Liver Transplantation for Hepatocellular Carcinoma

Background Orthotopic liver transplantation (OLT) is the best available option for early hepatocellular carcinoma (HCC), although its application is limited by stringent selection criteria, costs, and deceased donor graft shortage, particularly in Asia, where living donor liver transplant (LDLT) has been developed.
Hepatocellular carcinoma (HCC) is the third most common cause of cancer-related death worldwide.1 Orthotopic liver transplantation (OLT) is the best therapeutic option for early, unresectable HCC, although it is limited by graft shortage and the need for appropriate patient selection. In the late 1980s, the results after OLT for HCC were disappointing, with high early recurrence and 5-year survival rates ranging between 18 and 40%.2 This discouraging experience and shortage of deceased donor grafts compelled the transplant community to establish stringent selection criteria to predict posttransplant survival of HCC patients. Recognizing that patients with small, incidentally found tumors had survival rates after liver transplantation equivalent to those after transplantation for benign disease, Mazzaferro et al. in Milan established criteria for OLT in a landmark study published in 1996.3 They showed that a subgroup of patients with radiologic evidence of a single tumor ≤5 cm in diameter, or two to three tumors ≤3 cm in diameter had 5-year and recurrence-free survival rates of 75 and 83%, respectively. The Milan criteria were subsequently adopted by the United Network for Organ Sharing (UNOS) staging system for allocating organs for OLT in the United States.
OLT is limited by a shortage of deceased donor liver grafts, particularly in Asia, where the rate of deceased donors is negligible. To overcome this shortage, living donor liver transplantation (LDLT) has been developed with favorable preliminary results. Other areas of study include expanding the criteria for liver transplantation to include larger tumors, as shown by the group from the University of California, San Francisco (UCSF) and molecular profiling of HCC to improve prognostication and patient selection.
MILAN CRITERIA FOR LIVER TRANSPLANTATION IN HCC
In the past 10 years, results of OLT have improved steadily because of careful patient selection pioneered by the introduction of the Conventional Milan Criteria (CMC) in 1996.3 The aim of these criteria was to achieve a good outcome in patients who fulfilled the criteria and avoid a poor prognosis in patients who exceeded them. This aim was achieved by the Milan group, who showed that the 10-year overall survival surpassed 70% in 300 liver transplants for HCC that fulfilled the CMC. Such good results have been confirmed worldwide.4,5 The elements of the CMC, namely size and number of tumors, have been shown in multivariate analysis to be the only independent variables predicting patient survival and tumor recurrence, with other biological prognostic factors playing a role only within the “size and number” limits (Table 1).
TABLE 1.Prognostic factors affecting survival of 250 patients transplanted for HCC according to Conventional Milan Criteria at the National Cancer Institute of Milan10-year survival: multivariate analysisVariableHRCI (95%)P valueOverall patient survivalConventional Milan criteria (in vs out)3.11.35–6.93.007Tumor-free survivalConventional Milan criteria (in vs out)5.51.39–21.27.01Microsatellites (yes vs no)3.61.5–8.71.004Microvascular invasion (yes vs no)3.41.36–8.76.009Tumor grading (G3 vs G1-2)3.41.04–11.14.04
The successful outcome of OLT based on the CMC has led to more patients with HCC being routed to transplantation and an increasing number of proposals for expansion of the CMC.6,7 None of these expanded criteria are, however, supported by a robust statistical sample size or prospective validation. In order to investigate proposals to expand the CMC, an unprecedented multicenter study has been conducted in 24 European centers, collecting data from 466 patients transplanted for HCC whose tumors exceeded the CMC at posttransplant pathologic assessment (http://www.hcc-olt-metroticket.org).5,7 The results have been plotted in a tumor size-and-number Cartesian contour plot showing the 5-year survival probability according to the size and number of HCC nodules detected in the explanted liver. Based on a preliminary analysis, a “HCC forecast chart” has been developed, which can predict 5-year posttransplant survival rates on the basis of morphological tumor characteristics (Fig. 1). It is conceivable that similar chart models obtained from large sample sizes could replace the CMC for OLT in patients with HCC. Unlike the CMC or expanded proposals, which are based on tumor morphology, these chart models can incorporate important variables for OLT in HCC, including priority score for HCC and dropout rate based on donor availability at different centers. Preliminary ad interim analysis shows a significant shift of the isograms of the proposed chart depending on the presence of vascular invasion in explant specimens, confirming the need for reliable biological markers of important tumor characteristics, such as vascular invasion.
FIG. 1.HCC forecast chart showing probability of 5-year survival based on tumor size and number in explanted liver.
MILAN VERSUS EXPANDED CRITERIA FOR LIVER TRANSPLANTATION
Following the 1996 publication by the group from Milan, using a restrictive set of criteria for OLT in patients with HCC, excellent 5-year posttransplant patient survival of at least 70% has been reported from many centers.4,5 The growing experience and success of OLT for HCC have fueled controversies related to expansion of the Milan criteria for OLT, since many studies have suggested that tumor stage beyond the Milan criteria does not necessarily predict worse survival after OLT.8,9 Among the proposed expanded criteria, the UCSF criteria (single tumor nodule up to 6.5 cm; or three or fewer tumors, the largest of which is ≤4.5 cm with the sum of the tumor diameters ≤8 cm) reflect a modest expansion of tumor size limits beyond the Milan criteria.6 At least three transplant experiences from Europe and the United States, however, underlined the limitations of applicability of the UCSF criteria in the pretransplant setting, considering that most of the patients adhering to the UCSF were also within the Milan criteria.10–12 Even though the UCSF criteria have been independently validated in several studies, the overlapping population of patients adhering to the UCSF but not the Milan criteria is often negligible and estimated to be <10% of the total transplanted population.12,13 Such a limitation was evidenced by a multicenter study from France, in which 39 of 461 patients (8.7%) had explanted tumors beyond the Milan but within the UCSF criteria.10 Although the 5-year survival of 67% for patients within the UCSF criteria was equivalent to that of the 183 patients meeting the Milan criteria (and significantly better than the 34% 5-year survival rate among 238 patients exceeding both criteria), the 44 patients meeting UCSF but exceeding Milan criteria at pretransplant staging had a 5-year survival rate of only 48%, compared with 60% observed in the 272 patients within Milan criteria and with 37% in the 121 patients beyond both criteria.
The limitations of pretransplant imaging studies, exemplified by tumor understaging in 20% of patients, have been a major concern for liberalizing the existing criteria for OLT.5 The UCSF group applied their proposed criteria according to preoperative imaging in 138 patients over a 5-year period; the 1- and 5-year recurrence-free probabilities were 95 and 91%, and the respective probabilities for recurrence-free survival were 91 and 80%.14 The 106 patients with HCC meeting the Milan criteria (T1/2) had 1- and 5-year recurrence-free probabilities of 96 and 90%, respectively, compared with 93% at both 1 and 5 years for patients with HCC exceeding Milan but meeting UCSF criteria (T3A). Understaging by preoperative imaging was observed in 21% of T1/2 and 28% of T3A tumors. When explant tumor stage exceeded the UCSF criteria, the 1- and 5-year recurrence-free probabilities were 79 and 61%, compared with 98 and 97% within the UCSF criteria. Patients meeting T3A criteria did not have a significantly higher incidence of poorly differentiated tumor grade or vascular invasion.
In the current era of increasing demand and unrelenting organ shortage, the foundation of the debate regarding expansion of the Milan criteria for HCC may ultimately rest on what the transplant community would consider an acceptable survival after OLT for HCC. Some groups have proposed a 50% 5-year patient survival to be the minimum acceptable cutoff.5 This mark may have been surpassed by the UCSF group, who have applied expanded criteria to benefit an additional 10% of patients with HCC with respect to posttransplant survival and tumor recurrence.
