Neuroimaging of Semantic Processing in Schizophrenia: A Parametric Priming Approach

Abstract

The use of fMRI and other neuroimaging techniques in the study of cognitive language processes in psychiatric and non-psychiatric conditions has led at times to discrepant findings. Many issues complicate the study of language, especially in psychiatric populations. For example, the use of subtractive designs can produce misleading results. We propose and advocate for a semantic priming parametric approach to the study of semantic processing using fMRI methodology. Implications of this parametric approach are discussed in view of current functional neuroimaging research investigating the semantic processing disturbance of schizophrenia.

Introduction

Since the seminal works of German neurologist Carl Wernicke in the 1800’s, the neural basis of language comprehension has been the focus of considerable research (see Norris and Wise, 2000; Brown, Hagoort, and Kutas, 2000; for a review). As in the case of Wernicke, lesion and aphasia studies have served as one of the most profitable ways to investigate the neural substrate of language comprehension. Wernicke’s work suggested lesions of the left temporal lobe produced an inability to comprehend and process language, although the ability to produce language was preserved (Purves et al., 1997). Sperry’s landmark studies (e.g., 1974) with split-brain patients dramatically affirmed the left lateralization of language processing.

Several recent lesion studies have clarified the role of the left temporal lobe in lexico-semantic language comprehension (Graff-Radford et al., 1990; Gainotti et al., 1995; Funnell, 1995; Hodges et al., 1992; Caramazza and Berndt, 1978). Caramazza and Berndt (1978) presented a review of aphasia studies that mostly implicate left hemisphere regions. A lesion analysis showed that left posterior temporal/inferior parietal regions produced deficits of comprehension at the single word level (Hart and Gordon, 1990). Hodges et al. (1992) present multiple cases of semantic dementia with evidence implicating the left temporal lobe structures. Graff-Radford et al. (1990) presented a case of a right-handed physician diagnosed with Pick’s Disease, a neurodegenerative disorder, who had a “progressive difficulty with language (pg. 620)” and few other symptoms. The patient at first had difficulty learning new names of people he would meet. His difficulty progressed such that in a follow-up assessment he was inappropriately linking semantically related words in speech (e.g., “Jill, how is your work doing in out office?”[pg. 621]). The authors raised the striking point that grammar structure and punctuation is maintained in the midst of this lexico-semantic deficit. After the patient’s death, neuropathologic findings revealed a significantly smaller left hemisphere versus the right hemisphere, and a significantly smaller temporal pole, inferior and middle temporal gyri, anterior part of the superior temporal gyrus, and insula, all in the left hemisphere. Gainotti et al. (1995) conducted a meta-analysis of lesion case studies and revealed a consistent finding of the left temporal lobe implicated for semantic category impairment of object nouns. They review and present additional evidence for the hypothesis of lesions of the inferior temporal and temporal limbic structures constituting the pathophysiology of semantic disorders specifically related to living beings. Moreover, the authors highlight a controversy in lesion studies regarding selective language impairments.

Even though the traditional focus has been on the left hemisphere for language and semantic processing, several lines of evidence show that the right hemisphere does process auditory word and semantic representations. Evidence from the study of pure word deafness and other sources shows that speech sounds are processed bilaterally in the superior temporal region (Hickok and Poeppel, 2007). A study using single unit recording during neurosurgical procedures reported that both right and left hemispheres showed a similar number of units responsive to linguistic material; the left responses tended to be multi-modal and the responses on the right were unimodal (Ojemann et al., 2002). Category specific impairments can also be a result of either right or left damage (e.g.Tranel et al., 1997).

Some language structure empiricists posit that there is a lexical (word) representation that mediates between more semantic (conceptual) content and phonological (sounds) or orthographic (visual) elements (Damasio et al., 1996; but see Caramazza, 1996; 2000 for an opposing view). Many of these authors believe in a serial processing of language such that information flows from an independent semantic level to an independent lexical level to the phonological level and vice versa. These same investigators also believe that the impairments described above could solely exist at the lexical level of processing (e.g., Miceli et al., 1988; Caramazza and Berndt, 1978). Other investigators believe that lexical and semantic attributes are more or less processed simultaneously, and that the impairments described above are inclusive of a semantic level disruption (e.g. McCarthy and Warrington, 1985; Churchland and Sejnowski, 1988; Warrington, 1975).

