*2.1. Participants*

The study took place at the Department of Child and Adolescent Psychiatry, Psychotherapy and Psychosomatics of the Medical Center, University of Freiburg. Psychotherapists and general practitioners informed their patients about the study. They were then recruited by study staff. Some participants also became aware of the study via the local press or information on the Internet. Families did not receive any reward for their collaboration in the study.

Interested participants were instructed in detail on the procedure of the study, either in group meetings or individually. ADHD diagnoses were confirmed with Kiddie-SADS-Present and Lifetime Version (K-SADS-PL) [23]. Table 1 shows the characteristics of the participants.

Four of the participants (25%) had a disease at the beginning of the study (rhinitis (*n* = 2), influenza (*n* = 1), gastroenteritis (*n* = 1)).


**Table 1.** Participants' characteristics.

Subtypes: c: combined type; hi: predominantly hyperactive/impulsive; i: predominantly inattentive.

### *2.2. Inclusion and Exclusion Criteria*

Children and adolescents between the age of 7 and 18 attending at least 2nd grade of a general education school with a confirmed ADHD diagnosis according to the criteria of ICD-10 were included in the study. Children and their parents had to sign for informed consent.

Exclusion criteria were severe concomitant disease, neurological or organic comorbidities which cannot be subjected to dietary intervention. Patients could not participate if there was a lack of compliance either of the parents or children, or a lack of reading or writing skills. Concurrent drug therapy of ADHD or participation in other studies at the same time was not allowed. Children were not to be included when following a special diet (e.g., vegetarian, vegan).

#### *2.3. Measures*

The primary outcome was measured using the ADHD rating scale IV (ARS) that is frequently used in ADHD trials [24–34].

#### *2.4. Anamnesis Concerning Food Sensitivity and Allergies in the Beginning*

Participants were asked about existing food intolerances, such as allergic reactions to foodstuff or diagnosed food intolerances such as malabsorption or enzyme deficiency.

In the special dietary anamnesis, the children were asked about their preferences and aversions to certain foods.

#### *2.5. Conners' Rating Scale*

To assess daily changes of behavior more precisely, the abbreviated Conners´ scale (ACS) was used on a daily basis [15,35,36]. In addition to diagnostics, the Conners´ scales are important for treatment planning, monitoring, and therapy evaluation. The ACS used here is derived from the long version (105 items), the Conners 3®. This is composed of the items that achieved the highest scores in patients with ADHD and which react very sensitively to therapy effects. Therefore, they are suitable as a short-term follow-up and therapy evaluation [35]. It consists of ten selected items. The ten items are: (1) restless and overactive; (2) excitable impulsive; (3) disturbs other children; (4) fails to finish things short attention span; (5) constantly fidgeting; (6) inattentive, easily distracted; (7) demands must be met immediately—easily frustrated, (8) cries often and easily; (9) mood changes quickly and drastically (10) temper outbursts, explosive and unpredictable behavior.

Each item was assessed on a 4-point rating scale which resulted in a total score ranging from 0 to 3. With a time requirement of about five minutes, the ACS is a suitable instrument for daily progress monitoring or therapy evaluation. [36].

#### *2.6. Nutrition and Behavior Diary*

The nutrition and behavior diary, developed for this study, is based on the allergy diary described by Körner and Schareina [35]. It was kept daily as a 24-h recall protocol by the parents and/or children during the entire study in order to be able to track a temporal and causal relationship between the foods consumed and the occurring ADHD symptoms [34].

Leisure activities that may also affect ACS are also reported e.g., birthday parties, physical training, circus events, and school hiking days.

#### *2.7. Procedure*

Initial examination, verifying the ADHD diagnosis, and an assessment of medical health status was followed by a one-week retrospective ADHD rating scale IV [24]. T0 was considered baseline. Figure 1 shows the timeline of the study.


**Figure 1.** Timescales and measures for each appointment. Yellow bar: pre-diet phase, no change in everyday food intake; Orange bar: diet phase OD; Red bars: food challenge phase, testing the different main food groups. T0: physical examination, Baseline ARS; T1: physical examination, ARS; T2: physical examination, ARS; T3: physical examination, ARS; T4: physical examination, ARS, individual dietary recommendations.

> Between T0 and T4, parent ACS and 24-h nutrition and behavior protocols were kept daily. Participants were asked to keep their daily eating habits.

> From T1–T2 the children and their families are in a 4-week period of OD. During the diet phase, only a limited selection of hypoallergenic food was allowed to be eaten. The structure of this diet was based on the protocol of Egger et al. and Pelsser et al. [11,14]. Supplementation of vitamins and minerals was advised.

> At all time-points, physical examination was kept by a medical professional. At T0, the physical condition and basic neurological findings were additionally recorded.

> Throughout the study the families were advised by a nutritionist in order to avoid the risk of malnutrition and to facilitate the implementation of the diet.

> All children with an improvement of at least 40% in the ARS total between T1 and T2 were considered to be responders [14].

> During T2–T4 the reintroduction of usually consumed foods was proceeded at a time interval of 3–4 days testing each food. ACS questionnaire was completed daily and the nutrition and behavior diary was maintained.

> Food sensitivities were defined for foods that showed a repetitive increase in symptoms of at least 2 points on the ACS scale after ingestion compared to the three days before baseline. After identifying the intolerant food in the reintroduction phase, it was assessed whether the intolerant food was consumed before the diet.

#### *2.8. Statistics*

The data of 16 participants (out of 28) that completed the whole study was included in statistical analysis.

In cases in which subsamples exceeded five observations, *t*-tests were performed to compare ACS values on the day of reintroduction (dE0), and one, two or three days after reintroduction (dE + 1, dE + 2, dE + 3, etc.) of a particular food to the values one day before reintroduction (dE − 1). All subsamples were too small to apply more complex statistical analyses such as ANOVA with repeated measurements. All statistical analyses were performed with SPSS version 23.0 (IBM Corporation, Armonk, NY, USA).