LIVING DONOR LIVER TRANSPLANTATION FOR HCC: EASTERN EXPERIENCE
Liver transplantation offers the best chance of cure for early unresectable HCC. However, its role has been limited by the shortage of deceased donor liver grafts, which is particularly severe in Asia, where the deceased donor organ rates are fewer than 5 donors per million population, compared with 10–35 donors per million population in Western countries.15 In most Asian countries, HCC is the most common cancer and the most frequent indication for OLT, aggravating the unmet demand for liver grafts. The development of living donor liver transplantation (LDLT), especially adult-to-adult right lobe liver transplantation, has allowed more patients with HCC to benefit from OLT.16 LDLT can theoretically provide an unlimited source of liver grafts and eliminate the uncertainty of prolonged waiting times and the risk of dropout due to tumor progression. However, LDLT is a novel treatment for HCC with unresolved issues regarding indications and results.
Recent studies on LDLT for HCC suggest favorable long-term survival results.17,18 However, it remains unclear whether the outcome after LDLT for HCC is equivalent to that of deceased donor liver transplantation (DDLT). A study from a Korean group reported similar 3-year survival rates after LDLT and DDLT (91.4 vs 89.9%) in patients with tumors fulfilling the Milan criteria, after excluding perioperative mortality.13 However, others have found significantly higher rates of tumor recurrence after LDLT compared with DDLT for HCC.19 This may be related to selection bias, as LDLT eliminates the waiting period for grafts. In DDLT the waiting period provides time for a natural selection process in which patients with biologically more aggressive tumors drop out due to tumor progression. In addition, the ischemic-reperfusion injury associated with small-for-size grafts in LDLT and angiogenesis associated with liver regeneration may theoretically promote growth of tumors in the transplanted liver after LDLT, although the actual clinical impact of such biological processes remains unclear.20,21
Liver transplantation is conventionally offered to Child-Pugh class C patients with unresectable early HCC. Recently, there have been heated debates on whether liver transplantation should be used as first-line therapy for Child-Pugh class A patients with early HCC.22 While some previous studies showed that liver transplantation for early HCC may achieve better survival compared with resection, this may be partly related to selection bias in favor of transplantation because patients with more aggressive tumors drop off the waiting list for DDLT.19 Recent studies suggest that for patients with preserved liver function and early stage HCC, hepatic resection can achieve a 5-year survival rate of 70%, comparable to that after OLT.13,23
The availability of grafts from dedicated live donors has been considered one of the main arguments favoring LDLT as primary therapy for patients with early HCC and preserved liver function. However, even in Asian countries where LDLT is commonly performed, up to half of the patients with early HCC may not have suitable living donors for various reasons, including ABO-incompatibility, hepatitis serology, and patient refusal to accept living donation.18 Furthermore, the risks of donor hepatectomy, with morbidity and mortality rates of 14–21% and 0.25–1%, respectively, should be carefully balanced against the benefit of LDLT.19 Risking the life of a donor for HCC patients who have an alternative option of hepatic resection, which achieves long-term survival equivalent to LDLT, is ethically not acceptable to many Asian surgeons. Most Asian centers still consider resection as first-line treatment for HCC patients with preserved liver function and reserve LDLT as an option for salvage transplantation in patients with recurrent tumors.13,23,24
Another matter of debate in LDLT involves expanding the indications beyond the CMC or UCSF criteria. LDLT is currently being performed in some Asian centers for patients with HCC beyond the Milan criteria, with results that are expectedly worse than those for patients within the Milan criteria.13,17 Some transplant surgeons argue that despite the poorer results, LDLT for advanced HCC may be justified, since donors voluntarily accept the risks of donor hepatectomy to dedicate a graft for HCC patients, who may otherwise have no effective treatment options. However, others argue that the medical profession should not relegate the issue to individual donor autonomy.25 With the lack of clear data showing benefits of LDLT for advanced HCC, the medical community should take a conservative moral stand and limit the use of LDLT for HCC that meets the same criteria as DDLT.
LIVING DONOR LIVER TRANSPLANTATION FOR HCC: WESTERN EXPERIENCE
Over the past 10 years, LDLT has developed as an alternative to DDLT because of the scarcity of deceased donor livers. Patient survival after LDLT is similar to that after DDLT, despite data from the UNOS database showing lower post-LDLT graft survival, possibly due to the learning curve for LDLT and lower graft-to-recipient body weight ratio.26 In the United States, enthusiasm for LDLT peaked in 2001, when more than 500 LDLTs were performed; the aftermath of a widely-publicized donor death in 2002 led to a nationwide retrenchment, with no more than 325 procedures per year since then. Nevertheless, LDLT has an important role in the treatment of HCC. While previously there was concern over possible tumor stimulation due to regeneration after LDLT, it appears that the type of graft (living vs deceased donor) has little, if any, impact on post-OLT tumor progression.
Typically, LDLT results in a liver graft that is smaller than the expected liver volume of the recipient. The outcome of a relatively small donor organ depends not only on graft size but also on the recipient’s preoperative degree of liver failure and portal hypertension. Compared with patients awaiting transplant for end-stage cirrhosis, candidates with HCC generally have better-preserved liver function and less portal hypertension, and are thus better able to tolerate a small graft.
Ready availability is the most important advantage of LDLT for HCC. Posttransplant tumor recurrence is tied to pretransplant tumor stage; progression of tumor while awaiting transplant can only worsen the prognosis. This fact is reflected in the United States allocation scheme for deceased donor livers, which accords priority to patients with HCC meeting the Milan criteria. Since adoption of the Model of End-Stage Liver Disease organ allocation policy in 2002, candidates with T2 HCC (1 nodule between 2 and 5 cm; or 2–3 nodules, all ≤3 cm) have enjoyed priority such that in many regions of the United States, waiting times are short, obviating the need for LDLT.27 In some regions, however, longer waiting times and attendant higher dropout rates support the use of LDLT in cases of HCC within the Milan criteria.
The Milan criteria were adopted because they identify a subgroup of candidates with HCC for whom transplant results are similar to those in patients transplanted for end-stage cirrhosis without HCC. It is widely recognized, however, that many patients with HCC beyond the Milan criteria can be cured by OLT.8,9 In the United States, adoption of expanded priority criteria for DDLT, as proposed by the UCSF group, is currently under consideration. LDLT can be undertaken in candidates who do not meet criteria for waiting list priority. Broadening criteria based on tumor size and number will inevitably lead to more recurrence; nevertheless, Roayaie et al. demonstrated 55% freedom from recurrence at 5 years in patients transplanted with HCC between 5 and 7 cm and no macroscopic vascular invasion.28 Based on data such as these, many centers offer LDLT to patients with HCC meeting expanded criteria that are estimated to yield a 5-year survival of approximately 50%.5
SELECTION IN HCC: BIOLOGY OR MORPHOLOGY
The distinction between biology and morphology in simple terms can be described as behavior versus appearance. Ultimately, the behavior of HCC is the final deciding factor on patient outcome. The ability to predict the biology of HCC is desperately needed for patient selection in OLT. The current staging criteria for HCC takes into account tumor morphology but not tumor biology, with transplantable stages stratified according to tumor size and number. For treatment options other than liver transplantation (i.e., liver resection, chemotherapy, and cytoablative therapies), tumor morphology as described by the pathological TNM staging system is reasonably adequate. For liver transplantation, however, gross and microscopic morphology are inadequate for predicting outcomes because of the scarcity of the donor organs that must be judiciously allocated. The issue would be less significant if resources were unlimited.