Functional Neuroimaging and Semantic Processing

While Wernicke’s subjects most effectively refuted or supported his hypotheses posthumously (when their brains were examined), the subjects of today’s researchers can do this in vivo through extraordinary strides in brain imaging technology and experimental designs developed from recent advances in the understanding of neurobiological hemodynamics. Two methods of functional brain imaging are among the most common: positron emission tomography (PET) and magnetic resonance imaging (MRI). Several recent imaging studies have attempted to clarify the sites of semantic representations in the brain, and some of these are overviewed in Table 1. In studying language using neuroimaging, activity in one condition is usually compared to a second condition and/or to the baseline or resting state in the experiment. Unfortunately, several language related regions of the brain are also used during the baseline or resting state, making estimation of true language related activity difficult (see Raichle and Snyder, 2007 for a discussion of default mode activity). In addition, many of the studies of semantic and lexical processing employ what is known as the subtraction method (e.g., Pugh et al., 1996). This method assumes that the specific site of activity may be determined by subtracting the activation caused by a lower level representation or earlier stage of processing from the activation caused by the higher order representation of interest or later, more elaborated stage of processing. By “parceling out” the lower level representations, it is believed that the sites remaining are specific to the higher order representation. Although some of these studies show activation of temporal regions during semantic processing that would be consistent with the lesion literature, the activations were often either very small (Demonet et al., 1992; Price et al., 1997; Pugh et al., 1996) or no activation of temporal lobe regions was found when the lexical condition was subtracted from the semantic condition in order to isolate semantic processing (Petersen et al., 1988; Roskies et al., 2001; Fujamaki et al., 2000; Crosson et al., 1999; in Pugh et al., 1996, females showed no temporal lobe activation in semantic condition). Several of these subtraction studies did find inferior prefrontal activation that was attributed to semantic processing. This discrepancy between neuroimaging and lesion studies is more evident in the literature using the levels of processing task in which words are presented in the context of either a superficial or non-semantic task (e.g. is the word printed in upper or lower case?) versus a condition where words are presented in the context of a semantic task (e.g. is the word a living or nonliving object?). When the superficial or non-semantic task activation is subtracted from activation during performance of a semantic task in these studies, they consistently do not find temporal lobe activation that is related to semantic or deep as apposed to shallow processing; but they do consistently find LIPC activation (Buckner et al., 2001; Otten et al., 2001; Poldrack et al., 1999; Demb et al., 1995; Kapur et all, 1994; Petersen et al., 1988).

Table 1.

