesia (one-shot PEI) for percutaneous ablation of hepatic tumors. METHODS: Twenty-nine patients (27 with 51 hepatocellular carcinoma (HCC) nodules on cirrhosis, diameter range 1.0-9.0 cm; two patients with a single metastasis from the gastroenteric tract, 5.0 and 9.0 cm, respectively, in diameter) were treated with one-shot PEI. RESULTS: The total volume of alcohol delivered per patient ranged from 16 to 210 ml. Mean ethanol volume in all patients was 49 ml. Dynamic computed tomography (CT) examination showed complete necrosis in 41 of 50 lesions. Two patients died of hypovolemic shock due to massive upper gastrointestinal bleeding, 3 and 7 days, respectively, after the interventional procedure. All the remaining patients are alive (follow-up 5-14 months) except one who died of liver failure 5 months after. New HCC nodules occurred in six patients within 6 months and one intralesional relapse was recorded. CONCLUSION: In this preliminary experience, one-shot PEI is as effective in inducing liver tumor necrosis as traditional PEI; its advantages are shorter treatment time and the capability of treating larger and multiple liver lesions.

Pyogenic liver abscesses: 13 years of experience in percutaneous needle aspiration with US guidance.

PURPOSE: To determine the efficacy of percutaneous needle aspiration (PNA) with antibiotic therapy in treatment for pyogenic liver abscess (PLA). MATERIALS AND METHODS: One hundred fifteen patients (59 male; 56 female; age range, 16-86 years; mean age, 45.3 years) with 147 PLAs (mean diameter, 6.8 cm; range, 3-16 cm) underwent PNA with ultrasound (US) guidance and antibiotic therapy. Needle caliber (22-16 gauge) was tailored to PLA volume. If necessary, PNA was repeated every 3-7 days. RESULTS: Three hundred one PNAs were performed (range, 1-4 per patient; mean, 2.2 per patient). A single puncture was sufficient in 57 patients. Cure (normalization of clinical and laboratory parameters and resolution of hepatic lesions) was achieved in 113 patients (98.3%). Two patients with large PLAs required surgery. Patients were hospitalized 7-24 days (mean, 9 days). In the last eight patients, all abscesses were evacuated in one session. Neither complications nor deaths ensued. Recurrence of PLA was not observed in any patient during follow-up (6-36 months). CONCLUSION: US-guided PNA with antibiotic therapy in treatment for PLA is a valid alternative to prolonged catheter drainage.

Percutaneous ethanol injection under sonographic guidance of hepatocellular carcinoma in compensated and decompensated cirrhotic patients.

Forty-six patients with cirrhosis and 75 biopsy-proved hepatocellular carcinoma (HCC) nodules underwent percutaneous ethanol injection (PEI) regardless of number (up to five) and size (mean diameter, 3.6 cm) of tumoral lesions and clinical severity of cirrhosis (11 patients in Child's class C were included). Ethanol was injected under sonographic guidance through 20 to 22 gauge needles so as to obtain homogeneous hyperechogenicity of lesions. A total of 271 PEI sessions were carried out, delivering 2 to 14 ml per session. All nodules but one decreased in size, and seven were no longer appreciable on sonography. Recurrence was detected in two patients. The 3 year survival rate of all cases was 86%. Child's classes A and B patients fared better (3 yr survival 100%); 2 year survival of subjects with HCC < or = 3 cm was 92%. Multifocality did not affect survival. Most patients experienced mild pain at the site of injection, but only two major complications were encountered: partial chemical thrombosis of the left portal vein and cholangitis. Both cases were managed conservatively. In conclusion, PEI seems to offer a safe and valuable tool for therapy of HCC, especially in patients with good functional liver reserve and small (< or = 3 cm) tumors.

Unilocular hydatid liver cysts: treatment with US-guided, double percutaneous aspiration and alcohol injection.

Sixteen hydatid liver cysts in 14 patients were treated with a percutaneous double puncture-aspiration-injection (D-PAI) technique with alcohol used as the scolecidal agent. With ultrasound guidance, fine-needle drainage of cysts was performed, and 95% sterile alcohol was injected and left in situ to partly refill the cystic cavities. The same procedure, without reaspiration of the injected alcohol, was performed 3 days later. Viability of scoleces was assessed at each aspiration. Benzoimidazolic drugs were administered 1 week before and 3 weeks after the procedure, to reduce the risk of seeding scoleces. Follow-up ranged from 8 to 28 months (mean, 14 months). Six cysts disappeared within 40-75 days of completion of D-PAI. In the other patients, smaller liquid areas or hypo- or hyperechoic solid masses were observed. Anaphylactoid reactions did not occur. In one patient, a biliary fistula developed after the first aspiration; the second ethanol injection was postponed until 6 months later but was effective. Viable scoleces were found at the second aspiration in only two patients whose hepatic liver cysts completely healed. Serologic titers substantially decreased in seven cases and became negative in two.