Ideally, the TNM or morphology-based staging system would be able to stratify patients into homogeneous groups with the same outcomes. However, the current staging systems are not precise enough to segregate patients with HCC and cirrhosis into such homogeneous groups. As almost all patients with gross invasion of the hepatic venous system, positive lymph nodes, or metastatic disease experience recurrence and are therefore not candidates for transplantation, the N and M components of the TNM classification can immediately be eliminated from the organ allocation scheme. This leaves only the T component upon which we can base our biological prediction, namely tumor size and number.
In our efforts to refine our current staging systems, morphological or chemical factors have been studied, including microscopic vascular invasion, encapsulation, plasma albumin mRNA, and serum alpha-fetoprotein.5 To date, however, none of these have improved upon the current systems. Part of the problem has been radiologic techniques are not yet sufficient to perfectly define tumor number and size and will never be able to determine microscopic vascular invasion. Moreover, many new staging systems require pretreatment biopsy, which poses a small but real risk of tumor seeding.
To understand the biological behavior and identify genes associated with survival after OLT, Marsh and colleagues at the University of Pittsburgh performed microdissection on explanted tissue and studied DNA mutations near 9 tumor-associated gene loci to create an index of cumulative mutational damage, termed the fractional allelic imbalance (FAI).29,30 They found that FAI and vascular invasion were the strongest independent predictors of tumor-free survival. Thus, incorporation of gene mutational data allows desegregation of HCC patients from imprecise, morphology-based staging systems and allows improved prognostication.
CONCLUSIONS
While patients with early resectable HCC and preserved hepatic function should undergo surgical resection, in those with unresectable disease due to underlying liver dysfunction, orthotopic liver transplantation (OLT) offers the best chance for cure. In the past 10 years, results of OLT have steadily improved because of careful patient selection pioneered by the introduction of the Milan criteria in 1996. Supported by studies showing that many patients with tumor stage beyond the Milan criteria can be cured by OLT, a number of expanded criteria have been proposed. While expanding the criteria for OLT allows more patients to be eligible for transplantation, arguments against expanding the criteria include the increased risk of vascular invasion and tumor recurrence at higher stages of HCC. The principal limitation of OLT for HCC is the shortage of deceased donor living grafts, especially in Asia. The development of LDLT has allowed more patients to benefit from OLT with favorable preliminary survival results. Given the shortage of organs available for OLT and lack of predictive power of currently used staging systems, improved prognostic tools are needed to predict outcomes after OLT. Molecular markers of cancer progression may add significant discriminatory power to the current staging systems and may improve organ allocation schemes for patients with HCC.


Sonographic findings in bacterial meningitis in neonates and young infants

Cranial sonography plays an important role in the initial evaluation of infants with suspected bacterial meningitis and in monitoring for complications of the disease. Echogenic widening of the brain sulci, meningeal thickening and hyperemia suggest the diagnosis in an at-risk population. Sonography can identify the presence of extra-axial fluid collections, and color Doppler sonography can be very helpful in differentiating benign enlargement of subarachnoid spaces from subdural effusions. Intraventricular debris and stranding, and an irregular and echogenic ependyma are highly suggestive findings associated with ventriculitis. Sonography can play an important role in the detection of postinfectious hydrocephalus, in the determination of the level of obstruction, and in the evaluation of intracranial compliance. Focal or diffuse parenchymal involvement can represent parenchymal involvement by cerebritis, infarction, secondary hemorrhage or early abscess.
Introduction
Bacterial meningitis is an uncommon but serious condition in the newborn and infant child. The incidence of bacterial meningitis has shown a dramatic decline in the last 25 years in the United States [1]. But despite a number of recent advances in neonatal intensive care, rapid bacteriological assays, and potent antibiotics, neonatal bacterial meningitis remains an important cause of neurological disability worldwide [2–4]. Early diagnosis of the primary disease and its complications is essential for the prevention of neurodevelopmental sequelae. Cranial sonography is often the first imaging modality used in the evaluation of critically ill infants with suspected meningitis. Thus, familiarity with the pathophysiology and sonographic appearance of bacterial meningitis is important for the radiologist and neonatologist taking care of these patients. In this article we review and update the US features of bacterial meningitis and its complications with emphasis on the relationship between imaging findings and underlying pathological changes.
Pathophysiology of meningitis
Bacterial meningitis usually occurs as a result of bacteremia and sepsis, with initial seeding of the central nervous system via the choroid plexus. The infection then spreads into the cerebrospinal fluid (CSF) and can cause inflammation of the ventricular system (ventriculitis). Inflammation of the meninges typically follows [2, 5]. A key feature of arachnoiditis is the presence of vasculitis, predominantly in small and medium-size veins that traverse the subarachnoid space [5]. Meningeal inflammation extends to the walls of the bridging and cortical veins to cause thrombophlebitis and vascular occlusion, which is associated with cortical infarcts [5, 6]. A number of bacterial virulence factors and inflammatory cytokines contribute to the inflammatory process, resulting in diffuse cerebral edema, increased intracranial pressure, and alterations of cerebral blood flow [7–9]. Lipopolysaccharides found in the bacterial cell wall can lead to a disruption in the blood–brain barrier and invasion of microorganisms into deeper cerebral structures [10, 11]. Arachnoiditis and ventriculitis might also contribute to a more generalized encephalopathy characterized by neuronal loss, gliosis and periventricular leukomalacia [2]. Later pathological findings include diffuse cerebral cortical and white matter atrophy, hydrocephalus, which can also be seen in the early phase, multicystic encephalomalacia, porencephaly and ventricular septations [2, 3, 5, 12, 13].
In the acute phase of meningitis, marked vasodilatation of cortical vessels is often present as the result of potent vasogenic effects of bacterial toxins. In later stages of the disease, there is a global reduction in cerebral blood flow attributed to impairment of cerebral autoregulation and brain edema [14].
In the newborn infant, streptococcus group B, Escherichia coli, and Listeria monocytogenes are the most commonly isolated organisms in CSF. Although other gram-negative enteric organisms such as Klebsiella species and Citrobacter species are less common, they can have far more devastating consequences [15].
Sonographic features of meningitis
Sonographic abnormalities are present in approximately 65% of infants with acute bacterial meningitis [3, 16–22]. However, the frequency of imaging abnormalities in patients with a clinical presentation complicated by persistent seizures, abnormal neurological findings and a deterioration of CSF examination within the first 48 h can be as high as 100% [17]. The high incidence of positive sonograms in infants with suspected complications resulted in the recommendation by some authors to use sonography only when there is a clinical suspicion of a complication [3]. Han et al. [3] found that no infant without a clinical indication of complications of meningitis had clinically significant findings on sonography. However, other authors suggest a sonographic examination should be used on every infant with or without evidence of complications on the basis of reports of a high incidence of positive findings in infants without any clinical indication of complications [17, 23, 24]. Rosenberg et al. [23] suggest an initial examination at the time of diagnosis of bacterial meningitis and a follow-up study within 1 week if the initial study demonstrates any parenchymal or ventricular abnormality.
We recommend cranial sonography as a baseline study in every infant who has an adequate size fontanel if the diagnosis of bacterial meningitis is suspected clinically. Because the major advantage of sonography is its ability to be safely repeated, a second study should be performed if any clinical deterioration occurs, such as increasing head circumference, occurrence of new neurological findings, and lack of response to therapy. However, in patients with complicated bacterial meningitis whose clinical situation is sufficiently stable to leave the nursery, MRI should be the next study of choice. In children, MRI is widely accepted for its safety and high soft-tissue resolution. It is superior to sonography in showing the existence and extension of the complications, especially in the posterior fossa. It has the further advantage of not using ionizing radiation.
It is essential to use state-of-the-art equipment with optimized settings including linear, curved and vector probes with variable megahertz in order to perform a complete evaluation of the meninges because of the often subtle sonographic changes of bacterial meningitis [25, 26].