Citation	Type of Scan	Specifications	Type of Reference (Control) Task	Orthographic	Phonological	Semantic
Demonet et al., 1992	PET		Auditory		Auditory	Auditory
		Stimuli:	Tone triplets		Non-words	Adjective-noun pairs
		Task:	Monitor for rising pitch		Monitor for /b/ proceeded by /d/	Monitor for nouns of small animals with positive adjective
		Areas Implicated (and/or results):			Left and right STG, left inferior frontal (Broca’s area).	Left inferior temporal (very small), left inferior parietal, left prefrontal areas 8,9 (very small), superior frontal, left precuneus and posterior cingulate.
Pugh et al., 1996	fMRI		Visual	Visual	Visual	Visual
		Stimuli:	2 sets of visual lines (e.g. / /\/)	2 sets of letter strings in different cases (e.g. BtBT)	2 rhyming or nonrhyming nonwords (e.g. Lete - Jeat [rhyming])	2 categorically related or unrelated words (e.g. Corn - Rice [related])
		Task:	Same or different pattern?	Same pattern of upper/lower case alternation?	Rhyme or not rhyme?	Same category?
		Areas Implicated (and/or results):		Lateral extrastriate	Wide number of frontal and temporal regions Lateral orb, prefrontal dorsol and inferior frontal more associated with phonological than semantic	Middle and superior temporal gyri (males, but not females, showed more activity in category-line or case than rhyme-line or case).
Price et al., 1997	PET		Auditory		Auditory	Auditory
		Stimuli:	150 words corresponding to familiar objects		150 words corresponding to familiar objects	150 words corresponding to familiar objects
		Task:			How many syllables for each word?	Living or non-living object?
		Areas Implicated (and/or results):			Left temporal pole, left posterior middle temporal gyrus, head of the left caudate nucleus; less so left middle temporal gyrus, left inferior temporal gyrus, left superior temporal sulcus, and left medial superior frontal gyrus	Both supramarginal gyri, right angular gyrus, left precentral gyrus, left cuneus; less so left superior temporal gyrus and right medial frontal gyrus
Crosson et al., 1999	fMRI		Visual	Visual	Visual	Visual
		Stimuli:	Nonsensical consonant strings	2 test words sharing letters with any of 3 memory words	2 test words rhyming with any of 3 memory words	2 test words semantically related to any of 3 memory words
		Task:	Monitor for whether test word begins and ends with the same letter.	Monitor for whether test word has last three letters the same as any of 3 memory words.	Monitor for whether test word rhymes with any of 3 memory words.	Monitor for whether test word is semantically related to any of 3 memory words.
		Areas Implicated (and/or results):		Left prefrontal (Broca’s area), selective area of left lateral premotor (BA 6), extrastriate visual cortex	Selective areas of inferior frontal (BA 45, 46), selective areas of left lateral premotor (BA 6), left medial frontal, inferior temporo-occipital junction, left anterior thalamus, right cerebellum, midbrain	Left prefrontal (Broca’s area), selective area of inferior frontal (BA 47), left lateral premotor, left medial frontal, left posterior cortex (inferior temporal), brainstem-subcortical (left anterior and posterior thalamus)
Menard et al., 1996	PET		Visual	Visual	Visual	Visual
		Stimuli:	5 X’s or single crosshairs	Words	Words	Pictures
		Task:	Passive viewing	Passive viewing	Passive viewing	Passive viewing
		Areas Implicated (and/or results):		5 X’s: Left BA 19, left angular gyrus, left insula, left dorsolateral prefrontal; crosshairs: Left angular gyrus, dorsolateral prefrontal, Broca’s area, right inferior parietal, right frontal eye fields	Left angular gyrus, left supramarginal area, left Broca’s area, right supplementary motor area	Left BA 18 & 19, middle temporal, left paracentral, right BA 19, 17, & 18
Sergent et al., 1992	PET & fMRI		Visual
		Stimuli:	Point located in the center of a screen	Letters	Letters	Line drawings
		Task:	Concentrate on point	Normal or mirror-reverse orientation?	Has an “ee” sound or not (e.g. B, C, D, G, P, Z)?	Living or non-living?
		Areas Implicated (and/or results):		Left pulvinar, inferior parietal lobule, right inferior prefrontal gyrus	Left orbital frontal, left inferior frontal gyrus, left middle frontal gyrus	Left BA 18, fusiform gyrus, left lingual gyrus, left fusiform gyrus
Fujimaki et al., 2000	fMRI		Visual	Visual	Visual	Visual
		Stimuli:	Lines	Japanese pseudocharacters	Japanese katakana characters	String of Japanese katakana characters
		Task:	Vertical or horizontal?	Pseudocharacters contain horizontal element?	Does the character contain the target vowel?	Is the string a noun (or a verb) or meaningless?
		Areas Implicated (and/or results):		Lateral extrastriate cortex, posterior occipital-temporal sulcus, posterior inferior temporal area	Broca’s area/insula, posterior superior temporal sulcus, supramarginal gyrus, pre-central sulcus, supplementary motor area and anterior cingulate sulcus.	Lack of activation attributed to task.
Roskies et al., 2001	fMRI		Visual		Visual	Visual
		Stimuli:	Fixation stimulus		Word pairs	Word pairs
		Task:	Passive viewing		Rhyme or not rhyme?	3 different tasks: [1] Synonyms or not? [2] Easy categorization (i.e. Is the second word an exemplar of the first word?)? [3] Hard categorization?
		Areas Implicated (and/or results):			Left middle insular cortex, left precentral gyrus (Broca’s & −49, 3, 16), region (−55, −11, 38) in the left premotor cortex, right anterior thalamus, and many other areas not traditionally associated with phonological processing.	[1] BA 21 in middle temporal gyrus (weakly), [2] & [3] left medial and lateral opercular regions and left anterior region of the inferior frontal area, right cerebellar region
Hagoort et al., 1999	PET		Visual		Visual	Visual
		Stimuli:	Crosshair		German pseudowords	German Words
		Task:	Passive viewing		Reading	Reading
		Areas Implicated (and/or results):			Left inferior frontal gyrus, extriate cortex, middle fusiform gyrus, left superior temporal gyrus, left premotor cortex, cerebellum	Left lingual gyrus, right superior temporal gyrus, middle temporal gyrus, supplementary motor area, central parts of the cingulate
Wise et al., 1991	PET		Auditory
		Stimuli:	None		Nonwords	3 trials: [1] noun-noun word pairs semantically related or unrelated (e.g. fruit-apple and furniture shirt). [2] verb- noun word pairs semantically compatible or incompatible. [3] concrete noun.
		Task:	Instructed to “empty his mind”		Listen	[1] Signal when noun-noun pairs were semantically related. [2] Signal when noun-verb pairs were semantically compatible. [3] Think of a verb that is semantically compatible with the given noun and signal when done.
		Areas Implicated (and/or results):			Networks along both superior temporal gyri	[1] & [2] Networks along both superior temporal gyri. [3] Left posterior superior temporal gyrus, left posterior inferior frontal gyrus, left posterior middle frontal gyrus, supplementary motor area
Petersen et al., 1988	PET		Auditory & Visual
		Stimuli:	Fixation point	Visual words	Auditory words	Auditory & visual words
		Task:	Resting	Passive viewing	Speaking each presented word	Saying a use for each presented word
		Areas Implicated (and/or results):		Extrastiate cortex	Primary auditory cortex, left temporoparietal cortex, left anterior superior temporal cortex, inferior anterior cingulated cortex	Left inferior frontal area, BA 47
Sonty et al., 2003	fMRI		Visual
		Stimuli:	Pairs of all consonant strings		Visual words	Visual words
		Task:	Respond if letter strings were Identical		Respond only if word pairs are homonyms	Respond only if word pairs were synonyms
		Areas Implicated (and/or results):			Left inferior frontal gyrus, left posterior middle temporal gyrus, left anterior cingulate gyrus	Left inferior frontal gyrus, left anterior cingulate gyrus, left temporoparietal junction, left intraparietal sulcus, bilateral superior temporal sulcus
Suzuki and Sakai, 2003	fMRI		Auditory (Japanese)
		Stimuli:	Pairs of pseudowords		Sentences	Sentences
		Task:	Press one button if both had same accent pattern and another button if different		Press one button if the presented accent is correct another if incorrect	Press one button if the presented sentence is semantically correct and another if incorrect
		Areas Implicated (and/or results):			Bilateral precentral sulcus, right insula, left precentral gyrus, left intraparietal sulcus, bilateral superior temporal gyrus, anterior and posterior cingulated, cerebellum, and thalamus	Bilateral precentral sulcus, right middle frontal gyrus, left precentral gyrus, left supramarginal gyrus, bilateral superior temporal gyrus, left middle temporal gyrus, posterior cingulate, left caudate nucleus