Meningeal and extra-axial findings
In healthy individuals, the pia-arachnoidal membrane is seen as an echogenic line on the surface of the brain. Normal thickness of the membrane measured from the surface of a frontal gyrus (single layer) and within a sulcus (double layer) should not exceed 1.3 mm and 2 mm, respectively [27]. Echogenic widening of brain sulci, or meningeal thickening, is the most common and earliest sonographic sign of meningitis, seen in 26–83% of affected patients (Fig. 1) [3, 16–20, 28]. Prominent cortical vessels can be seen within the pia-arachnoid on color Doppler sonography (Fig. 2). These findings reflect the intense inflammatory exudate that accumulates in the depths of the fissures and sulci, especially around the pial and subarachnoid vessels [5]. Despite their common occurrence, signs of meningeal inflammation are temporary and unrelated to any significant clinical or neurological outcome [3, 16, 20].
Fig. 1Thickened meninges. a Coronal sonogram through frontal lobes in an 11-week-old infant with group streptococcus group B meningitis demonstrates diffuse echogenic thickening of the leptomeninges (arrows) and prominent extra-axial fluid spaces (asterisk). b, c Coronal sonogram on a different infant with group streptococcus group B meningitis (b) shows marked thickening of the suprasellar cisterns (arrows), compared to a normal infant (c)Fig. 2Vasodilatation of pial vessels. Angled sagittal midline color Doppler sonogram in a 3-week-old infant with streptococcus group B meningitis shows prominent vascularity along the surface of the brain parenchyma and a patent superior sagittal sinus (arrowheads)
Accumulation of extra-axial fluid might be present in 8–33% of infants with bacterial meningitis. Most commonly, these represent sterile, reactive subdural effusions that have no prognostic significance [3, 16, 19, 20, 28]. On sonography, they appear as hypoechoic concave fluid spaces, sometimes containing mobile echogenic debris (Fig. 3). Empyema is a very rare complication of meningitis, present in up to 1% of affected patients [3, 5, 17, 24]. Although it is often difficult to differentiate a sterile effusion from an early empyema [28], an enlarging complex extra-axial fluid space is a concerning finding. Such spaces can become quite large and cause a mass effect on the adjacent brain parenchyma [29] (Fig. 4). Clinical findings including persistent fever, new focal neurological signs or seizures are not sufficient for suspicion of subdural empyema because they are not specific for the diagnosis of empyema [30]. Hence, a combination of imaging modalities and clinical evaluation is necessary for the early diagnosis of subdural empyema. The final diagnosis is based on the analysis of the subdural effusion [31].
Fig. 3Subdural effusion. a Coronal midline sonogram in a 3-week-old infant with streptococcus group B meningitis shows echogenic debris within subdural fluid. b Axial diffusion-weighted MR image shows markedly hyperintense signal in the extra-axial fluid consistent with restricted diffusion caused by meningeal edema or pusFig. 4Subdural empyema. a Angled sagittal sonogram in a 1-week-old infant with E. coli meningitis shows thickened septations in the subdural space (arrows). b Repeated sonogram at 2 weeks of age shows a complex heterogeneous collection consistent with focal empyema (arrows). Needle aspiration confirmed the presence of pus
The distinction between subarachnoid and subdural location of extra-axial fluid is important in the management of infants with meningitis. Isolated subarachnoid fluid spaces up to 3.3 mm are considered incidental findings of no clinical importance in meningitic infants, whereas neurosurgical evacuation is the therapy of choice for infected subdural effusions (empyema) [25, 32]. Early detection with frequent sonographic monitoring of subdural effusions might lessen the neurological sequelae in infantile and neonatal purulent meningitis [33]. Color Doppler sonography can be very helpful in differentiating benign enlargement of subarachnoid spaces from subdural effusions [34, 35]. When subarachnoid fluid is present cortical vessels on the brain surface are surrounded by fluid, whereas fluid in the subdural space compresses the cortical vessels along the surface of the brain (Fig. 5).
Fig. 5Subdural fluid. Midline coronal color Doppler sonogram in an 11-week-old infant with group streptococcus group B meningitis shows cortical vessels along the surface of the left hemisphere (blue vessels). Vasculature is located in the pia-arachnoid space and is not surrounded by fluid. This finding strongly suggests that fluid is in the subdural space. Note the superior sagittal sinus (asterisk)
Intraventricular findings
The most common sonographic signs of ventriculitis include an irregular and echogenic ependyma, the presence of intraventricular debris and stranding, often associated with ventricular dilatation. Debris in the ventricles can be caused by any infecting organism; however, it is most frequently seen with E. coli meningitis [3, 36]. The amount and coarseness of intraventricular debris can vary considerably (Fig. 6) and reflects the extent of ventriculitis. Sonographic resolution of intraventricular debris reflects the efficacy of antibiotic treatment [37]. Inflammation within the ventricles can cause intraventricular adhesions and formation of septae as a more chronic complication of meningitis in about 10% of patients [21, 28, 38]. These adhesions can cause compartmentalization in the ventricles, leading to intraventricular cyst formation (Fig. 7). The identification of the ventricular septations is very important in planning for appropriate shunt placement. Sonography is the study of choice for the demonstration of these septations, often demonstrating them better than CT [38].
Fig. 6Ventriculitis. a–c Coronal (a), left sagittal (b), and mastoid sonograms (c) obtained in a 12-day-old premature infant with E. coli meningitis show extensive septations and echogenic debris clots filling the lateral, third and fourth ventricles. Note the echogenic thickening of edematous ependyma (arrows). d Repeat coronal sonogram at 19 days of age shows a decrease in size and heterogeneity of the intraventricular debris. Note progression of ventricular dilatationFig. 7Cyst formation. Coronal image obtained in a 5-week-old infant with E. coli meningitis shows a midline cyst displacing the third ventricle (arrow) superiorly and to the right
Although histopathological studies have shown exudative inflammation of the choroid plexus (plexitis) and of the ependymal lining (ventriculitis) in up to 93% of those autopsied [5, 13], only those with more severe involvement exhibit abnormal findings on cranial sonography [3, 16, 20, 28]. By US examination, the choroid plexus can appear more echogenic and its contours irregular and poorly defined [16, 28, 38, 39]. The ependyma can have a thick, irregular and echogenic appearance, as well [20, 28, 37–39].
Parenchymal findings
Abnormal parenchymal echogenicity
Areas of abnormal brain echogenicity have been reported in 12% to 65% of infants with bacterial meningitis [3, 20, 28]. Lesions can be focal or diffuse and can represent parenchymal involvement by cerebritis, infarction, secondary hemorrhage or early abscess [3, 17, 40]. The presence and size of parenchymal lesions are associated with significant neurological sequelae and are indicators of a poor prognosis [3].
One of the most devastating complications of bacterial meningitis is abscess formation. It has been reported with a frequency of between 1% and 18% in newborns with meningitis [2, 3, 16, 21, 28]. Mortality rates are significant (15–75%), and up to 66% of survivors develop neurological sequelae [41, 42].
Most cerebral abscesses are caused by a member of the Enterobacteriaceae family (Citrobacter and Enterobacter species) [43, 44]. Citrobacter koseri (formerly C. diversus) is the main causative agent leading to abscess formation in the brain [43, 45]. Up to 77% of infected patients develop an intracerebral abscess. The major pathological feature of Citrobacter meningitis is vasculitis followed by infarction, with necrosis and liquefaction of large portions of the white matter of the hemispheres [45, 46]. Hemorrhagic necrosis and liquefaction can also occur [43, 46]. Surgical drainage of these lesions is not recommended to avoid further damage to surrounding brain parenchyma [46].
The sonographic appearance of abscess varies with the stage of the infection. During the initial stage of cerebritis, sonography might only show a poorly marginated area of increased echogenicity with increased vascularity using color or power Doppler [2] (Fig. 8). As the abscess matures the lesion becomes a well-circumscribed, complex solid mass with highly echogenic walls [3, 21]. After progression with/or without antibiotic therapy the lesions progress to cavitation with marked peripheral hyperemia [16, 21, 47, 48]. Sonographic differentiation between hemorrhagic necrosis and abscess is not always possible, and percutaneous sampling of the intracavitary fluid might be necessary. Sonographic guidance can be useful for puncture, aspiration, and irrigation of the abscess cavity [49, 50].
Fig. 8Liquefactive cerebritis. a, b Coronal (a) and sagittal right (b) sonograms through the frontal lobes in a full-term infant with Citrobacter meningitis show extensive echogenic cerebritis involving the right frontal lobe and basal ganglia. c Repeated sonogram 5 days later shows early liquefaction of the frontal lobe (arrow). d, e Coronal sonogram obtained after 7 days (d) demonstrates complete liquefaction of involved brain and surrounding hyperemia on color Doppler sonography (e). Needle aspiration revealed necrotic tissue with no organism
Brain edema
In the acute stage of meningitis, both intra- and extracellular edema can occur. As a result, the lateral ventricles as well as the other cisternal structures can be compressed or obliterated [5]. The range of ventricular size is quite wide, from mild compression to complete sonographic obliteration, the latter being a poor prognostic factor [28, 51]. On sonography, there might be a diffuse or heterogeneous increase in the echogenicity of the brain with effacement of the sulci and gyri [20, 23, 28, 50, 52] (Fig. 9). Increased intracranial pressure is associated with increased pulsatility of arterial flow, reflected in elevated resistive index (RI) values on pulsed Doppler sonography. Other causes of elevated pulsatility of flow include venous thrombosis (Fig. 10), large extra-axial fluid collections, and postinfectious hydrocephalus. Retrograde blood flow during diastole is an indication of markedly altered intracranial compliance [53–57]. When equivalent antegrade and retrograde blood flow is present during numerous cardiac cycles, this might be an indication of nonviable brain blood flow [35, 58].
Fig. 9Brain edema. Coronal sonogram in a 7-day-old infant with group B streptococcus meningitis shows generalized edema with compression of lateral ventricles and sulci and diffuse increased heterogeneity of the cerebral hemispheresFig. 10Sagittal sinus thrombosis, nonviable blood flow. a Coronal color Doppler image an 18-day-old infant with group B streptococcus meningitis shows flow limited to internal carotid arteries at the base of the brain. b On the magnified coronal color Doppler image no flow is identified in the superficial sagittal sinus (arrows), and the thrombosis of the sinus was also confirmed on sagittal scans using high-sensitivity Doppler settings (not shown). c Duplex Doppler waveform of the anterior cerebral artery without fontanel compression shows reversal of flow during the entire diastolic phase
Diffuse cerebral atrophy, multicystic encephalopathy, and porencephaly might be seen as the end-stage of complications of bacterial meningitis.
Hydrocephalus
Ventricular dilatation is present in 14–65% of infants with bacterial meningitis and can occur in either the acute or the chronic phase of the disease [16–21, 28]. The level of obstruction to CSF flow is usually outside the ventricular system but can occur within the narrowest portions of the ventricles as a result of ependymitis and secondary adhesion. Common locations for intraventricular obstruction include the aqueduct of Sylvius and the exit foramina of the fourth ventricle [16].
Sonography can play an important role in the detection of hydrocephalus, in the determination of the level of obstruction, and in the evaluation of intracranial compliance. In aqueduct stenosis the lateral and third ventricles are disproportionately dilated, the aqueduct is thickened and echogenic and the fourth ventricle is of normal size (Fig. 11). Detection of CSF flow through the aqueduct of Sylvius is possible by imaging the aqueduct using the mastoid fontanel view. Using power Doppler sonography, the anterior fontanel is compressed and quickly released. Particulate debris within the CSF allows power Doppler signal to be detected when CSF flows in a retrograde fashion through a patent aqueduct into the third ventricle [59].
Fig. 11Postinfectious hydrocephalus. a Midline sagittal sonogram in an infant with aqueductal stenosis following group B streptococcus meningitis shows dilatation of the lateral and third ventricles; the fourth ventricle is normal. b Mastoid fontanel view of another infant with group B streptococcus meningitis shows markedly dilated lateral, third, and fourth ventricles secondary to obstruction of the fourth ventricle outlet foramina. Note the echogenic particle in the third ventricle, which could be debris or a clot
Pulsed Doppler interrogation of the anterior cerebral artery before and after compression of the anterior fontanel can be a useful adjunct in the serial monitoring of infants with postinfectious hydrocephalus [53, 54, 57]. Increasing response to fontanel compression as manifested by increasing changes in arterial RI can be an indication for shunt placement in infants with rapidly progressive hydrocephalus.
Sonographic evaluation of the thoracolumbar spine in infants with meningitis might reveal the presence of echogenic debris within the spinal subarachnoid space. This finding has been associated with a higher risk of progressive hydrocephalus [60].
Conclusion
Cranial sonography continues to be an excellent front-line imaging modality in the initial diagnosis and monitoring of infants with acute bacterial meningitis and its potential complications. Its utility is enhanced by the use of alternative scanning approaches and Doppler techniques for identification of ventriculitis, extra-axial fluid collections, and hemodynamic alterations. Spinal sonography might also play a role in assessing the risk of progressive hydrocephalus.

meningitis
doppler
children
ultrasonography
bacterial infections
central nervous system infections


Contrast discrimination: Second responses reveal the relationship between the mean and variance of visual signals

To explain the relationship between first- and second-response accuracies in a detection experiment, Swets, Tanner, and Birdsall [Swets, J., Tanner, W. P., Jr., & Birdsall, T. G. (1961). Decision processes in perception. Psychological Review, 68, 301–340] proposed that the variance of visual signals increased with their means. However, both a low threshold and intrinsic uncertainty produce similar relationships. I measured the relationship between first- and second-response accuracies for suprathreshold contrast discrimination, which is thought to be unaffected by sensory thresholds and intrinsic uncertainty. The results are consistent with a slowly increasing variance.
1
Introduction
First applied to psychophysical data by Tanner
and Swets (1954), signal-detection theory (SDT) posits that
all stimuli elicit some sensation. However, due to noise, sensations experienced
in the absence of stimulus can sometimes be more intense than sensations
actually elicited by a stimulus. Crucial evidence for these faint hallucinations
comes from Swets, Tanner, and Birdsall’s
(1961) two-response, four-alternative forced-choice (2R4AFC)
detection experiment, in which observers reported both their first and second
choices for the temporal position of a visual target.1 SDT
predicts that second-guessing should be better than chance, and this is what
Swets et al. found.
1.1
Signal-detection theory
According to SDT (Green & Swets,
1966), each stimulus X, gives rise
to a Gaussian probability-density function (PDF)of sensory intensity x. In its simplest
form, all PDF’s have the same standard deviation, i.e.,
σX = σ,  ∀X.
1.2
Increasing variance
Simple SDT proved incapable of explaining Swets et al.’s (1961) 2R4AFC detection experiment.
Instead, they proposed that sensation variance increased with sensation mean:Increases in the “sigma-to-mean ratio”2
r = dσX/dμX,
produce decreases in both first- and second-response accuracies, but the
second-response accuracies to decrease faster. Swets et al. tried several
values for this ratio and obtained as good fit to their data when
r = 0.25.
1.3
Intrinsic uncertainty
Elsewhere (Solomon, 2007),
Swets et al.’s (1961)
2R4AFC data have been successfully fit with an alternative model,
incorporating intrinsic uncertainty. Intrinsic-uncertainty models posit that
perceived intensity depends on the maximum activity in several independent
sensory mechanisms, only one of which is actually sensitive to the stimulus.