The rather robust implication of the inferior frontal areas in lexico-semantic imaging studies argues for a network of concertedly working regions as the mechanism underlying semantic language processing. One tentative explanation offered by Roskies et al. (see also Wagner et al., 2001; Kotz et al., 2002; Copland et al., 2003; and Thompsen-Schill et al., 1997) is that the inferior frontal areas may correspond to “control processes” and the temporal areas may correspond to “semantic stores”. According to this hypothesis, the frontal areas would become activated to “access, select, gate, or retrieve semantic information” widely distributed in the temporal cortex, and their level of activation would vary according to a number of conditions, including level of semantic ambiguity and “difficulty” of semantic task.

Semantic Processing and Schizophrenia

Bleuler (1911/1950) stated, “Almost every schizophrenic who is hospitalized hears voices ‘voices,’ occasionally or continually.” Sibersweig and Stern (1996) claim that close to 74% of schizophrenic patients ‘hear’ things inaudible to the general populace. Auditory hallucinations are often seen as a hallmark symptom of schizophrenia, and are arguably the most significant forms of evidence pointing to a disease-based disruption in auditory language processing. Bleuler (1911/1950) also observed another particularly troubling phenomenon in schizophrenic language processing, namely the inappropriate intrusions of otherwise common associations. He and other researchers noted that the inappropriate intrusions were at times uniform in presentation, such that, “They result in a kind of speech error, in which a word that is strongly associated with a previous word in an utterance displaces contextually relevant parts later in the utterance or influences the next utterance (Spitzer et al., 1994, pg. 485).” These clinical observations were indicative of the general disruption in lexico-semantic language processing often observed in schizophrenia so much so that according to Bleuler, the associative disturbance characteristic of schizophrenic language was deemed one of the “4 A’s” (autism, ambivalence, affect, and association) of schizophrenia. The 4 A’s were historically viewed by Bleuler’s as fundamental characteristics of the schizophrenic disease. Informed by Bleuler’s original hypothesis, many researchers have focused upon schizophrenia’s impaired language processing using various word association paradigms (e.g., Chapman, Chapman, and Miller, 1964). Maher (1983) suggested that the associative intrusions and derailments characteristic of schizophrenic speech might be due to an overactive semantic priming effect. Most semantic priming tasks build upon the simple word association paradigm by incorporating a processing speed component as the dependent variable (see Neely, 1991, for a review). In these tasks two words are presented (most often visually). The initial word is often referred to as the cue or prime, and the subsequent word is often referred to as the target or probe (e.g. Vinogradov, Ober, and Shenaut, 1992; Moritz et al., 2001). The time between the beginning of the cue word and the beginning of the target word is referred to as the stimulus onset asynchrony (SOA), the time between the end of the cue word and the beginning of the target word is called the inter-stimulus interval (ISI), and the time between the end of the previous target word and the next cue word is known as the inter-trial interval (ITI). These are all illustrated in Figure 1.

Figure 1.

Semantic Priming Structure and Terms. SOA=stimulus onset asynchrony. ISI=inter-stimulus interval. ITI=inter-trial interval.

In a priming experiment, responses to a target word are consistently accelerated following a semantically associated cue word versus a semantically unrelated cue word, and this phenomenon is referred to as a priming effect (Meyer and Schvaneveldt, 1971). Performance on these tasks is thought to be a correlate of the speed of information running through human semantic association networks (Spitzer, 1997). One of two methodological approaches is generally typical of any semantic priming task: lexical decision or word pronunciation. For a lexical decision task, the subject is asked to identify whether the target word is a valid English word. For a word pronunciation task, the subject is asked to pronounce the target word.

Assuming that within normal individuals active associations quickly decay or are inhibited (Posner and Snyder, 1975), thus preventing them from intruding into discourse, Maher believed schizophrenic patients might have a disruption in the decay or inhibitory process (see Kwapil et al., 1990) and thus show an aberrant spread of activation in semantic networks. Drawing from the work of Meyer and Schvaneveldt (1971), who developed the lexical decision task and were the first to identify the lexical priming effect among normal subjects, Maher hypothesized that schizophrenic subjects would show an even greater priming effect. Furthermore, Maher et al. proposed that this deficit reflected a failure of fast, obligatory, automatic processing that is engaged by relatively short SOAs (Moritz et al., 2001).

A number of researchers have provided evidence in support of Maher’s hypothesis (Manschreck et al., 1988; Spitzer et al., 1994; Kwapil et al., 1990; Baving et al., 2001; Spitzer et al., 1993; Spitzer et al., 1993b; Weisbrod et al., 1998; Moritz et al., 2001; Moritz et al., 2001b; Moritz et al., 2002). However, a number of researchers have also provided evidence conflicting with Maher’s original hypothesis (Vinogradov, Ober, and Shenaut, 1992; Barch et al., 1996; Barch et al., 1999; Henik et al., 1995; Chapin et al., 1989; Blum and Freides, 1995; Passerieux et al., 1997). There are a number of postulated methodological reasons for the above authors’ contradictory findings, including a lack of consideration of length of illness (see Maher et al., 1996), medication effects (see Moritz et al., 1999), and differing levels of thought disorder (see Moritz et al., 2001).

Semantic Processing, Functional Neuroimaging, and Schizophrenia

We argue that the use of a parametric approach is preferable to the subtraction method given that lexical representations may automatically or obligatorily activate semantic representations, even when the task does not require it (Price et al., 1996; Poeppel, 1996; Binder et al., 1997) and also that the activation of lexical and semantic representations may at least partially overlap or may occur in a recursive manner. In sentence processing, it has been shown that the semantic representation of a word is activated before the word can be uniquely identified or before the isolation point of a word (Ven Petten et al., 1999).