Given a sufficient number M, of these mechanisms, the
variance of their maximum activity will decrease as the intensity of the
stimulus decreases (see Pelli,
1985, for a graphical demonstration of this). Thus, to
some degree, intrinsic uncertainty mimics Swets et al.’s proposal of
increasing variance. With suprathreshold stimuli, the maximum activity
always occurs in the appropriately tuned mechanism, and the others have no
influence on perception.
1.4
Low-threshold theory
At odds with SDT is the idea of a sensory threshold, which weak stimuli
must exceed to be detected. In a detection task, stimuli that do not exceed
the threshold can be selected only when no other stimulus exceeds it, and
the observer is forced to make a choice. Swets
et al. (1961) developed this idea into a
“low-threshold” hybrid of signal-detection and threshold
theories. Unlike other models with this name, Swets et al. claimed theirs
could fit the 2R4AFC results. Elsewhere (Solomon, 2007), I have corroborated this claim, and
shown that the fit is not quite as good as those produced by models
including either intrinsic uncertainty or increasing variance.
1.5
This study
Neither intrinsic uncertainty (Pelli, 1985; Tanner, 1961) nor Swets et al.’s (1961) low-threshold
theory requires sensation variance to increase with sensation mean. These
theories are somewhat special because they are thought to affect the
visibility of only very faint stimuli. Increasing variance, on the other
hand, has implications for suprathreshold contrast discrimination. For this
reason, I decided to conduct a 2R4AFC contrast-discrimination experiment.
The goal was to obtain an estimate of the sigma-to-mean ratio, which would
not be contaminated by intrinsic uncertainty or a low threshold.
2
Methods
There were five observers: the author (JAS), another psychophysicist who
understood the purposes of the experiment (MJM), two experienced psychophysical
observers who were naïve to the purposes of this experiment (FV and MT) and
one further observer who had no previous laboratory experience (NN). As
described below, NN produced a very high proportion of “finger
errors.” This suggested to us a general unreliability, and no further
analyses were performed on his data.
The Psychophysica (Watson & Solomon,
1997a) software used in these experiments is available at
http://vision.arc.nasa.gov/mathematica/psychophysica.html.
The 23.5-cd/m2 display (a Sony GDM F-520 CRT) was viewed in a
dark room from 1.15 m. Luminances of vertically adjacent
pixels were effectively independent, and could obtain any value between 1.06 and
46 cd/m2. Stimuli were horizontal,
cosine-phase Gabor patterns whose wavelength and spatial spread were
λ = 0.25° and σ = 0.18°, respectively. Stimuli were flashed simultaneously, in
four positions, each marked by four dark spots. The centers of these positions
formed a 5.6° × 5.6° square
centered on fixation (see Fig.
1).
On each trial, three stimuli appeared with a pedestal contrast, which
varied between blocks of 90 trials each. The contrast of the fourth stimulus was
somewhat greater. After each 0.18-s stimulus exposure, observers gave two
responses. The first response indicated which of the four positions the observer
thought most likely to have contained the high-contrast target. The second
responses from JAS and MJM indicated their second choices for the target
position. Following their second responses, JAS and MJM received auditory
feedback indicating which—if either—of their responses was
correct.
The naïve observers were not told that three of the four stimuli would
have the same contrast. They were instructed merely to indicate their choices
for the positions containing the two highest contrasts, in order. This
encouraged them to fully consider their second responses, even when they felt
confident about their first. The naïve observers received no
feedback.
Although I was primarily concerned with suprathreshold contrast
discrimination, I was also eager to replicate Swets
et al.’s (1961) findings at detection threshold. Since
I was therefore committed to measuring both the left and right ends of the
threshold-vs.-contrast function (Nachmias &
Sainsbury, 1974; Fig.
2), I decided to devote a few
extra trials to get the middle as well. (Note: due to limited availability, FV
performed only the critical conditions, i.e., those with supra-threshold
pedestals.)
Table 1 shows the number of trials each observer performed with each
pedestal contrast. In it, and in the discussion below, I use the conventional
decibel scale of contrast energy: if m is the maximum
available contrast, then an x dB stimulus is one that has
a contrast of
m10x/20.
Prior to each trial, the quest procedure (Watson & Pelli, 1983) estimated the performance
threshold ct, i.e., the contrast
increment required for 62%-accurate first responses. This is halfway between
chance performance (25%) and a hypothetical ceiling of 99%.
As a means of more accurately estimating the ceiling, or equivalently, the
frequency of finger errors, a −10 dB increment was used
on one-ninth of the trials. For JAS, the target was given an increment of either
ct − 2 dB or
ct + 2 dB, with equal probability, on the remaining
trials. For the other observers, target increments were either
ct − 2 dB or
ct . This modification allowed
better sampling of their psychometric functions. Finally, to further encourage
the naïve observers to fully consider their second responses, one of the
three alternatives to each of the “obvious” (−10 dB) targets was fixed at −16 dB.
3
Results
3.1
Psychometric functions
For each observer and each pedestal, first-response accuracies were
maximum-likelihood3
fit with a modified Gaussian distribution.In the preceding expression, c is the
increment (in dB), Ψ1 is the
probability of a correct first response and f is the
PDF defined in Eq. (1). Threshold
ct, and
σ were free parameters, but the frequency
of finger errors δ, was not allowed to vary
with pedestal contrast. These psychometric fits were obtained for purely
descriptive purposes. Unlike some of the fits described below, these were
not driven by any particular model of performance. Best-fitting values for
δ were 0.006, 0.002, 0.048, 0.018 and 0.095
for JAS, MJM, FV, MT and NN, respectively. When debriefed, NN reported a
tendency to respond before the end of a trial.
3.2
Threshold-vs.-contrast functions (first response
only)
Fig. 2 shows how threshold
varies with pedestal contrast. JAS’s and MJM’s thresholds were
similar, and formed the classic “dipper” shaped function. MT did
not suffer as much masking. That is, his thresholds with high-contrast
pedestals were lower than the JAS’s and MJM’s. However, his
detection threshold—obtained with pedestals having zero contrast (or
−∞ dB)—was similar: between −24 and −23 dB. FV’s thresholds with high-contrast pedestals fall
within the range spanned by the other observers’, thus we can be
reasonably confident that these pedestals exceeded her detection threshold,
as they did for the other observers.
3.3
Second-vs.-first-response-accuracy functions:
Detection
Fig. 3 shows how first- and second-response accuracies co-varied
when, as in Swets et al.’s
(1961) experiment, there was no pedestal. Appendix
A contains a full description
of the raw data. Several features of Fig.
3 deserve a detailed description.
The axes differ from those used by Swets et
al. (1961). For the horizontal axes, instead of signal
strength, which may not be a linear function of contrast, I prefer
first-response accuracy Ψ1. For
the vertical axes, Swets et al. used second-response accuracy, divided by
the proportion of first-response errors. However, both first- and
second-response accuracies are subject to measurement error. When one
uncertain statistic is divided by another, the confidence intervals for the
quotient are necessarily very large. To avoid this problem, I get rid of the
denominator and plot simply second-response accuracy
Ψ2.
One argument against this way of plotting the results is that a large
portion of the graph will be wasted because
Ψ2 ⩽ 1 − Ψ1. A dotted line has been
added to each graph to indicate this upper limit for second-response
accuracy. Similarly, Ψ2 ⩽ Ψ1. Of course, given a
finite number of trials, we may find that the frequency of correct second
responses P2 exceeds the frequency
of correct first responses P1, but
only a perverse observer would have a greater
probability of being correct in his or her second
response. Therefore I have added another dotted line to each graph to
indicate this other upper limit for second-response accuracy.
Each point in Fig. 3
represents data collected with a unique target contrast. Several of these
points reflect only a few responses made at the beginning of the experiment,
before the adaptive staircase had converged. We can thus have little
confidence in the likelihood of a correct first or second response with
these targets. To convey this confidence (or lack thereof), I have plotted
95% confidence intervals, both horizontally and vertically, about each
point. These intervals are based on binomial probabilities, calculated from
the range defined by the limits described in the preceding paragraph (see
Appendix B for details).
3.4
Modeling finger errors
SDT can be modified to accommodate finger errors. Let
ψ1 denote the first-response
accuracy without errors. For those trials containing a first-response finger
error, the probability of a correct first response is (1 − ψ1)/3. Thus, if the
finger-error rate is δ, the overall probability
of a correct first response is (1 − δ)ψ1 + δ(1 − ψ1)/3.
To derive the formula for second-response accuracy, it helps to
understand that first-response finger-errors will be incorrect with
probability 1 − [(1 − ψ1)/3] = (2 + ψ1)/3. Without loss of
generality, we may assume that observers correct some proportion
ε of first-response finger errors with
their second response. Thus on these trials, the probability of a correct
second response is ψ1. When
first-response finger-errors are not explicitly corrected, I will assume
that the second response is completely random. On these latter trials, the
second response will be correct with probability [(2 + ψ1)/3]/3 = (2 + ψ1)/9. Thus, on those
trials in which a first-response finger error occurred, the second-response
accuracy should beSecond-response accuracy overall will be (1 − δ)ψ2 + δ
[εψ1 + (1 − ε)(2 + ψ1)/9], where
ψ2 would have been the
second-response accuracy, had there been no first-response finger
errors.
To estimate ε, trials containing an
“obvious” (−10 dB) increment and an
incorrect first response were examined. (Because the highest pedestals had
the potential for masking even these large increments, they were excluded
from this analysis.) On these trials, we may assert that
ψ1 = 1, and we can then solve Eq. (4) for ε.
Solutions were 0.70, 0, 0.58 and 0 for JAS, MJM, FV and MT,
respectively.
3.5
Maximum-likelihood fits
These values of ε were assumed when
calculating the curves in Figs.
3–6. In Fig. 3, the solid black curves represent the
prediction of simple SDT, that is, when r = 0 in Eq. (2). The dashed lines represent the prediction of
high-threshold theory, which ascribes all errors to unlucky guesses rather
than faint hallucinations. (See Swets et al.,
1961 or Solomon,
2007, for derivations of these predictions.)
Maximum-likelihood fits were also obtained for three further
modifications of SDT. They were: (i) increasing variance with power-law
transduction, (ii) intrinsic uncertainty and (iii) low-threshold theory.
Details of these three models can be found in Appendix C, and receiver-operating characteristics
for all three models applied to a yes/no-detection task appear in
Nachmias (1972). The fits
appear as solid green, blue and red curves, respectively, in Fig. 3.
Goodness-of-fit is indicated by the generalized (log) likelihood-ratios
in Table 2. Specifically, these values reflect the maximum log
likelihoods, minus the conventional upper-bound on log likelihood described
in Footnote 3. Note that unlike
some generalized likelihood-ratios (Mood,
Graybill, & Boes, 1974), these cannot be expected to
follow the chi-square distribution because there are so many conditions
(i.e., specific increment contrasts) containing only one or two trials
(Wichmann & Hill,
2001).
Only for JAS, low-threshold theory produced, by far, the best fits of
the three SDT models. In fact, the best-fitting “low” threshold
for JAS was effectively a high threshold, never exceeded by zero-contrast
pedestals. That is why JAS’s red curve in Fig. 3 is visually indistinguishable from the dashed
black line. Since JAS’s results are consistent with a high threshold,
they are inconsistent with the findings and conclusions of Swets et al. (1961).
For the other two observers, the sigma-to-mean ratios of the
best-fitting increasing-variance models were between 0.26 and 0.28; similar
to Swets et al.’s (1961)
estimate of 0.25. Thus, these results can be considered a successful
replication of Swets et al.’s. At the end of this section, I speculate
on why JAS’s results differ.
3.6
Transducer-independent estimates of
r
At detection threshold, as described above, the raw data were simply
fit with a multiplicative-noise/power-law-transducer version of SDT.
However, with suprathreshold pedestals, we cannot be certain what shape the
transducer takes. Increasing-variance models (e.g., Kontsevich, Chen, & Tyler, 2002) use a
simple power-law transducer, but constant-noise models (e.g., Legge & Foley’s, 1980), use a
transducer that is initially expansive, then compressive, as the pedestal
increases. The compressive non-linearity is required to produce masking;
i.e., threshold elevation from high-contrast pedestals.
We do not really have to worry about the form of transducer, because
SDT’s predictions for the relationship between first- and
second-response accuracies are independent of signal transduction
(Solomon, 2007; Swets et al., 1961). We merely need to
quantify how these predictions change with the sigma-to-mean ratio, and find
the values most consistent with the data. This examination of a
transducer-independent facet of contrast-discrimination data is
complementary to attempts at modeling contrast-discrimination data without
putting any constraint on the form of the transducer (Katkov, Tsodyks, & Sagi, 2006a; Katkov, Tsodyks,
& Sagi, 2006b; Klein,
2006).
Transducer-independent estimates of the sigma-to-mean ratio
r were obtained by maximizing the likelihood of
observing second-response accuracies
P2, given the first-response
accuracies P1. A complete
description of this process appears in Appendix D. The best fits were 0.56 for JAS, 0.32 for MJM and
0.31 for MT. These values are illustrated in Fig.
4. All of these fits are comparable to the
maximum-likelihood fits described above.
3.7
Binning accuracy
Fig. 4 is less cluttered than
Fig. 3. It has fewer data
points and no horizontal confidence intervals. Nonetheless, the same data
appear in both figures. For legibility, I have decided to combine data from
increments producing similar first-response accuracies, as determined by the
psychometric functions described above. I have adopted the relatively
arbitrary decision to use 5 dB bin-widths. There is one
visible consequence of this manipulation: a rightward shift for one data
point in JAS’s panel. However, without binning, the suprathreshold
data presented below would be impossible to read.
I have also decided to forgo plotting data from increments producing
both floor (i.e., 0.25) and ceiling (i.e., 1 − δ, see Eq.
(3)) accuracies. Such data are
worthless at discriminating between candidate models. Finally, also for the
sake of legibility, I have also decided to cull data points representing
fewer than 10 trials. Of course, these latter data are not completely
worthless; they have not been excluded from any model fits. A complete
description of the binned data appears in Appendix A.
3.8
Second-vs.-first-response-accuracy functions: Suprathreshold
discrimination
Fig. 5 shows how first- and
second-response accuracies co-varied for the four highest pedestals. (The
binned data are tabulated in Appendix A.) Plotting conventions have been inherited from
Fig. 4.
It should be apparent that the second responses with these
suprathreshold pedestals tend to be more accurate than the second responses
at detection threshold. Using the same procedure as was described for the
detection data (above and in Appendix D), values for the sigma-to-mean ratio
r were found that maximized the likelihood of
observing second-response accuracies
P2, given the first-response
accuracies P1. The best fits were
0.11 for JAS, 0.16 for MJM, 0.21 for FV and 0.09 for MT. These values are
illustrated in Fig. 5.
These values of r are smaller than those
required to fit the detection data. FV’s relatively high value may
have something to do with her relatively high finger-error rate. No
detection data from FV are available for comparison.
Pedestal-by-pedestal estimates of r appear in
Fig. 6. Most of these
estimates remain near or below the value of 0.25, selected by Swets et al. (1961), when neither the
effect of a low threshold nor that of intrinsic uncertainty is considered.
The results from JAS are different; best-fitting values of
r start at 0.56, and decrease to 0 as pedestal
intensity increases.