If presentation of a word (lexical condition) can automatically activate semantic information, then subtraction of a lexical condition from a semantic condition would also remove part of the semantic activation associated with the word when a subtraction design is used. One method for alleviating this difficulty is to manipulate either lexical or semantic attributes in a parametric manner and to identify regions whose activation also varies with the manipulation.

This sort of parametric approach has been used to elucidate the regions associated with the phonological processing of words (see Hickok and Poeppel, 2007). Okada and Hickok (2006) used words that varied according to what they describe as neighborhood density. Neighborhood density refers to how many similar sounding “neighbors” there are for a particular word. High neighborhood density words have many words that sound similar to a particular target word, and low neighborhood density words have fewer words that sound similar. The investigators found greater activation for higher density words than lower density words in the middle and posterior regions of the superior temporal sulcus.

Our laboratory has used this parametric approach to examine semantic processing (Wible et al., 2006; Han et al., 2007). Since semantic relatedness between two words has been quantified based on the work of cognitive scientists (e.g., Nelson et al., 1993), differing levels of semantic processing can be manipulated within a task. One example of differing levels of semantic processing is illustrated by the concept of connectivity (Nelson et al., 1993). Connectivity refers to how many semantically associated connections exist between semantically associated words of a particular target word. The semantic priming paradigm offers an experimental structure that lends itself well to parametric approaches in the study of connectivity semantics. Assuming a spreading activation model of semantic processing, presentation of the prime and target words would result in a parallel and distributed cascading effect of activation spreading through semantically related networks of word knowledge. Word pairs high in connectivity would share more overlapping cortical processing space and would therefore show less activation than word pairs low in connectivity (see Figure 2).

Figure 2.

Whole-brain activation patterns to word pairs varying by connectivity (high, low, unrelated) for 13 control participants. High connectivity word pairs elicit the least activation, low connectivity word pairs elicit more activation, and unrelated word pairs elicit the most activation across left temporal and frontal regions associated with semantic processing.

Using this as our theoretical rationale, we recently provided the first neuroimaging evidence to support a breakdown in the lexical-semantic processing abilities of participants with schizophrenia in left and right frontal and temporal lobe regions using a semantic priming parametric approach (Han et al., 2007). Employing a three-step parametric approach to assess lexical-semantic processing (high connectivity, low connectivity, and unrelated word pairs), we showed that schizophrenia patients were abnormal when compared to matched controls at processing our three-step parametric of high connectivity < low connectivity < unrelated word pairs, and that this semantic processing abnormality was associated with language-related clinical symptoms as indicated by the Scale for the Assessment of Positive Symptoms (SAPS; Andreasen, 1984). More specifically, lexical-semantic abnormality in regions corresponding to Broca’s area, the supramarginal gyrus, the posterior middle and superior temporal lobes, and homologous regions in the right hemisphere were associated with auditory hallucinations.

Other researchers have investigated semantic processing in schizophrenia using functional neuroimaging (fMRI, PET) techniques, though few have focused their efforts specifically on semantic processing in schizophrenia. Kubicki et al. (2003) used visually presented words in a levels of processing (LOP) paradigm and showed left inferior frontal underactivation and superior temporal gyrus overactivation among schizophrenic participants. The authors reasoned this pattern as evidence for “a disease-related disruption of a distributed frontal temporal network.” Kuperberg et al. (2008) used sentences that varied according to abstract or concrete and congruous or incongruous to test the hypothesis that schizophrenia patients may not adequately recruit the dorsolateral prefrontal cortex for more demanding semantically integrative processes. The authors found that while schizophrenia patients were able to recruit left temporal and inferior frontal cortices in a comparable way to control participants, they failed to show activation in the dorsolateral prefrontal cortex, medial frontal, and parietal cortices during incongruous (relative to congruous) sentences and in the dorsolateral prefrontal cortex to concrete (relative to abstract) sentences when compared to control subjects. Kircher et al. (2008) presented evidence in favor of reduced left hippocampal activity among schizophrenia patients while completing a semantic word generation task.

In conclusion, we advocate for the use of a semantic priming parametric approach to study semantic processing in schizophrenia. Future research is needed to determine the relevance of this functional neuroimaging approach to the study of clinical symptomatology and disease progression. Furthermore, future research is needed to compare the present approach to more traditional subtraction method approaches.