JAS’s small-pedestal estimates of r are
strangely high. As noted above, they are not incompatible with the notion
that visual noise never exceeds the threshold of visibility in the absence
of a stimulus. Previous attempts to replicate Swets et al.’s (1961) 2R4AFC results have also met
with mixed success. Despite their chronological precedence, Kincaid and Hamilton’s (1959) results
have been described as both successful and unsuccessful replications of
Swets et al.’s (Green & Swets,
1966 and Blackwell,
1963, respectively). As yet, I have not been able to
track down a copy of Kincaid and Hamilton’s publication. One further
attempt to replicate Swets et al. was described by Eijkman and Vendrik (1963). They reported
that second responses for light detection were greater than chance in just
one of three observers.
An alternative interpretation for JAS’s high-threshold-like
performance is that he simply ignored sensory information and selected his
second responses more-or-less randomly. This explanation would be easier to
swallow if all his estimates of r were high. However,
with suprathreshold pedestals, his r is no higher
than that of the other observers. Expectation may have caused JAS to change
his strategy with pedestal intensity, but I have no definitive
answer.
4
Discussion
The most equitable summary of these results is that they are consistent
with a performance-limiting source of noise, which increases slightly with
suprathreshold contrast.
Best estimates for the rate varied from 0.09 to 0.21. I wondered whether
such small sigma-to-mean ratios would be sufficient to model the high
contrast-discrimination thresholds obtained with high-contrast pedestals, or
whether a saturating transducer function for stimulus contrast would also be
necessary. Previous attempts (Kontsevich et al.,
2002; Solomon,
2007) to fit contrast-discrimination data without compressive
transduction have not focused on the minimum necessary sigma-to-mean ratio, but
that ratio can be inferred from the published parameter values.
4.1
Fitting contrast discrimination
In those previous attempts, the standard deviation of visual signals
was allowed to increase as a decelerating power function of the mean. Specifically,(Kontsevich et al. considered only suprathreshold contrast and
thus could set σ0 = 0; Solomon used
σ0 = 1.) Therefore, the sigma-to-mean ratios decreased
as the means increased. From the best-fitting parameter values, I have used
a contrast of 100% to infer the minimum sigma-to-mean ratios required to
explain contrast discrimination without compressive transduction. The
smallest of these ratios was 0.13 (obtained using the parameter values fit
to observer SV with “sustained” stimuli in Kontsevich et al., 2002). Thus it seems
that the sigma-to-mean ratios estimated in the present study may in fact be
able to produce appreciable masking.
Four different models were maximum-likelihood fit to all of
JAS’s, MJM’s and MT’s 2R4AFC data. Details of all four
models appear in Solomon (2007).
One of these models was a four-parameter, non-linear transducer model with
constant Gaussian noise (i.e., where r = 0). This transducer is initially
expansive, then compressive, as the input increases. Foley (1994) obtained good fits to 2AFC
contrast-discrimination thresholds with this model, but we already know this
model will over-estimate second-response accuracies, particularly in a
(zero-pedestal) detection experiment (Solomon,
2007; Swets et al.,
1961).
In the other three models that were fit to JAS’s, MJM’s and
MT’s data, the variance of visual signals was allowed to increase with
the mean. Two of these models have already proven capable of producing
acceptable fits to some of Foley’s
(1994) 2AFC thresholds (see Fig. 13 of Solomon, 2007). In one of these, a
power-law transducer is responsible for the ‘dip’ in the
contrast-discrimination function. In the other, intrinsic uncertainty
produces the dip. The remaining increasing-variance model explored in this
paper uses a low threshold to produce the dip.
Fit details appear in Table
3. Initially, four
parameters were allowed to vary freely in each fit. For JAS and MJM the
best-fitting model was the one with increasing variance model and intrinsic
uncertainty. In general, the fits improved as uncertainty
M, increased. For JAS and MJM, the fits of the
increasing-variance/intrinsic-uncertainty model remained superior when
M was fixed at a value of 10,000. When the
relationship between signal mean and standard deviation was forced to be
linear (i.e., q = 1 in Eq. (5)), the fits of the
increasing-variance/intrinsic-uncertainty model remained superior. They even
remained superior when M was fixed at a value of
1000. Thus, all of JAS and MJM’s data can be satisfyingly summarized
by a relatively simple model, combining increasing variance with intrinsic
uncertainty. Within the context of this model the best-fitting values of
r (regardless of constraints on
M or q) were 0.16 for JAS
and 0.14 for MJM. These values are nearly identical to the
transducer-independent estimates (0.14 for JAS and 0.16 for MJM), described
above.
When MT’s data were fit with a 3-parameter
increasing-variance/intrinsic uncertainty model, the best-fitting values for
the sigma-to-mean ratio and intrinsic uncertainty were
r = 0.11 and
M = 440,
respectively. However, his data are best-fit by the constant-variance,
4-parameter, nonlinear-transducer model (Foley,
1994). Thus, in two out of three cases, the
contrast-discrimination data can be satisfyingly summarized by a 3-parameter
model of intrinsic uncertainty and increasing variance. Compressive
transduction is not required.
4.2
Sensory thresholds for contrast
discrimination
Although “sensory threshold” means different things to
different people (Swets et al.,
1961), it is usually understood to be some sort of
barrier weak stimuli must overcome to be perceived (Swets, 1961). However, it is no less valid
to apply the concept to the task of contrast discrimination, even with large
pedestals. That is, forced-choice errors may occur simply because all the
alternatives appear identical and the observer simply guesses
incorrectly.
Inspection of Fig. 5 should
be sufficient to rule out any “high” sensory threshold for
contrast discrimination. The data shown there are even less similar to the
(dashed) high-threshold prediction than Swets et
al.’s (1961) detection data (not shown). However,
some proportion of correct second responses may indeed have been just lucky
guesses, which is to say my data cannot rule out a “low
threshold” for “suprathreshold” contrast
discrimination.
4.3
Other models
The logic of this study hinges on the assumption that unmasked,
suprathreshold contrast discrimination can be modeled with a single sensory
mechanism. Although this assumption is popular, it is not completely
uncontroversial. Before I describe other possible models, I should first
stress the importance of the word “unmasked.” In a highly
influential paper, Foley (1994)
argued that the mechanism responsible for contrast discrimination was not
immune to the activity in differently tuned mechanisms. By manipulating the
spatial phase, orientation and temporal frequency of masking stimuli,
Foley and Boynton (1994) were
able to probe the interactions between mechanisms responsible for contrast
discrimination. However, when no masks are present, most models (including
all of Foley’s) consider contrast discrimination to be mediated by a
single mechanism or channel; the one best tuned to the target.
There are three notable exceptions. Teo and
Heeger (1994) and Yu, Klein,
and Levi (2004) have developed models with greater
physiological plausibility, in which individual mechanisms have very limited
dynamic ranges. Elsewhere (Watson & Solomon,
1997b) I have argued this type of model is well
approximated by the more popular, single-mechanism model for contrast
discrimination. The two types of model can be considered equivalent when
performance-limiting noise is added after the outputs of multiple mechanisms
are combined.
The third exception was recently proposed by Henning and Wichmann (2007) to account for their finding
that the low-contrast “dip” of threshold-vs.-contrast functions
(e.g., Fig. 2) disappears in the
presence of a notched-noise mask. This result suggests the dip is due to
off-frequency looking. That interpretation may be correct, but I am
obligated to note their results are also consistent with intrinsic
uncertainty, which would attribute a less-pronounced dip to uncertainty
reduction. Indeed, Blackwell
(1998) argued that noise, both within the
detector’s pass band and outside it, could reduce intrinsic
uncertainty and facilitate detection. She also provided psychophysical
evidence for this facilitation.

contrast discrimination detection threshold uncertainty psychophysics noise